%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:33:38 AM UTC 2026
% Result : Unsatisfiable 89.85s 15.26s
% Output : CNFRefutation 89.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 92
% Syntax : Number of formulae : 668 ( 443 unt; 0 typ; 0 def)
% Number of atoms : 2978 (1790 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 5563 ( 655 ~; 738 |; 0 &;4170 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 1434 ( 0 ^;1434 !; 0 ?;1434 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_p__0,type,
p__0: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_s_1,type,
s_1: $i > $i ).
thf(tp_s_4,type,
s_4: $i > $i ).
thf(tp_s_5,type,
s_5: $i > $i > $i ).
thf(tp_s_6,type,
s_6: $i > $i > $i ).
thf(tp_s_7,type,
s_7: $i > $i ).
thf(tp_times,type,
times: $i > $i > $i ).
thf(1,axiom,
! [X6: $i,X3: $i] :
( ~ ( less @ ( plus @ X6 @ n1 ) @ X3 )
| ( less @ X6 @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(2,axiom,
! [X1: $i,X2: $i] :
( ~ ( less @ n1 @ X1 )
| ( n1
!= ( times @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
thf(3,axiom,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( less @ X1 @ X2 )
| ( less @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(4,axiom,
! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ( X1 != n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
thf(5,axiom,
! [X1: $i] : ( less @ n0 @ ( plus @ X1 @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(6,axiom,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ( ( plus @ X1 @ ( times @ X4 @ X3 ) )
!= ( plus @ X2 @ ( times @ X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
thf(7,axiom,
! [X2: $i,X1: $i] :
( ( n1
!= ( times @ X2 @ X1 ) )
| ( X1 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(8,axiom,
! [X1: $i,X2: $i] :
( ( n1
!= ( times @ X1 @ X2 ) )
| ( X1 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(9,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ ( times @ X2 @ X3 ) @ ( times @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(10,axiom,
! [X1: $i,X2: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ X1 )
= ( times @ X1 @ ( plus @ X2 @ n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(11,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ ( times @ X3 @ X2 ) )
= ( times @ ( plus @ X1 @ X3 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(12,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ ( times @ X1 @ X3 ) @ ( times @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(13,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ ( times @ X1 @ X3 ) )
= ( times @ X1 @ ( plus @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(14,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( times @ X1 @ X2 ) @ ( times @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(15,axiom,
! [X1: $i] :
( ( times @ n1 @ X1 )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(16,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( times @ X1 @ X2 ) @ X3 )
= ( times @ X1 @ ( times @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(17,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( times @ X2 @ X3 ) )
= ( times @ ( times @ X1 @ X2 ) @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(18,axiom,
! [X1: $i] :
( ( times @ X1 @ n1 )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(19,axiom,
! [X1: $i] :
( ( plus @ X1 @ n1 )
!= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(20,axiom,
! [X1: $i,X2: $i] :
( ( times @ X1 @ X2 )
= ( times @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(21,axiom,
! [X1: $i] :
( ( plus @ n1 @ ( plus @ X1 @ n1 ) )
!= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(22,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( X1 != X2 )
| ( ( plus @ X3 @ X1 )
= ( plus @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(23,axiom,
! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X2 )
| ( X1 = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(24,axiom,
! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X1 )
| ( X2 = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(25,axiom,
! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X1 @ X2 ) )
| ( X2 = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(26,axiom,
! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X2 @ X1 ) )
| ( X2 = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(27,axiom,
! [X1: $i] :
( ( plus @ n0 @ X1 )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(28,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X1 @ X3 ) )
| ( X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(29,axiom,
! [X1: $i,X2: $i] :
( ( plus @ X1 @ X2 )
= ( plus @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(30,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( plus @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( plus @ X1 @ X2 ) @ X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(31,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ X1 @ ( plus @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(32,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X3 @ X2 ) )
| ( X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(33,axiom,
! [X1: $i] :
( ( plus @ X1 @ n0 )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(34,axiom,
! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ( ( plus @ X2 @ ( times @ X4 @ X3 ) )
!= ( plus @ X1 @ ( times @ X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(35,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(36,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,negated_conjecture,
p__0 = p__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_57) ).
thf(38,negated_conjecture,
! [X10: $i,X38: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_56) ).
thf(39,negated_conjecture,
! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( ( plus @ n0 @ ( times @ X12 @ X7 ) )
= ( times @ X12 @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_55) ).
thf(40,negated_conjecture,
! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( n1
!= ( times @ X12 @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_54) ).
thf(41,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( ( s_1 @ X10 )
= p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_53) ).
thf(42,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( ( plus @ n0 @ ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) ) )
= ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_52) ).
thf(43,negated_conjecture,
! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_51) ).
thf(44,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) )
= ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
thf(45,negated_conjecture,
! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49) ).
thf(46,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) )
= X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_48) ).
thf(47,negated_conjecture,
! [X7: $i,X10: $i] :
( ( X7 != p__0 )
| ( X10 != n1 )
| ( X10 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_47) ).
thf(48,negated_conjecture,
! [X7: $i] :
( ( X7 != p__0 )
| ( X7 = p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_46) ).
thf(49,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( X10 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_45) ).
thf(50,negated_conjecture,
! [X7: $i] :
( ( X7 != p__0 )
| ( less @ n1 @ X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44) ).
thf(51,negated_conjecture,
! [X10: $i,X37: $i,X7: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X37 @ X7 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X37 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_43) ).
thf(52,negated_conjecture,
p__0 = p__0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42) ).
thf(53,negated_conjecture,
( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_41) ).
thf(54,negated_conjecture,
! [X7: $i,X35: $i,X36: $i] :
( ( X7 != p__0 )
| ( ( times @ X35 @ X36 )
!= X7 )
| ( X35 = n1 )
| ( X35 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_40) ).
thf(55,negated_conjecture,
! [X33: $i,X34: $i] :
( ( ( times @ X33 @ X34 )
!= p__0 )
| ( ( times @ X33 @ X34 )
= p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_39) ).
thf(56,negated_conjecture,
! [X33: $i] :
( ( X33 != n1 )
| ( X33 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38) ).
thf(57,negated_conjecture,
! [X33: $i] :
( ( X33 != p__0 )
| ( X33 = p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
thf(58,negated_conjecture,
( ( plus @ n0 @ n1 )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
thf(59,negated_conjecture,
( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
thf(60,negated_conjecture,
( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 )
| ( less @ n0 @ p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
thf(61,negated_conjecture,
! [X8: $i] :
( ( X8 = n0 )
| ( less @ X8 @ n0 )
| ( less @ n0 @ X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
thf(62,negated_conjecture,
! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
thf(63,negated_conjecture,
! [X32: $i] :
( ( X32 != n1 )
| ( X32 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
thf(64,negated_conjecture,
! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( less @ X8 @ p__0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
thf(65,negated_conjecture,
! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
thf(66,negated_conjecture,
! [X23: $i] :
( ( X23 != n1 )
| ( X23 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
thf(67,negated_conjecture,
! [X10: $i,X8: $i,X9: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X10
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X10
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
thf(68,negated_conjecture,
! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( plus @ X8 @ ( times @ X9 @ p__0 ) ) @ ( times @ X22 @ p__0 ) )
= ( plus @ X8 @ ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
thf(69,negated_conjecture,
! [X11: $i] :
( ( plus @ n1 @ ( plus @ X11 @ n1 ) )
!= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
thf(70,negated_conjecture,
! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ X8 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
thf(71,negated_conjecture,
! [X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
thf(72,negated_conjecture,
! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(73,negated_conjecture,
! [X15: $i,X31: $i] :
( ( X15
!= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) )
| ( X15
= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
thf(74,negated_conjecture,
! [X28: $i,X27: $i,X29: $i,X30: $i] :
( ( X28
!= ( plus @ X27 @ ( times @ X29 @ ( plus @ X30 @ n1 ) ) ) )
| ( X28
= ( plus @ X27 @ ( times @ X29 @ ( plus @ X30 @ n1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(75,negated_conjecture,
! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(76,negated_conjecture,
( ~ ( less @ n0 @ p__0 )
| ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
thf(77,negated_conjecture,
! [X24: $i] :
( ( X24 != n1 )
| ( X24 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
thf(78,negated_conjecture,
! [X28: $i] :
( ( X28 != n1 )
| ( X28 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
thf(79,negated_conjecture,
! [X27: $i] :
( ( X27 != n1 )
| ( X27 = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
thf(80,negated_conjecture,
! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ X8 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(81,negated_conjecture,
! [X23: $i,X24: $i,X25: $i,X26: $i] :
( ( X23
!= ( plus @ X24 @ ( times @ X25 @ ( plus @ X26 @ n1 ) ) ) )
| ( X23
= ( plus @ X24 @ ( times @ X25 @ ( plus @ X26 @ n1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(82,negated_conjecture,
! [X7: $i,X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X7
!= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
thf(83,negated_conjecture,
n1 = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(84,negated_conjecture,
! [X14: $i,X21: $i] :
( ( X14
!= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) )
| ( X14
= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(85,negated_conjecture,
! [X1: $i,X13: $i] :
~ ( element @ X1 @ X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(86,negated_conjecture,
! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(87,negated_conjecture,
! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X8 != n0 )
| ( X8 = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(88,negated_conjecture,
! [X10: $i,X12: $i,X1: $i,X20: $i,X11: $i] :
( ( ( plus @ X10 @ ( plus @ X12 @ n1 ) )
!= ( plus @ X1 @ ( times @ X20 @ ( plus @ X11 @ n1 ) ) ) )
| ( ( plus @ X10 @ ( plus @ X12 @ n1 ) )
= ( plus @ X1 @ ( times @ X20 @ ( plus @ X11 @ n1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(89,negated_conjecture,
! [X18: $i,X19: $i] :
( ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
!= n1 )
| ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
= n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(90,negated_conjecture,
! [X14: $i,X15: $i,X16: $i,X17: $i] :
( ( X14
!= ( plus @ X15 @ ( times @ X16 @ ( plus @ X17 @ n1 ) ) ) )
| ( X14
= ( plus @ X15 @ ( times @ X16 @ ( plus @ X17 @ n1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(91,negated_conjecture,
! [X10: $i,X12: $i,X13: $i] :
~ ( element @ ( plus @ X10 @ ( plus @ X12 @ n1 ) ) @ X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(92,negated_conjecture,
! [X10: $i,X1: $i,X11: $i] :
( ( plus @ X10 @ ( plus @ ( plus @ ( times @ X1 @ ( plus @ X11 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ X11 @ ( plus @ X10 @ n1 ) ) ) @ n1 ) )
= ( plus @ X1 @ ( times @ ( plus @ X1 @ ( plus @ X10 @ n1 ) ) @ ( plus @ X11 @ n1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(93,negated_conjecture,
! [X7: $i,X8: $i,X9: $i] :
( ( X7
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(94,plain,
$false = $false,
inference(unfold_def,[status(thm)],[36]) ).
thf(95,plain,
( ( ! [X6: $i,X3: $i] :
( ~ ( less @ ( plus @ X6 @ n1 ) @ X3 )
| ( less @ X6 @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(96,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( less @ n1 @ X1 )
| ( n1
!= ( times @ X2 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(97,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( less @ X1 @ X2 )
| ( less @ X2 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ( X1 != n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(99,plain,
( ( ! [X1: $i] : ( less @ n0 @ ( plus @ X1 @ n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(100,plain,
( ( ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ( ( plus @ X1 @ ( times @ X4 @ X3 ) )
!= ( plus @ X2 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(101,plain,
( ( ! [X2: $i,X1: $i] :
( ( n1
!= ( times @ X2 @ X1 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(102,plain,
( ( ! [X1: $i,X2: $i] :
( ( n1
!= ( times @ X1 @ X2 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(103,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ ( times @ X2 @ X3 ) @ ( times @ X1 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(104,plain,
( ( ! [X1: $i,X2: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ X1 )
= ( times @ X1 @ ( plus @ X2 @ n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(105,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ ( times @ X3 @ X2 ) )
= ( times @ ( plus @ X1 @ X3 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(106,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ ( times @ X1 @ X3 ) @ ( times @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(107,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ ( times @ X1 @ X3 ) )
= ( times @ X1 @ ( plus @ X3 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(108,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( times @ X1 @ X2 ) @ ( times @ X1 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(109,plain,
( ( ! [X1: $i] :
( ( times @ n1 @ X1 )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(110,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( times @ X1 @ X2 ) @ X3 )
= ( times @ X1 @ ( times @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(111,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( times @ X2 @ X3 ) )
= ( times @ ( times @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(112,plain,
( ( ! [X1: $i] :
( ( times @ X1 @ n1 )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(113,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n1 )
!= n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(114,plain,
( ( ! [X1: $i,X2: $i] :
( ( times @ X1 @ X2 )
= ( times @ X2 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(115,plain,
( ( ! [X1: $i] :
( ( plus @ n1 @ ( plus @ X1 @ n1 ) )
!= n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(116,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( X1 != X2 )
| ( ( plus @ X3 @ X1 )
= ( plus @ X3 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(117,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X2 )
| ( X1 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(118,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X1 )
| ( X2 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(119,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X1 @ X2 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(120,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X2 @ X1 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(121,plain,
( ( ! [X1: $i] :
( ( plus @ n0 @ X1 )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(122,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X1 @ X3 ) )
| ( X2 = X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(123,plain,
( ( ! [X1: $i,X2: $i] :
( ( plus @ X1 @ X2 )
= ( plus @ X2 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(124,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( plus @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(125,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ X1 @ ( plus @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(126,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X3 @ X2 ) )
| ( X1 = X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(127,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n0 )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(128,plain,
( ( ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ( ( plus @ X2 @ ( times @ X4 @ X3 ) )
!= ( plus @ X1 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(129,plain,
( ( p__0 = p__0 )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(130,plain,
( ( ! [X10: $i,X38: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(131,plain,
( ( ! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( ( plus @ n0 @ ( times @ X12 @ X7 ) )
= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(132,plain,
( ( ! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( n1
!= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(133,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( s_1 @ X10 )
= p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(134,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( plus @ n0 @ ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) ) )
= ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(135,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(136,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) )
= ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(137,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(138,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) )
= X10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(139,plain,
( ( ! [X7: $i,X10: $i] :
( ( X7 != p__0 )
| ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(140,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( X7 = p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(141,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( X10 = X10 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(142,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( less @ n1 @ X7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(143,plain,
( ( ! [X10: $i,X37: $i,X7: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X37 @ X7 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X37 @ X7 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(144,plain,
( ( p__0 = p__0 )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(145,plain,
( ( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(146,plain,
( ( ! [X7: $i,X35: $i,X36: $i] :
( ( X7 != p__0 )
| ( ( times @ X35 @ X36 )
!= X7 )
| ( X35 = n1 )
| ( X35 = X7 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(147,plain,
( ( ! [X33: $i,X34: $i] :
( ( ( times @ X33 @ X34 )
!= p__0 )
| ( ( times @ X33 @ X34 )
= p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(148,plain,
( ( ! [X33: $i] :
( ( X33 != n1 )
| ( X33 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(149,plain,
( ( ! [X33: $i] :
( ( X33 != p__0 )
| ( X33 = p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(150,plain,
( ( ( plus @ n0 @ n1 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(151,plain,
( ( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(152,plain,
( ( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 )
| ( less @ n0 @ p__0 ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(153,plain,
( ( ! [X8: $i] :
( ( X8 = n0 )
| ( less @ X8 @ n0 )
| ( less @ n0 @ X8 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(154,plain,
( ( ! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(155,plain,
( ( ! [X32: $i] :
( ( X32 != n1 )
| ( X32 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(156,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( less @ X8 @ p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(157,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(158,plain,
( ( ! [X23: $i] :
( ( X23 != n1 )
| ( X23 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(159,plain,
( ( ! [X10: $i,X8: $i,X9: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X10
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X10
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(160,plain,
( ( ! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( plus @ X8 @ ( times @ X9 @ p__0 ) ) @ ( times @ X22 @ p__0 ) )
= ( plus @ X8 @ ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(161,plain,
( ( ! [X11: $i] :
( ( plus @ n1 @ ( plus @ X11 @ n1 ) )
!= n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(162,plain,
( ( ! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ X8 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(163,plain,
( ( ! [X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(164,plain,
( ( ! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(165,plain,
( ( ! [X15: $i,X31: $i] :
( ( X15
!= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) )
| ( X15
= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(166,plain,
( ( ! [X28: $i,X27: $i,X29: $i,X30: $i] :
( ( X28
!= ( plus @ X27 @ ( times @ X29 @ ( plus @ X30 @ n1 ) ) ) )
| ( X28
= ( plus @ X27 @ ( times @ X29 @ ( plus @ X30 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(167,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(168,plain,
( ( ~ ( less @ n0 @ p__0 )
| ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(169,plain,
( ( ! [X24: $i] :
( ( X24 != n1 )
| ( X24 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(170,plain,
( ( ! [X28: $i] :
( ( X28 != n1 )
| ( X28 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(171,plain,
( ( ! [X27: $i] :
( ( X27 != n1 )
| ( X27 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(172,plain,
( ( ! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ X8 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(173,plain,
( ( ! [X23: $i,X24: $i,X25: $i,X26: $i] :
( ( X23
!= ( plus @ X24 @ ( times @ X25 @ ( plus @ X26 @ n1 ) ) ) )
| ( X23
= ( plus @ X24 @ ( times @ X25 @ ( plus @ X26 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(174,plain,
( ( ! [X7: $i,X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X7
!= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(175,plain,
( ( n1 = n1 )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(176,plain,
( ( ! [X14: $i,X21: $i] :
( ( X14
!= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) )
| ( X14
= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(177,plain,
( ( ! [X1: $i,X13: $i] :
~ ( element @ X1 @ X13 ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(178,plain,
( ( ! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(179,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X8 != n0 )
| ( X8 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(180,plain,
( ( ! [X10: $i,X12: $i,X1: $i,X20: $i,X11: $i] :
( ( ( plus @ X10 @ ( plus @ X12 @ n1 ) )
!= ( plus @ X1 @ ( times @ X20 @ ( plus @ X11 @ n1 ) ) ) )
| ( ( plus @ X10 @ ( plus @ X12 @ n1 ) )
= ( plus @ X1 @ ( times @ X20 @ ( plus @ X11 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(181,plain,
( ( ! [X18: $i,X19: $i] :
( ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
!= n1 )
| ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
= n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(182,plain,
( ( ! [X14: $i,X15: $i,X16: $i,X17: $i] :
( ( X14
!= ( plus @ X15 @ ( times @ X16 @ ( plus @ X17 @ n1 ) ) ) )
| ( X14
= ( plus @ X15 @ ( times @ X16 @ ( plus @ X17 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(183,plain,
( ( ! [X10: $i,X12: $i,X13: $i] :
~ ( element @ ( plus @ X10 @ ( plus @ X12 @ n1 ) ) @ X13 ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(184,plain,
( ( ! [X10: $i,X1: $i,X11: $i] :
( ( plus @ X10 @ ( plus @ ( plus @ ( times @ X1 @ ( plus @ X11 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ X11 @ ( plus @ X10 @ n1 ) ) ) @ n1 ) )
= ( plus @ X1 @ ( times @ ( plus @ X1 @ ( plus @ X10 @ n1 ) ) @ ( plus @ X11 @ n1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(185,plain,
( ( ! [X7: $i,X8: $i,X9: $i] :
( ( X7
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(186,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[94]) ).
thf(187,plain,
( ( ! [X7: $i,X8: $i,X9: $i] :
( ( X7
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(188,plain,
( ( ! [X10: $i,X1: $i,X11: $i] :
( ( plus @ X10 @ ( plus @ ( plus @ ( times @ X1 @ ( plus @ X11 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ X11 @ ( plus @ X10 @ n1 ) ) ) @ n1 ) )
= ( plus @ X1 @ ( times @ ( plus @ X1 @ ( plus @ X10 @ n1 ) ) @ ( plus @ X11 @ n1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(189,plain,
( ( ! [X10: $i,X12: $i,X13: $i] :
~ ( element @ ( plus @ X10 @ ( plus @ X12 @ n1 ) ) @ X13 ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(190,plain,
( ( ! [X14: $i,X15: $i,X16: $i,X17: $i] :
( ( X14
!= ( plus @ X15 @ ( times @ X16 @ ( plus @ X17 @ n1 ) ) ) )
| ( X14
= ( plus @ X15 @ ( times @ X16 @ ( plus @ X17 @ n1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(191,plain,
( ( ! [X18: $i,X19: $i] :
( ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
!= n1 )
| ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
= n1 ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(192,plain,
( ( ! [X10: $i,X12: $i,X1: $i,X20: $i,X11: $i] :
( ( ( plus @ X10 @ ( plus @ X12 @ n1 ) )
!= ( plus @ X1 @ ( times @ X20 @ ( plus @ X11 @ n1 ) ) ) )
| ( ( plus @ X10 @ ( plus @ X12 @ n1 ) )
= ( plus @ X1 @ ( times @ X20 @ ( plus @ X11 @ n1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(193,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X8 != n0 )
| ( X8 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(194,plain,
( ( ! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(195,plain,
( ( ! [X1: $i,X13: $i] :
~ ( element @ X1 @ X13 ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(196,plain,
( ( ! [X14: $i,X21: $i] :
( ( X14
!= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) )
| ( X14
= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(197,plain,
( ( n1 = n1 )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(198,plain,
( ( ! [X7: $i,X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X7
!= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(199,plain,
( ( ! [X23: $i,X24: $i,X25: $i,X26: $i] :
( ( X23
!= ( plus @ X24 @ ( times @ X25 @ ( plus @ X26 @ n1 ) ) ) )
| ( X23
= ( plus @ X24 @ ( times @ X25 @ ( plus @ X26 @ n1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(200,plain,
( ( ! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ X8 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(201,plain,
( ( ! [X27: $i] :
( ( X27 != n1 )
| ( X27 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(202,plain,
( ( ! [X28: $i] :
( ( X28 != n1 )
| ( X28 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(203,plain,
( ( ! [X24: $i] :
( ( X24 != n1 )
| ( X24 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(204,plain,
( ( ~ ( less @ n0 @ p__0 )
| ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(205,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(206,plain,
( ( ! [X28: $i,X27: $i,X29: $i,X30: $i] :
( ( X28
!= ( plus @ X27 @ ( times @ X29 @ ( plus @ X30 @ n1 ) ) ) )
| ( X28
= ( plus @ X27 @ ( times @ X29 @ ( plus @ X30 @ n1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(207,plain,
( ( ! [X15: $i,X31: $i] :
( ( X15
!= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) )
| ( X15
= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(208,plain,
( ( ! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(209,plain,
( ( ! [X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(210,plain,
( ( ! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ X8 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(211,plain,
( ( ! [X11: $i] :
( ( plus @ n1 @ ( plus @ X11 @ n1 ) )
!= n1 ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(212,plain,
( ( ! [X8: $i,X9: $i,X22: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( plus @ X8 @ ( times @ X9 @ p__0 ) ) @ ( times @ X22 @ p__0 ) )
= ( plus @ X8 @ ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(213,plain,
( ( ! [X10: $i,X8: $i,X9: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X10
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X10
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(214,plain,
( ( ! [X23: $i] :
( ( X23 != n1 )
| ( X23 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(215,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(216,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ( less @ X8 @ p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(217,plain,
( ( ! [X32: $i] :
( ( X32 != n1 )
| ( X32 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(218,plain,
( ( ! [X7: $i] :
( ~ ( less @ n0 @ p__0 )
| ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(219,plain,
( ( ! [X8: $i] :
( ( X8 = n0 )
| ( less @ X8 @ n0 )
| ( less @ n0 @ X8 ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(220,plain,
( ( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 )
| ( less @ n0 @ p__0 ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(221,plain,
( ( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(222,plain,
( ( ( plus @ n0 @ n1 )
= n1 )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(223,plain,
( ( ! [X33: $i] :
( ( X33 != p__0 )
| ( X33 = p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(224,plain,
( ( ! [X33: $i] :
( ( X33 != n1 )
| ( X33 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(225,plain,
( ( ! [X33: $i,X34: $i] :
( ( ( times @ X33 @ X34 )
!= p__0 )
| ( ( times @ X33 @ X34 )
= p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(226,plain,
( ( ! [X7: $i,X35: $i,X36: $i] :
( ( X7 != p__0 )
| ( ( times @ X35 @ X36 )
!= X7 )
| ( X35 = n1 )
| ( X35 = X7 ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(227,plain,
( ( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(228,plain,
( ( p__0 = p__0 )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(229,plain,
( ( ! [X10: $i,X37: $i,X7: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X37 @ X7 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X37 @ X7 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(230,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( less @ n1 @ X7 ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(231,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( X10 = X10 ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(232,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( X7 = p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(233,plain,
( ( ! [X7: $i,X10: $i] :
( ( X7 != p__0 )
| ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(234,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) )
= X10 ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(235,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(236,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) )
= ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(237,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(238,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( plus @ n0 @ ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) ) )
= ( times @ ( s_4 @ X10 ) @ ( s_1 @ X10 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(239,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( s_1 @ X10 )
= p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(240,plain,
( ( ! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( n1
!= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(241,plain,
( ( ! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( ( plus @ n0 @ ( times @ X12 @ X7 ) )
= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(242,plain,
( ( ! [X10: $i,X38: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(243,plain,
( ( p__0 = p__0 )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(244,plain,
( ( ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ( ( plus @ X2 @ ( times @ X4 @ X3 ) )
!= ( plus @ X1 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(245,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n0 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(246,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X3 @ X2 ) )
| ( X1 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(247,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ X1 @ ( plus @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(248,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( plus @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(249,plain,
( ( ! [X1: $i,X2: $i] :
( ( plus @ X1 @ X2 )
= ( plus @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(250,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X1 @ X3 ) )
| ( X2 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(251,plain,
( ( ! [X1: $i] :
( ( plus @ n0 @ X1 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(252,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X2 @ X1 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(253,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X1 @ X2 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(254,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X1 )
| ( X2 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(255,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X2 )
| ( X1 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(256,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( X1 != X2 )
| ( ( plus @ X3 @ X1 )
= ( plus @ X3 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(257,plain,
( ( ! [X1: $i] :
( ( plus @ n1 @ ( plus @ X1 @ n1 ) )
!= n1 ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(258,plain,
( ( ! [X1: $i,X2: $i] :
( ( times @ X1 @ X2 )
= ( times @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(259,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n1 )
!= n0 ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(260,plain,
( ( ! [X1: $i] :
( ( times @ X1 @ n1 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(261,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( times @ X2 @ X3 ) )
= ( times @ ( times @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(262,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( times @ X1 @ X2 ) @ X3 )
= ( times @ X1 @ ( times @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(263,plain,
( ( ! [X1: $i] :
( ( times @ n1 @ X1 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(264,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( times @ X1 @ X2 ) @ ( times @ X1 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(265,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ ( times @ X1 @ X3 ) )
= ( times @ X1 @ ( plus @ X3 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(266,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ ( times @ X1 @ X3 ) @ ( times @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(267,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ ( times @ X3 @ X2 ) )
= ( times @ ( plus @ X1 @ X3 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(268,plain,
( ( ! [X1: $i,X2: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ X1 )
= ( times @ X1 @ ( plus @ X2 @ n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(269,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ ( times @ X2 @ X3 ) @ ( times @ X1 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(270,plain,
( ( ! [X1: $i,X2: $i] :
( ( n1
!= ( times @ X1 @ X2 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(271,plain,
( ( ! [X2: $i,X1: $i] :
( ( n1
!= ( times @ X2 @ X1 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(272,plain,
( ( ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ( ( plus @ X1 @ ( times @ X4 @ X3 ) )
!= ( plus @ X2 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(273,plain,
( ( ! [X1: $i] : ( less @ n0 @ ( plus @ X1 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(274,plain,
( ( ! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ( X1 != n1 ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(275,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( less @ X1 @ X2 )
| ( less @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(276,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( less @ n1 @ X1 )
| ( n1
!= ( times @ X2 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(277,plain,
( ( ! [X6: $i,X3: $i] :
( ~ ( less @ ( plus @ X6 @ n1 ) @ X3 )
| ( less @ X6 @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(278,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[186]) ).
thf(279,plain,
( ( ! [SX0: $i] :
( ( SX0 != p__0 )
| ( SX0 = p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(280,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SX0
!= ( plus @ SX1 @ ( times @ ( plus @ SX2 @ SX3 ) @ p__0 ) ) )
| ( SX0
= ( plus @ SX1 @ ( times @ ( plus @ SX2 @ SX3 ) @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(281,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( plus @ SX0 @ ( plus @ SX1 @ n1 ) )
!= n1 )
| ( ( plus @ SX0 @ ( plus @ SX1 @ n1 ) )
= n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(282,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( plus @ SX0 @ SX1 )
!= SX1 )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(283,plain,
( ( ! [SX0: $i] :
( ( SX0 != p__0 )
| ( SX0 = p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(284,plain,
( ( ! [SX0: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SX0 != n0 )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(285,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(286,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(287,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( plus @ SX1 @ ( times @ SX2 @ ( plus @ SX3 @ n1 ) ) ) )
| ( SX0
= ( plus @ SX1 @ ( times @ SX2 @ ( plus @ SX3 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(288,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(289,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(290,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ SX0 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SX0 @ p__0 )
| ( ( plus @ SX0 @ ( times @ SX1 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SX2 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(291,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( plus @ n0 @ ( times @ SX1 @ p__0 ) ) )
| ( SX0
= ( plus @ n0 @ ( times @ SX1 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(292,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( plus @ SX0 @ SX1 )
!= SX0 )
| ( SX1 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(293,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != p__0 )
| ( SX1 != n1 )
| ( SX1 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(294,plain,
( ( ! [SX0: $i] :
( ~ ( less @ n1 @ SX0 )
| ( SX0 != n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(295,plain,
( ( ! [SX0: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( s_5 @ p__0 @ SX0 )
!= n0 )
| ( SX0
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SX0 ) @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(296,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( less @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX2 )
| ~ ( less @ SX1 @ SX2 )
| ( ( plus @ SX1 @ ( times @ SX3 @ SX2 ) )
!= ( plus @ SX0 @ ( times @ SX4 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(297,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( n1
!= ( times @ SX0 @ SX1 ) )
| ( SX1 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(298,plain,
( ( ! [SX0: $i] :
( ( plus @ SX0 @ n1 )
!= n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(299,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( plus @ SX0 @ ( plus @ SX1 @ n1 ) )
!= ( plus @ SX2 @ ( times @ SX3 @ ( plus @ SX4 @ n1 ) ) ) )
| ( ( plus @ SX0 @ ( plus @ SX1 @ n1 ) )
= ( plus @ SX2 @ ( times @ SX3 @ ( plus @ SX4 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( times @ SX0 @ SX1 )
!= p__0 )
| ( ( times @ SX0 @ SX1 )
= p__0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SX0
!= ( plus @ SX1 @ ( times @ SX2 @ p__0 ) ) )
| ( SX0
= ( plus @ SX1 @ ( times @ SX2 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(302,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( plus @ n0 @ ( times @ SX1 @ SX2 ) ) )
| ( SX0
= ( plus @ n0 @ ( times @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(303,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( plus @ SX0 @ SX1 ) )
| ( SX1 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( plus @ SX1 @ SX0 ) )
| ( SX1 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(305,plain,
( ( ! [SX0: $i] :
( ( SX0 != p__0 )
| ( less @ n1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(306,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != p__0 )
| ( n1
!= ( times @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(307,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0 != SX1 )
| ( ( plus @ SX2 @ SX0 )
= ( plus @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( plus @ n0 @ ( times @ SX1 @ p__0 ) ) )
| ( SX0
= ( plus @ n0 @ ( times @ SX1 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(309,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( less @ n0 @ SX0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SX0 @ p__0 )
| ( ( plus @ SX0 @ ( times @ SX1 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SX2 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(310,plain,
( ( ! [SX0: $i] :
( ( plus @ n1 @ ( plus @ SX0 @ n1 ) )
!= n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( n1
!= ( times @ SX0 @ SX1 ) )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(312,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( plus @ SX1 @ ( times @ SX2 @ ( plus @ SX3 @ n1 ) ) ) )
| ( SX0
= ( plus @ SX1 @ ( times @ SX2 @ ( plus @ SX3 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(314,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( plus @ SX0 @ SX1 )
!= ( plus @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ n1 @ SX0 )
| ( n1
!= ( times @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(317,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(318,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != p__0 )
| ( ( plus @ n0 @ ( times @ SX1 @ SX0 ) )
= ( times @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(319,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( plus @ SX1 @ ( times @ SX2 @ p__0 ) ) )
| ( SX0
= ( plus @ SX1 @ ( times @ SX2 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( plus @ SX1 @ ( times @ SX2 @ ( plus @ SX3 @ n1 ) ) ) )
| ( SX0
= ( plus @ SX1 @ ( times @ SX2 @ ( plus @ SX3 @ n1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(321,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0 != p__0 )
| ( ( times @ SX1 @ SX2 )
!= SX0 )
| ( SX1 = n1 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(322,plain,
( ( ! [SX0: $i] :
( ( plus @ n1 @ ( plus @ SX0 @ n1 ) )
!= n1 ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(323,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(324,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( plus @ n0 @ ( times @ SX1 @ p__0 ) ) )
| ( SX0
= ( plus @ n0 @ ( times @ SX1 @ p__0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(325,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( plus @ SX0 @ SX1 )
!= ( plus @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(326,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(327,plain,
( ( ! [SX0: $i] :
( ( SX0 != n1 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(328,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( less @ SX0 @ SX1 )
| ~ ( less @ SX0 @ SX2 )
| ~ ( less @ SX1 @ SX2 )
| ( ( plus @ SX0 @ ( times @ SX3 @ SX2 ) )
!= ( plus @ SX1 @ ( times @ SX4 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(329,plain,
! [SV1: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( plus @ SV1 @ ( plus @ ( plus @ ( times @ SY171 @ ( plus @ SY172 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ SY172 @ ( plus @ SV1 @ n1 ) ) ) @ n1 ) )
= ( plus @ SY171 @ ( times @ ( plus @ SY171 @ ( plus @ SV1 @ n1 ) ) @ ( plus @ SY172 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(330,plain,
! [SV2: $i] :
( ( ! [SY173: $i,SY174: $i] :
~ ( element @ ( plus @ SV2 @ ( plus @ SY173 @ n1 ) ) @ SY174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(331,plain,
! [SV3: $i] :
( ( ! [SY175: $i] :
~ ( element @ SV3 @ SY175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(332,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(333,plain,
! [SV4: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( SV4
= ( plus @ ( s_5 @ p__0 @ SV4 ) @ ( times @ ( s_6 @ p__0 @ SV4 ) @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(334,plain,
! [SV5: $i] :
( ( ! [SY176: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( times @ SV5 @ p__0 ) @ ( times @ SY176 @ p__0 ) )
= ( times @ ( plus @ SV5 @ SY176 ) @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(335,plain,
! [SV6: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( plus @ SV6 @ ( times @ SY177 @ p__0 ) ) @ ( times @ SY178 @ p__0 ) )
= ( plus @ SV6 @ ( plus @ ( times @ SY177 @ p__0 ) @ ( times @ SY178 @ p__0 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(336,plain,
! [SV7: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV7 @ p__0 )
| ( less @ SV7 @ p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(337,plain,
! [SV8: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( less @ ( s_5 @ p__0 @ SV8 ) @ p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(338,plain,
! [SV9: $i] :
( ( ( SV9 = n0 )
| ( less @ SV9 @ n0 )
| ( less @ n0 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(339,plain,
( ( ( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(340,plain,
( ( ( ~ ( less @ n1 @ p__0 ) )
= $true )
| ( ( less @ n1 @ p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(341,plain,
( ( ( ~ ( less @ n1 @ p__0 ) )
= $true )
| ( ( less @ n1 @ p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(342,plain,
! [SV10: $i] :
( ( ( SV10 = n1 )
| ( SV10 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(343,plain,
! [SV11: $i] :
( ( ( SV11 = n1 )
| ( ( times @ ( s_1 @ SV11 ) @ ( s_4 @ SV11 ) )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(344,plain,
! [SV12: $i] :
( ( ( SV12 = n1 )
| ( ( times @ ( s_4 @ SV12 ) @ ( s_1 @ SV12 ) )
= ( times @ ( s_1 @ SV12 ) @ ( s_4 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(345,plain,
! [SV13: $i] :
( ( ( SV13 = n1 )
| ( ( plus @ n0 @ ( times @ ( s_4 @ SV13 ) @ ( s_1 @ SV13 ) ) )
= ( times @ ( s_4 @ SV13 ) @ ( s_1 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(346,plain,
! [SV14: $i] :
( ( ( SV14 = n1 )
| ( ( s_1 @ SV14 )
= p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(347,plain,
! [SV15: $i] :
( ( ( plus @ SV15 @ n0 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(348,plain,
! [SV16: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ( plus @ ( plus @ SV16 @ SY179 ) @ SY180 )
= ( plus @ SV16 @ ( plus @ SY179 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(349,plain,
! [SV17: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ( plus @ SV17 @ ( plus @ SY181 @ SY182 ) )
= ( plus @ ( plus @ SV17 @ SY181 ) @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(350,plain,
! [SV18: $i] :
( ( ! [SY183: $i] :
( ( plus @ SV18 @ SY183 )
= ( plus @ SY183 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(351,plain,
! [SV19: $i] :
( ( ( plus @ n0 @ SV19 )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(352,plain,
! [SV20: $i] :
( ( ! [SY184: $i] :
( ( times @ SV20 @ SY184 )
= ( times @ SY184 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(353,plain,
! [SV21: $i] :
( ( ( times @ SV21 @ n1 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(354,plain,
! [SV22: $i] :
( ( ! [SY185: $i,SY186: $i] :
( ( times @ SV22 @ ( times @ SY185 @ SY186 ) )
= ( times @ ( times @ SV22 @ SY185 ) @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(355,plain,
! [SV23: $i] :
( ( ! [SY187: $i,SY188: $i] :
( ( times @ ( times @ SV23 @ SY187 ) @ SY188 )
= ( times @ SV23 @ ( times @ SY187 @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(356,plain,
! [SV24: $i] :
( ( ( times @ n1 @ SV24 )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(357,plain,
! [SV25: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ( times @ SV25 @ ( plus @ SY189 @ SY190 ) )
= ( plus @ ( times @ SV25 @ SY189 ) @ ( times @ SV25 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(358,plain,
! [SV26: $i] :
( ( ! [SY191: $i,SY192: $i] :
( ( plus @ ( times @ SV26 @ SY191 ) @ ( times @ SV26 @ SY192 ) )
= ( times @ SV26 @ ( plus @ SY192 @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(359,plain,
! [SV27: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ( times @ ( plus @ SV27 @ SY193 ) @ SY194 )
= ( plus @ ( times @ SV27 @ SY194 ) @ ( times @ SY193 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(360,plain,
! [SV28: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ( plus @ ( times @ SV28 @ SY195 ) @ ( times @ SY196 @ SY195 ) )
= ( times @ ( plus @ SV28 @ SY196 ) @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(361,plain,
! [SV29: $i] :
( ( ! [SY197: $i] :
( ( plus @ ( times @ SV29 @ SY197 ) @ SV29 )
= ( times @ SV29 @ ( plus @ SY197 @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(362,plain,
! [SV30: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ( times @ ( plus @ SV30 @ SY198 ) @ SY199 )
= ( plus @ ( times @ SY198 @ SY199 ) @ ( times @ SV30 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(363,plain,
! [SV31: $i] :
( ( less @ n0 @ ( plus @ SV31 @ n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(364,plain,
! [SV32: $i] :
( ( ! [SY200: $i] :
( ( SV32 = SY200 )
| ( less @ SV32 @ SY200 )
| ( less @ SY200 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(365,plain,
! [SV33: $i] :
( ( ! [SY201: $i] :
( ~ ( less @ ( plus @ SV33 @ n1 ) @ SY201 )
| ( less @ SV33 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(366,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(367,plain,
! [SV34: $i] :
( ( ( SV34 != p__0 )
| ( SV34 = p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(368,plain,
! [SV35: $i] :
( ( ! [SY202: $i,SY203: $i,SY204: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SV35
!= ( plus @ SY202 @ ( times @ ( plus @ SY203 @ SY204 ) @ p__0 ) ) )
| ( SV35
= ( plus @ SY202 @ ( times @ ( plus @ SY203 @ SY204 ) @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(369,plain,
! [SV36: $i] :
( ( ! [SY205: $i] :
( ( ( plus @ SV36 @ ( plus @ SY205 @ n1 ) )
!= n1 )
| ( ( plus @ SV36 @ ( plus @ SY205 @ n1 ) )
= n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(370,plain,
! [SV37: $i] :
( ( ! [SY206: $i] :
( ( ( plus @ SV37 @ SY206 )
!= SY206 )
| ( SV37 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(371,plain,
! [SV38: $i] :
( ( ( SV38 != p__0 )
| ( SV38 = p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(372,plain,
! [SV39: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( SV39 != n0 )
| ( SV39 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(373,plain,
! [SV40: $i] :
( ( ( SV40 != n1 )
| ( SV40 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(374,plain,
! [SV41: $i] :
( ( ( SV41 != n1 )
| ( SV41 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(375,plain,
! [SV42: $i] :
( ( ! [SY207: $i,SY208: $i,SY209: $i] :
( ( SV42
!= ( plus @ SY207 @ ( times @ SY208 @ ( plus @ SY209 @ n1 ) ) ) )
| ( SV42
= ( plus @ SY207 @ ( times @ SY208 @ ( plus @ SY209 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(376,plain,
! [SV43: $i] :
( ( ( SV43 != n1 )
| ( SV43 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(377,plain,
! [SV44: $i] :
( ( ( SV44 != n1 )
| ( SV44 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(378,plain,
! [SV45: $i] :
( ( ! [SY210: $i,SY211: $i] :
( ~ ( less @ SV45 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SY210 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY211 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(379,plain,
! [SV46: $i] :
( ( ! [SY212: $i] :
( ( SV46
!= ( plus @ n0 @ ( times @ SY212 @ p__0 ) ) )
| ( SV46
= ( plus @ n0 @ ( times @ SY212 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(380,plain,
! [SV47: $i] :
( ( ! [SY213: $i] :
( ( ( plus @ SV47 @ SY213 )
!= SV47 )
| ( SY213 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(381,plain,
! [SV48: $i] :
( ( ! [SY214: $i] :
( ( SV48 != p__0 )
| ( SY214 != n1 )
| ( SY214 = n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(382,plain,
! [SV49: $i] :
( ( ~ ( less @ n1 @ SV49 )
| ( SV49 != n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(383,plain,
! [SV50: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( ( s_5 @ p__0 @ SV50 )
!= n0 )
| ( SV50
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV50 ) @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(384,plain,
! [SV51: $i] :
( ( ! [SY215: $i,SY216: $i,SY217: $i,SY218: $i] :
( ~ ( less @ SV51 @ SY215 )
| ~ ( less @ SV51 @ SY216 )
| ~ ( less @ SY215 @ SY216 )
| ( ( plus @ SY215 @ ( times @ SY217 @ SY216 ) )
!= ( plus @ SV51 @ ( times @ SY218 @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(385,plain,
! [SV52: $i] :
( ( ! [SY219: $i] :
( ( n1
!= ( times @ SV52 @ SY219 ) )
| ( SY219 = n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(386,plain,
! [SV53: $i] :
( ( ( plus @ SV53 @ n1 )
!= n0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(387,plain,
! [SV54: $i] :
( ( ! [SY220: $i,SY221: $i,SY222: $i,SY223: $i] :
( ( ( plus @ SV54 @ ( plus @ SY220 @ n1 ) )
!= ( plus @ SY221 @ ( times @ SY222 @ ( plus @ SY223 @ n1 ) ) ) )
| ( ( plus @ SV54 @ ( plus @ SY220 @ n1 ) )
= ( plus @ SY221 @ ( times @ SY222 @ ( plus @ SY223 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(388,plain,
! [SV55: $i] :
( ( ! [SY224: $i] :
( ( ( times @ SV55 @ SY224 )
!= p__0 )
| ( ( times @ SV55 @ SY224 )
= p__0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(389,plain,
! [SV56: $i] :
( ( ! [SY225: $i,SY226: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SV56
!= ( plus @ SY225 @ ( times @ SY226 @ p__0 ) ) )
| ( SV56
= ( plus @ SY225 @ ( times @ SY226 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(390,plain,
! [SV57: $i] :
( ( ! [SY227: $i,SY228: $i] :
( ( SV57
!= ( plus @ n0 @ ( times @ SY227 @ SY228 ) ) )
| ( SV57
= ( plus @ n0 @ ( times @ SY227 @ SY228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(391,plain,
! [SV58: $i] :
( ( ! [SY229: $i] :
( ( SV58
!= ( plus @ SV58 @ SY229 ) )
| ( SY229 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(392,plain,
! [SV59: $i] :
( ( ! [SY230: $i] :
( ( SV59
!= ( plus @ SY230 @ SV59 ) )
| ( SY230 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(393,plain,
! [SV60: $i] :
( ( ( SV60 != p__0 )
| ( less @ n1 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(394,plain,
! [SV61: $i] :
( ( ! [SY231: $i] :
( ( SV61 != p__0 )
| ( n1
!= ( times @ SY231 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(395,plain,
! [SV62: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ( SV62 != SY232 )
| ( ( plus @ SY233 @ SV62 )
= ( plus @ SY233 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(396,plain,
! [SV63: $i] :
( ( ! [SY234: $i] :
( ( SV63
!= ( plus @ n0 @ ( times @ SY234 @ p__0 ) ) )
| ( SV63
= ( plus @ n0 @ ( times @ SY234 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(397,plain,
! [SV64: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( less @ n0 @ SV64 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SY235 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY236 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(398,plain,
! [SV65: $i] :
( ( ( plus @ n1 @ ( plus @ SV65 @ n1 ) )
!= n1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(399,plain,
! [SV66: $i] :
( ( ! [SY237: $i] :
( ( n1
!= ( times @ SV66 @ SY237 ) )
| ( SV66 = n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(400,plain,
! [SV67: $i] :
( ( ( SV67 != n1 )
| ( SV67 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(401,plain,
! [SV68: $i] :
( ( ! [SY238: $i,SY239: $i,SY240: $i] :
( ( SV68
!= ( plus @ SY238 @ ( times @ SY239 @ ( plus @ SY240 @ n1 ) ) ) )
| ( SV68
= ( plus @ SY238 @ ( times @ SY239 @ ( plus @ SY240 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(402,plain,
! [SV69: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ( ( plus @ SV69 @ SY241 )
!= ( plus @ SV69 @ SY242 ) )
| ( SY241 = SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(403,plain,
! [SV70: $i] :
( ( ( SV70 != n1 )
| ( SV70 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(404,plain,
! [SV71: $i] :
( ( ! [SY243: $i] :
( ~ ( less @ n1 @ SV71 )
| ( n1
!= ( times @ SY243 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(405,plain,
! [SV72: $i] :
( ( ( SV72 != n1 )
| ( SV72 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(406,plain,
! [SV73: $i] :
( ( ! [SY244: $i] :
( ( SV73 != p__0 )
| ( ( plus @ n0 @ ( times @ SY244 @ SV73 ) )
= ( times @ SY244 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(407,plain,
! [SV74: $i] :
( ( ! [SY245: $i,SY246: $i] :
( ( SV74
!= ( plus @ SY245 @ ( times @ SY246 @ p__0 ) ) )
| ( SV74
= ( plus @ SY245 @ ( times @ SY246 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(408,plain,
! [SV75: $i] :
( ( ! [SY247: $i,SY248: $i,SY249: $i] :
( ( SV75
!= ( plus @ SY247 @ ( times @ SY248 @ ( plus @ SY249 @ n1 ) ) ) )
| ( SV75
= ( plus @ SY247 @ ( times @ SY248 @ ( plus @ SY249 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(409,plain,
! [SV76: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ( SV76 != p__0 )
| ( ( times @ SY250 @ SY251 )
!= SV76 )
| ( SY250 = n1 )
| ( SY250 = SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(410,plain,
! [SV77: $i] :
( ( ( plus @ n1 @ ( plus @ SV77 @ n1 ) )
!= n1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(411,plain,
! [SV78: $i] :
( ( ( SV78 != n1 )
| ( SV78 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(412,plain,
! [SV79: $i] :
( ( ! [SY252: $i] :
( ( SV79
!= ( plus @ n0 @ ( times @ SY252 @ p__0 ) ) )
| ( SV79
= ( plus @ n0 @ ( times @ SY252 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(413,plain,
! [SV80: $i] :
( ( ! [SY253: $i,SY254: $i] :
( ( ( plus @ SV80 @ SY253 )
!= ( plus @ SY254 @ SY253 ) )
| ( SV80 = SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(414,plain,
! [SV81: $i] :
( ( ( SV81 != n1 )
| ( SV81 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(415,plain,
! [SV82: $i] :
( ( ( SV82 != n1 )
| ( SV82 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(416,plain,
! [SV83: $i] :
( ( ! [SY255: $i,SY256: $i,SY257: $i,SY258: $i] :
( ~ ( less @ SV83 @ SY255 )
| ~ ( less @ SV83 @ SY256 )
| ~ ( less @ SY255 @ SY256 )
| ( ( plus @ SV83 @ ( times @ SY257 @ SY256 ) )
!= ( plus @ SY255 @ ( times @ SY258 @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(417,plain,
! [SV84: $i,SV1: $i] :
( ( ! [SY259: $i] :
( ( plus @ SV1 @ ( plus @ ( plus @ ( times @ SV84 @ ( plus @ SY259 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ SY259 @ ( plus @ SV1 @ n1 ) ) ) @ n1 ) )
= ( plus @ SV84 @ ( times @ ( plus @ SV84 @ ( plus @ SV1 @ n1 ) ) @ ( plus @ SY259 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(418,plain,
! [SV85: $i,SV2: $i] :
( ( ! [SY260: $i] :
~ ( element @ ( plus @ SV2 @ ( plus @ SV85 @ n1 ) ) @ SY260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(419,plain,
! [SV86: $i,SV3: $i] :
( ( ~ ( element @ SV3 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(420,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(421,plain,
! [SV4: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( SV4
= ( plus @ ( s_5 @ p__0 @ SV4 ) @ ( times @ ( s_6 @ p__0 @ SV4 ) @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(422,plain,
! [SV87: $i,SV5: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( times @ SV5 @ p__0 ) @ ( times @ SV87 @ p__0 ) )
= ( times @ ( plus @ SV5 @ SV87 ) @ p__0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(423,plain,
! [SV88: $i,SV6: $i] :
( ( ! [SY261: $i] :
( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( plus @ SV6 @ ( times @ SV88 @ p__0 ) ) @ ( times @ SY261 @ p__0 ) )
= ( plus @ SV6 @ ( plus @ ( times @ SV88 @ p__0 ) @ ( times @ SY261 @ p__0 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(424,plain,
! [SV7: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ~ ( less @ SV7 @ p__0 )
| ( less @ SV7 @ p__0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(425,plain,
! [SV8: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( less @ ( s_5 @ p__0 @ SV8 ) @ p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(426,plain,
! [SV9: $i] :
( ( ( SV9 = n0 )
= $true )
| ( ( ( less @ SV9 @ n0 )
| ( less @ n0 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(427,plain,
( ( ( less @ ( plus @ n0 @ n1 ) @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(428,plain,
( ( ( less @ n1 @ p__0 )
= $false )
| ( ( less @ n1 @ p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(429,plain,
( ( ( less @ n1 @ p__0 )
= $false )
| ( ( less @ n1 @ p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(430,plain,
! [SV10: $i] :
( ( ( SV10 = n1 )
= $true )
| ( ( SV10 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(431,plain,
! [SV11: $i] :
( ( ( SV11 = n1 )
= $true )
| ( ( ( times @ ( s_1 @ SV11 ) @ ( s_4 @ SV11 ) )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(432,plain,
! [SV12: $i] :
( ( ( SV12 = n1 )
= $true )
| ( ( ( times @ ( s_4 @ SV12 ) @ ( s_1 @ SV12 ) )
= ( times @ ( s_1 @ SV12 ) @ ( s_4 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(433,plain,
! [SV13: $i] :
( ( ( SV13 = n1 )
= $true )
| ( ( ( plus @ n0 @ ( times @ ( s_4 @ SV13 ) @ ( s_1 @ SV13 ) ) )
= ( times @ ( s_4 @ SV13 ) @ ( s_1 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(434,plain,
! [SV14: $i] :
( ( ( SV14 = n1 )
= $true )
| ( ( ( s_1 @ SV14 )
= p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(435,plain,
! [SV89: $i,SV16: $i] :
( ( ! [SY262: $i] :
( ( plus @ ( plus @ SV16 @ SV89 ) @ SY262 )
= ( plus @ SV16 @ ( plus @ SV89 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(436,plain,
! [SV90: $i,SV17: $i] :
( ( ! [SY263: $i] :
( ( plus @ SV17 @ ( plus @ SV90 @ SY263 ) )
= ( plus @ ( plus @ SV17 @ SV90 ) @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(437,plain,
! [SV91: $i,SV18: $i] :
( ( ( plus @ SV18 @ SV91 )
= ( plus @ SV91 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(438,plain,
! [SV92: $i,SV20: $i] :
( ( ( times @ SV20 @ SV92 )
= ( times @ SV92 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(439,plain,
! [SV93: $i,SV22: $i] :
( ( ! [SY264: $i] :
( ( times @ SV22 @ ( times @ SV93 @ SY264 ) )
= ( times @ ( times @ SV22 @ SV93 ) @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(440,plain,
! [SV94: $i,SV23: $i] :
( ( ! [SY265: $i] :
( ( times @ ( times @ SV23 @ SV94 ) @ SY265 )
= ( times @ SV23 @ ( times @ SV94 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(441,plain,
! [SV95: $i,SV25: $i] :
( ( ! [SY266: $i] :
( ( times @ SV25 @ ( plus @ SV95 @ SY266 ) )
= ( plus @ ( times @ SV25 @ SV95 ) @ ( times @ SV25 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(442,plain,
! [SV96: $i,SV26: $i] :
( ( ! [SY267: $i] :
( ( plus @ ( times @ SV26 @ SV96 ) @ ( times @ SV26 @ SY267 ) )
= ( times @ SV26 @ ( plus @ SY267 @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(443,plain,
! [SV97: $i,SV27: $i] :
( ( ! [SY268: $i] :
( ( times @ ( plus @ SV27 @ SV97 ) @ SY268 )
= ( plus @ ( times @ SV27 @ SY268 ) @ ( times @ SV97 @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(444,plain,
! [SV98: $i,SV28: $i] :
( ( ! [SY269: $i] :
( ( plus @ ( times @ SV28 @ SV98 ) @ ( times @ SY269 @ SV98 ) )
= ( times @ ( plus @ SV28 @ SY269 ) @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(445,plain,
! [SV99: $i,SV29: $i] :
( ( ( plus @ ( times @ SV29 @ SV99 ) @ SV29 )
= ( times @ SV29 @ ( plus @ SV99 @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(446,plain,
! [SV100: $i,SV30: $i] :
( ( ! [SY270: $i] :
( ( times @ ( plus @ SV30 @ SV100 ) @ SY270 )
= ( plus @ ( times @ SV100 @ SY270 ) @ ( times @ SV30 @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(447,plain,
! [SV101: $i,SV32: $i] :
( ( ( SV32 = SV101 )
| ( less @ SV32 @ SV101 )
| ( less @ SV101 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(448,plain,
! [SV102: $i,SV33: $i] :
( ( ~ ( less @ ( plus @ SV33 @ n1 ) @ SV102 )
| ( less @ SV33 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(449,plain,
! [SV34: $i] :
( ( ( SV34 != p__0 )
= $true )
| ( ( SV34 = p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(450,plain,
! [SV103: $i,SV35: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SV35
!= ( plus @ SV103 @ ( times @ ( plus @ SY271 @ SY272 ) @ p__0 ) ) )
| ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SY271 @ SY272 ) @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(451,plain,
! [SV104: $i,SV36: $i] :
( ( ( ( plus @ SV36 @ ( plus @ SV104 @ n1 ) )
!= n1 )
| ( ( plus @ SV36 @ ( plus @ SV104 @ n1 ) )
= n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(452,plain,
! [SV105: $i,SV37: $i] :
( ( ( ( plus @ SV37 @ SV105 )
!= SV105 )
| ( SV37 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(453,plain,
! [SV38: $i] :
( ( ( SV38 != p__0 )
= $true )
| ( ( SV38 = p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(454,plain,
! [SV39: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ( SV39 != n0 )
| ( SV39 = n0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(455,plain,
! [SV40: $i] :
( ( ( SV40 != n1 )
= $true )
| ( ( SV40 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(456,plain,
! [SV41: $i] :
( ( ( SV41 != n1 )
= $true )
| ( ( SV41 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(457,plain,
! [SV106: $i,SV42: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ( SV42
!= ( plus @ SV106 @ ( times @ SY273 @ ( plus @ SY274 @ n1 ) ) ) )
| ( SV42
= ( plus @ SV106 @ ( times @ SY273 @ ( plus @ SY274 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(458,plain,
! [SV43: $i] :
( ( ( SV43 != n1 )
= $true )
| ( ( SV43 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(459,plain,
! [SV44: $i] :
( ( ( SV44 != n1 )
= $true )
| ( ( SV44 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(460,plain,
! [SV107: $i,SV45: $i] :
( ( ! [SY275: $i] :
( ~ ( less @ SV45 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY275 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(461,plain,
! [SV108: $i,SV46: $i] :
( ( ( SV46
!= ( plus @ n0 @ ( times @ SV108 @ p__0 ) ) )
| ( SV46
= ( plus @ n0 @ ( times @ SV108 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(462,plain,
! [SV109: $i,SV47: $i] :
( ( ( ( plus @ SV47 @ SV109 )
!= SV47 )
| ( SV109 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(463,plain,
! [SV110: $i,SV48: $i] :
( ( ( SV48 != p__0 )
| ( SV110 != n1 )
| ( SV110 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(464,plain,
! [SV49: $i] :
( ( ( ~ ( less @ n1 @ SV49 ) )
= $true )
| ( ( SV49 != n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(465,plain,
! [SV50: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ( ( s_5 @ p__0 @ SV50 )
!= n0 )
| ( SV50
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV50 ) @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(466,plain,
! [SV111: $i,SV51: $i] :
( ( ! [SY276: $i,SY277: $i,SY278: $i] :
( ~ ( less @ SV51 @ SV111 )
| ~ ( less @ SV51 @ SY276 )
| ~ ( less @ SV111 @ SY276 )
| ( ( plus @ SV111 @ ( times @ SY277 @ SY276 ) )
!= ( plus @ SV51 @ ( times @ SY278 @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(467,plain,
! [SV112: $i,SV52: $i] :
( ( ( n1
!= ( times @ SV52 @ SV112 ) )
| ( SV112 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(468,plain,
! [SV53: $i] :
( ( ( plus @ SV53 @ n1 )
= n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(469,plain,
! [SV113: $i,SV54: $i] :
( ( ! [SY279: $i,SY280: $i,SY281: $i] :
( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
!= ( plus @ SY279 @ ( times @ SY280 @ ( plus @ SY281 @ n1 ) ) ) )
| ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SY279 @ ( times @ SY280 @ ( plus @ SY281 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(470,plain,
! [SV114: $i,SV55: $i] :
( ( ( ( times @ SV55 @ SV114 )
!= p__0 )
| ( ( times @ SV55 @ SV114 )
= p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(471,plain,
! [SV115: $i,SV56: $i] :
( ( ! [SY282: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SV56
!= ( plus @ SV115 @ ( times @ SY282 @ p__0 ) ) )
| ( SV56
= ( plus @ SV115 @ ( times @ SY282 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(472,plain,
! [SV116: $i,SV57: $i] :
( ( ! [SY283: $i] :
( ( SV57
!= ( plus @ n0 @ ( times @ SV116 @ SY283 ) ) )
| ( SV57
= ( plus @ n0 @ ( times @ SV116 @ SY283 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(473,plain,
! [SV117: $i,SV58: $i] :
( ( ( SV58
!= ( plus @ SV58 @ SV117 ) )
| ( SV117 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(474,plain,
! [SV118: $i,SV59: $i] :
( ( ( SV59
!= ( plus @ SV118 @ SV59 ) )
| ( SV118 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(475,plain,
! [SV60: $i] :
( ( ( SV60 != p__0 )
= $true )
| ( ( less @ n1 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(476,plain,
! [SV119: $i,SV61: $i] :
( ( ( SV61 != p__0 )
| ( n1
!= ( times @ SV119 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(477,plain,
! [SV120: $i,SV62: $i] :
( ( ! [SY284: $i] :
( ( SV62 != SV120 )
| ( ( plus @ SY284 @ SV62 )
= ( plus @ SY284 @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(478,plain,
! [SV121: $i,SV63: $i] :
( ( ( SV63
!= ( plus @ n0 @ ( times @ SV121 @ p__0 ) ) )
| ( SV63
= ( plus @ n0 @ ( times @ SV121 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(479,plain,
! [SV122: $i,SV64: $i] :
( ( ! [SY285: $i] :
( ~ ( less @ n0 @ SV64 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY285 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(480,plain,
! [SV65: $i] :
( ( ( plus @ n1 @ ( plus @ SV65 @ n1 ) )
= n1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(481,plain,
! [SV123: $i,SV66: $i] :
( ( ( n1
!= ( times @ SV66 @ SV123 ) )
| ( SV66 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(482,plain,
! [SV67: $i] :
( ( ( SV67 != n1 )
= $true )
| ( ( SV67 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(483,plain,
! [SV124: $i,SV68: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ( SV68
!= ( plus @ SV124 @ ( times @ SY286 @ ( plus @ SY287 @ n1 ) ) ) )
| ( SV68
= ( plus @ SV124 @ ( times @ SY286 @ ( plus @ SY287 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(484,plain,
! [SV125: $i,SV69: $i] :
( ( ! [SY288: $i] :
( ( ( plus @ SV69 @ SV125 )
!= ( plus @ SV69 @ SY288 ) )
| ( SV125 = SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(485,plain,
! [SV70: $i] :
( ( ( SV70 != n1 )
= $true )
| ( ( SV70 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(486,plain,
! [SV126: $i,SV71: $i] :
( ( ~ ( less @ n1 @ SV71 )
| ( n1
!= ( times @ SV126 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(487,plain,
! [SV72: $i] :
( ( ( SV72 != n1 )
= $true )
| ( ( SV72 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(488,plain,
! [SV127: $i,SV73: $i] :
( ( ( SV73 != p__0 )
| ( ( plus @ n0 @ ( times @ SV127 @ SV73 ) )
= ( times @ SV127 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(489,plain,
! [SV128: $i,SV74: $i] :
( ( ! [SY289: $i] :
( ( SV74
!= ( plus @ SV128 @ ( times @ SY289 @ p__0 ) ) )
| ( SV74
= ( plus @ SV128 @ ( times @ SY289 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(490,plain,
! [SV129: $i,SV75: $i] :
( ( ! [SY290: $i,SY291: $i] :
( ( SV75
!= ( plus @ SV129 @ ( times @ SY290 @ ( plus @ SY291 @ n1 ) ) ) )
| ( SV75
= ( plus @ SV129 @ ( times @ SY290 @ ( plus @ SY291 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(491,plain,
! [SV130: $i,SV76: $i] :
( ( ! [SY292: $i] :
( ( SV76 != p__0 )
| ( ( times @ SV130 @ SY292 )
!= SV76 )
| ( SV130 = n1 )
| ( SV130 = SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(492,plain,
! [SV77: $i] :
( ( ( plus @ n1 @ ( plus @ SV77 @ n1 ) )
= n1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(493,plain,
! [SV78: $i] :
( ( ( SV78 != n1 )
= $true )
| ( ( SV78 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(494,plain,
! [SV131: $i,SV79: $i] :
( ( ( SV79
!= ( plus @ n0 @ ( times @ SV131 @ p__0 ) ) )
| ( SV79
= ( plus @ n0 @ ( times @ SV131 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(495,plain,
! [SV132: $i,SV80: $i] :
( ( ! [SY293: $i] :
( ( ( plus @ SV80 @ SV132 )
!= ( plus @ SY293 @ SV132 ) )
| ( SV80 = SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(496,plain,
! [SV81: $i] :
( ( ( SV81 != n1 )
= $true )
| ( ( SV81 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(497,plain,
! [SV82: $i] :
( ( ( SV82 != n1 )
= $true )
| ( ( SV82 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(498,plain,
! [SV133: $i,SV83: $i] :
( ( ! [SY294: $i,SY295: $i,SY296: $i] :
( ~ ( less @ SV83 @ SV133 )
| ~ ( less @ SV83 @ SY294 )
| ~ ( less @ SV133 @ SY294 )
| ( ( plus @ SV83 @ ( times @ SY295 @ SY294 ) )
!= ( plus @ SV133 @ ( times @ SY296 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(499,plain,
! [SV134: $i,SV84: $i,SV1: $i] :
( ( ( plus @ SV1 @ ( plus @ ( plus @ ( times @ SV84 @ ( plus @ SV134 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ SV134 @ ( plus @ SV1 @ n1 ) ) ) @ n1 ) )
= ( plus @ SV84 @ ( times @ ( plus @ SV84 @ ( plus @ SV1 @ n1 ) ) @ ( plus @ SV134 @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(500,plain,
! [SV135: $i,SV85: $i,SV2: $i] :
( ( ~ ( element @ ( plus @ SV2 @ ( plus @ SV85 @ n1 ) ) @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(501,plain,
! [SV86: $i,SV3: $i] :
( ( element @ SV3 @ SV86 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(502,plain,
! [SV4: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( SV4
= ( plus @ ( s_5 @ p__0 @ SV4 ) @ ( times @ ( s_6 @ p__0 @ SV4 ) @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(503,plain,
! [SV87: $i,SV5: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ( plus @ ( times @ SV5 @ p__0 ) @ ( times @ SV87 @ p__0 ) )
= ( times @ ( plus @ SV5 @ SV87 ) @ p__0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(504,plain,
! [SV136: $i,SV88: $i,SV6: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( ( plus @ ( plus @ SV6 @ ( times @ SV88 @ p__0 ) ) @ ( times @ SV136 @ p__0 ) )
= ( plus @ SV6 @ ( plus @ ( times @ SV88 @ p__0 ) @ ( times @ SV136 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(505,plain,
! [SV7: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ~ ( less @ SV7 @ p__0 )
| ( less @ SV7 @ p__0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(506,plain,
! [SV8: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ ( s_5 @ p__0 @ SV8 ) @ p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(507,plain,
! [SV9: $i] :
( ( ( less @ SV9 @ n0 )
= $true )
| ( ( less @ n0 @ SV9 )
= $true )
| ( ( SV9 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(508,plain,
! [SV137: $i,SV89: $i,SV16: $i] :
( ( ( plus @ ( plus @ SV16 @ SV89 ) @ SV137 )
= ( plus @ SV16 @ ( plus @ SV89 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(509,plain,
! [SV138: $i,SV90: $i,SV17: $i] :
( ( ( plus @ SV17 @ ( plus @ SV90 @ SV138 ) )
= ( plus @ ( plus @ SV17 @ SV90 ) @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(510,plain,
! [SV139: $i,SV93: $i,SV22: $i] :
( ( ( times @ SV22 @ ( times @ SV93 @ SV139 ) )
= ( times @ ( times @ SV22 @ SV93 ) @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(511,plain,
! [SV140: $i,SV94: $i,SV23: $i] :
( ( ( times @ ( times @ SV23 @ SV94 ) @ SV140 )
= ( times @ SV23 @ ( times @ SV94 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(512,plain,
! [SV141: $i,SV95: $i,SV25: $i] :
( ( ( times @ SV25 @ ( plus @ SV95 @ SV141 ) )
= ( plus @ ( times @ SV25 @ SV95 ) @ ( times @ SV25 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(513,plain,
! [SV142: $i,SV96: $i,SV26: $i] :
( ( ( plus @ ( times @ SV26 @ SV96 ) @ ( times @ SV26 @ SV142 ) )
= ( times @ SV26 @ ( plus @ SV142 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(514,plain,
! [SV143: $i,SV97: $i,SV27: $i] :
( ( ( times @ ( plus @ SV27 @ SV97 ) @ SV143 )
= ( plus @ ( times @ SV27 @ SV143 ) @ ( times @ SV97 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(515,plain,
! [SV144: $i,SV98: $i,SV28: $i] :
( ( ( plus @ ( times @ SV28 @ SV98 ) @ ( times @ SV144 @ SV98 ) )
= ( times @ ( plus @ SV28 @ SV144 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(516,plain,
! [SV145: $i,SV100: $i,SV30: $i] :
( ( ( times @ ( plus @ SV30 @ SV100 ) @ SV145 )
= ( plus @ ( times @ SV100 @ SV145 ) @ ( times @ SV30 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(517,plain,
! [SV101: $i,SV32: $i] :
( ( ( SV32 = SV101 )
= $true )
| ( ( ( less @ SV32 @ SV101 )
| ( less @ SV101 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(518,plain,
! [SV102: $i,SV33: $i] :
( ( ( ~ ( less @ ( plus @ SV33 @ n1 ) @ SV102 ) )
= $true )
| ( ( less @ SV33 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(519,plain,
! [SV34: $i] :
( ( ( SV34 = p__0 )
= $false )
| ( ( SV34 = p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(520,plain,
! [SV146: $i,SV103: $i,SV35: $i] :
( ( ! [SY297: $i] :
( ~ ( less @ n0 @ p__0 )
| ( SV35
!= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SY297 ) @ p__0 ) ) )
| ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SY297 ) @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(521,plain,
! [SV104: $i,SV36: $i] :
( ( ( ( plus @ SV36 @ ( plus @ SV104 @ n1 ) )
!= n1 )
= $true )
| ( ( ( plus @ SV36 @ ( plus @ SV104 @ n1 ) )
= n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(522,plain,
! [SV105: $i,SV37: $i] :
( ( ( ( plus @ SV37 @ SV105 )
!= SV105 )
= $true )
| ( ( SV37 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(523,plain,
! [SV38: $i] :
( ( ( SV38 = p__0 )
= $false )
| ( ( SV38 = p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(524,plain,
! [SV39: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ( SV39 != n0 )
| ( SV39 = n0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(525,plain,
! [SV40: $i] :
( ( ( SV40 = n1 )
= $false )
| ( ( SV40 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(526,plain,
! [SV41: $i] :
( ( ( SV41 = n1 )
= $false )
| ( ( SV41 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(527,plain,
! [SV147: $i,SV106: $i,SV42: $i] :
( ( ! [SY298: $i] :
( ( SV42
!= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SY298 @ n1 ) ) ) )
| ( SV42
= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SY298 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(528,plain,
! [SV43: $i] :
( ( ( SV43 = n1 )
= $false )
| ( ( SV43 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(529,plain,
! [SV44: $i] :
( ( ( SV44 = n1 )
= $false )
| ( ( SV44 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(530,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ~ ( less @ SV45 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(531,plain,
! [SV108: $i,SV46: $i] :
( ( ( SV46
!= ( plus @ n0 @ ( times @ SV108 @ p__0 ) ) )
= $true )
| ( ( SV46
= ( plus @ n0 @ ( times @ SV108 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(532,plain,
! [SV109: $i,SV47: $i] :
( ( ( ( plus @ SV47 @ SV109 )
!= SV47 )
= $true )
| ( ( SV109 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(533,plain,
! [SV110: $i,SV48: $i] :
( ( ( SV48 != p__0 )
= $true )
| ( ( ( SV110 != n1 )
| ( SV110 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(534,plain,
! [SV49: $i] :
( ( ( less @ n1 @ SV49 )
= $false )
| ( ( SV49 != n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(535,plain,
! [SV50: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ( ( s_5 @ p__0 @ SV50 )
!= n0 )
| ( SV50
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV50 ) @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(536,plain,
! [SV149: $i,SV111: $i,SV51: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( less @ SV51 @ SV111 )
| ~ ( less @ SV51 @ SV149 )
| ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SY299 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SY300 @ SV149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(537,plain,
! [SV112: $i,SV52: $i] :
( ( ( n1
!= ( times @ SV52 @ SV112 ) )
= $true )
| ( ( SV112 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(538,plain,
! [SV150: $i,SV113: $i,SV54: $i] :
( ( ! [SY301: $i,SY302: $i] :
( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
!= ( plus @ SV150 @ ( times @ SY301 @ ( plus @ SY302 @ n1 ) ) ) )
| ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SV150 @ ( times @ SY301 @ ( plus @ SY302 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(539,plain,
! [SV114: $i,SV55: $i] :
( ( ( ( times @ SV55 @ SV114 )
!= p__0 )
= $true )
| ( ( ( times @ SV55 @ SV114 )
= p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(540,plain,
! [SV151: $i,SV115: $i,SV56: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( SV56
!= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
| ( SV56
= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(541,plain,
! [SV152: $i,SV116: $i,SV57: $i] :
( ( ( SV57
!= ( plus @ n0 @ ( times @ SV116 @ SV152 ) ) )
| ( SV57
= ( plus @ n0 @ ( times @ SV116 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(542,plain,
! [SV117: $i,SV58: $i] :
( ( ( SV58
!= ( plus @ SV58 @ SV117 ) )
= $true )
| ( ( SV117 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(543,plain,
! [SV118: $i,SV59: $i] :
( ( ( SV59
!= ( plus @ SV118 @ SV59 ) )
= $true )
| ( ( SV118 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(544,plain,
! [SV60: $i] :
( ( ( SV60 = p__0 )
= $false )
| ( ( less @ n1 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(545,plain,
! [SV119: $i,SV61: $i] :
( ( ( SV61 != p__0 )
= $true )
| ( ( n1
!= ( times @ SV119 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(546,plain,
! [SV153: $i,SV120: $i,SV62: $i] :
( ( ( SV62 != SV120 )
| ( ( plus @ SV153 @ SV62 )
= ( plus @ SV153 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(547,plain,
! [SV121: $i,SV63: $i] :
( ( ( SV63
!= ( plus @ n0 @ ( times @ SV121 @ p__0 ) ) )
= $true )
| ( ( SV63
= ( plus @ n0 @ ( times @ SV121 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(548,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ~ ( less @ n0 @ SV64 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(549,plain,
! [SV123: $i,SV66: $i] :
( ( ( n1
!= ( times @ SV66 @ SV123 ) )
= $true )
| ( ( SV66 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(550,plain,
! [SV67: $i] :
( ( ( SV67 = n1 )
= $false )
| ( ( SV67 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(551,plain,
! [SV155: $i,SV124: $i,SV68: $i] :
( ( ! [SY303: $i] :
( ( SV68
!= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SY303 @ n1 ) ) ) )
| ( SV68
= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SY303 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(552,plain,
! [SV156: $i,SV125: $i,SV69: $i] :
( ( ( ( plus @ SV69 @ SV125 )
!= ( plus @ SV69 @ SV156 ) )
| ( SV125 = SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(553,plain,
! [SV70: $i] :
( ( ( SV70 = n1 )
= $false )
| ( ( SV70 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(554,plain,
! [SV126: $i,SV71: $i] :
( ( ( ~ ( less @ n1 @ SV71 ) )
= $true )
| ( ( n1
!= ( times @ SV126 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(555,plain,
! [SV72: $i] :
( ( ( SV72 = n1 )
= $false )
| ( ( SV72 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(556,plain,
! [SV127: $i,SV73: $i] :
( ( ( SV73 != p__0 )
= $true )
| ( ( ( plus @ n0 @ ( times @ SV127 @ SV73 ) )
= ( times @ SV127 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(557,plain,
! [SV157: $i,SV128: $i,SV74: $i] :
( ( ( SV74
!= ( plus @ SV128 @ ( times @ SV157 @ p__0 ) ) )
| ( SV74
= ( plus @ SV128 @ ( times @ SV157 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(558,plain,
! [SV158: $i,SV129: $i,SV75: $i] :
( ( ! [SY304: $i] :
( ( SV75
!= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SY304 @ n1 ) ) ) )
| ( SV75
= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SY304 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(559,plain,
! [SV159: $i,SV130: $i,SV76: $i] :
( ( ( SV76 != p__0 )
| ( ( times @ SV130 @ SV159 )
!= SV76 )
| ( SV130 = n1 )
| ( SV130 = SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(560,plain,
! [SV78: $i] :
( ( ( SV78 = n1 )
= $false )
| ( ( SV78 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(561,plain,
! [SV131: $i,SV79: $i] :
( ( ( SV79
!= ( plus @ n0 @ ( times @ SV131 @ p__0 ) ) )
= $true )
| ( ( SV79
= ( plus @ n0 @ ( times @ SV131 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(562,plain,
! [SV160: $i,SV132: $i,SV80: $i] :
( ( ( ( plus @ SV80 @ SV132 )
!= ( plus @ SV160 @ SV132 ) )
| ( SV80 = SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(563,plain,
! [SV81: $i] :
( ( ( SV81 = n1 )
= $false )
| ( ( SV81 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(564,plain,
! [SV82: $i] :
( ( ( SV82 = n1 )
= $false )
| ( ( SV82 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(565,plain,
! [SV161: $i,SV133: $i,SV83: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ( less @ SV83 @ SV133 )
| ~ ( less @ SV83 @ SV161 )
| ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SY305 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SY306 @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(566,plain,
! [SV135: $i,SV85: $i,SV2: $i] :
( ( element @ ( plus @ SV2 @ ( plus @ SV85 @ n1 ) ) @ SV135 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(567,plain,
! [SV87: $i,SV5: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ( plus @ ( times @ SV5 @ p__0 ) @ ( times @ SV87 @ p__0 ) )
= ( times @ ( plus @ SV5 @ SV87 ) @ p__0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(568,plain,
! [SV136: $i,SV88: $i,SV6: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ( plus @ ( plus @ SV6 @ ( times @ SV88 @ p__0 ) ) @ ( times @ SV136 @ p__0 ) )
= ( plus @ SV6 @ ( plus @ ( times @ SV88 @ p__0 ) @ ( times @ SV136 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(569,plain,
! [SV7: $i] :
( ( ( ~ ( less @ SV7 @ p__0 ) )
= $true )
| ( ( less @ SV7 @ p__0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(570,plain,
! [SV101: $i,SV32: $i] :
( ( ( less @ SV32 @ SV101 )
= $true )
| ( ( less @ SV101 @ SV32 )
= $true )
| ( ( SV32 = SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(571,plain,
! [SV102: $i,SV33: $i] :
( ( ( less @ ( plus @ SV33 @ n1 ) @ SV102 )
= $false )
| ( ( less @ SV33 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(572,plain,
! [SV162: $i,SV146: $i,SV103: $i,SV35: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ( SV35
!= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
| ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(573,plain,
! [SV104: $i,SV36: $i] :
( ( ( ( plus @ SV36 @ ( plus @ SV104 @ n1 ) )
= n1 )
= $false )
| ( ( ( plus @ SV36 @ ( plus @ SV104 @ n1 ) )
= n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(574,plain,
! [SV105: $i,SV37: $i] :
( ( ( ( plus @ SV37 @ SV105 )
= SV105 )
= $false )
| ( ( SV37 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(575,plain,
! [SV39: $i] :
( ( ( SV39 != n0 )
= $true )
| ( ( SV39 = n0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(576,plain,
! [SV163: $i,SV147: $i,SV106: $i,SV42: $i] :
( ( ( SV42
!= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SV163 @ n1 ) ) ) )
| ( SV42
= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SV163 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(577,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( ~ ( less @ SV45 @ n0 ) )
= $true )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(578,plain,
! [SV108: $i,SV46: $i] :
( ( ( SV46
= ( plus @ n0 @ ( times @ SV108 @ p__0 ) ) )
= $false )
| ( ( SV46
= ( plus @ n0 @ ( times @ SV108 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(579,plain,
! [SV109: $i,SV47: $i] :
( ( ( ( plus @ SV47 @ SV109 )
= SV47 )
= $false )
| ( ( SV109 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(580,plain,
! [SV110: $i,SV48: $i] :
( ( ( SV48 = p__0 )
= $false )
| ( ( ( SV110 != n1 )
| ( SV110 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(581,plain,
! [SV49: $i] :
( ( ( SV49 = n1 )
= $false )
| ( ( less @ n1 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(582,plain,
! [SV50: $i] :
( ( ( ( s_5 @ p__0 @ SV50 )
!= n0 )
= $true )
| ( ( SV50
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV50 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(583,plain,
! [SV164: $i,SV149: $i,SV111: $i,SV51: $i] :
( ( ! [SY307: $i] :
( ~ ( less @ SV51 @ SV111 )
| ~ ( less @ SV51 @ SV149 )
| ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SY307 @ SV149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(584,plain,
! [SV112: $i,SV52: $i] :
( ( ( n1
= ( times @ SV52 @ SV112 ) )
= $false )
| ( ( SV112 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(585,plain,
! [SV165: $i,SV150: $i,SV113: $i,SV54: $i] :
( ( ! [SY308: $i] :
( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
!= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SY308 @ n1 ) ) ) )
| ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SY308 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(586,plain,
! [SV114: $i,SV55: $i] :
( ( ( ( times @ SV55 @ SV114 )
= p__0 )
= $false )
| ( ( ( times @ SV55 @ SV114 )
= p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(587,plain,
! [SV151: $i,SV115: $i,SV56: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ( SV56
!= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
| ( SV56
= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(588,plain,
! [SV152: $i,SV116: $i,SV57: $i] :
( ( ( SV57
!= ( plus @ n0 @ ( times @ SV116 @ SV152 ) ) )
= $true )
| ( ( SV57
= ( plus @ n0 @ ( times @ SV116 @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(589,plain,
! [SV117: $i,SV58: $i] :
( ( ( SV58
= ( plus @ SV58 @ SV117 ) )
= $false )
| ( ( SV117 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(590,plain,
! [SV118: $i,SV59: $i] :
( ( ( SV59
= ( plus @ SV118 @ SV59 ) )
= $false )
| ( ( SV118 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(591,plain,
! [SV119: $i,SV61: $i] :
( ( ( SV61 = p__0 )
= $false )
| ( ( n1
!= ( times @ SV119 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(592,plain,
! [SV153: $i,SV120: $i,SV62: $i] :
( ( ( SV62 != SV120 )
= $true )
| ( ( ( plus @ SV153 @ SV62 )
= ( plus @ SV153 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(593,plain,
! [SV121: $i,SV63: $i] :
( ( ( SV63
= ( plus @ n0 @ ( times @ SV121 @ p__0 ) ) )
= $false )
| ( ( SV63
= ( plus @ n0 @ ( times @ SV121 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(594,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( ~ ( less @ n0 @ SV64 ) )
= $true )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(595,plain,
! [SV123: $i,SV66: $i] :
( ( ( n1
= ( times @ SV66 @ SV123 ) )
= $false )
| ( ( SV66 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(596,plain,
! [SV166: $i,SV155: $i,SV124: $i,SV68: $i] :
( ( ( SV68
!= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SV166 @ n1 ) ) ) )
| ( SV68
= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SV166 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(597,plain,
! [SV156: $i,SV125: $i,SV69: $i] :
( ( ( ( plus @ SV69 @ SV125 )
!= ( plus @ SV69 @ SV156 ) )
= $true )
| ( ( SV125 = SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(598,plain,
! [SV126: $i,SV71: $i] :
( ( ( less @ n1 @ SV71 )
= $false )
| ( ( n1
!= ( times @ SV126 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(599,plain,
! [SV127: $i,SV73: $i] :
( ( ( SV73 = p__0 )
= $false )
| ( ( ( plus @ n0 @ ( times @ SV127 @ SV73 ) )
= ( times @ SV127 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(600,plain,
! [SV157: $i,SV128: $i,SV74: $i] :
( ( ( SV74
!= ( plus @ SV128 @ ( times @ SV157 @ p__0 ) ) )
= $true )
| ( ( SV74
= ( plus @ SV128 @ ( times @ SV157 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(601,plain,
! [SV167: $i,SV158: $i,SV129: $i,SV75: $i] :
( ( ( SV75
!= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SV167 @ n1 ) ) ) )
| ( SV75
= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SV167 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(602,plain,
! [SV159: $i,SV130: $i,SV76: $i] :
( ( ( SV76 != p__0 )
= $true )
| ( ( ( ( times @ SV130 @ SV159 )
!= SV76 )
| ( SV130 = n1 )
| ( SV130 = SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(603,plain,
! [SV131: $i,SV79: $i] :
( ( ( SV79
= ( plus @ n0 @ ( times @ SV131 @ p__0 ) ) )
= $false )
| ( ( SV79
= ( plus @ n0 @ ( times @ SV131 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(604,plain,
! [SV160: $i,SV132: $i,SV80: $i] :
( ( ( ( plus @ SV80 @ SV132 )
!= ( plus @ SV160 @ SV132 ) )
= $true )
| ( ( SV80 = SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(605,plain,
! [SV168: $i,SV161: $i,SV133: $i,SV83: $i] :
( ( ! [SY309: $i] :
( ~ ( less @ SV83 @ SV133 )
| ~ ( less @ SV83 @ SV161 )
| ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SY309 @ SV161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(606,plain,
! [SV136: $i,SV88: $i,SV6: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ( plus @ ( plus @ SV6 @ ( times @ SV88 @ p__0 ) ) @ ( times @ SV136 @ p__0 ) )
= ( plus @ SV6 @ ( plus @ ( times @ SV88 @ p__0 ) @ ( times @ SV136 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(607,plain,
! [SV7: $i] :
( ( ( less @ SV7 @ p__0 )
= $false )
| ( ( less @ SV7 @ p__0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(608,plain,
! [SV162: $i,SV146: $i,SV103: $i,SV35: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ( SV35
!= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
| ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(609,plain,
! [SV39: $i] :
( ( ( SV39 = n0 )
= $false )
| ( ( SV39 = n0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(610,plain,
! [SV163: $i,SV147: $i,SV106: $i,SV42: $i] :
( ( ( SV42
!= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SV163 @ n1 ) ) ) )
= $true )
| ( ( SV42
= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SV163 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(611,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( less @ SV45 @ n0 )
= $false )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(612,plain,
! [SV48: $i,SV110: $i] :
( ( ( SV110 != n1 )
= $true )
| ( ( SV110 = n1 )
= $true )
| ( ( SV48 = p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(613,plain,
! [SV50: $i] :
( ( ( ( s_5 @ p__0 @ SV50 )
= n0 )
= $false )
| ( ( SV50
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV50 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(614,plain,
! [SV169: $i,SV164: $i,SV149: $i,SV111: $i,SV51: $i] :
( ( ~ ( less @ SV51 @ SV111 )
| ~ ( less @ SV51 @ SV149 )
| ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(615,plain,
! [SV170: $i,SV165: $i,SV150: $i,SV113: $i,SV54: $i] :
( ( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
!= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SV170 @ n1 ) ) ) )
| ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SV170 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(616,plain,
! [SV151: $i,SV115: $i,SV56: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ( SV56
!= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
| ( SV56
= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(617,plain,
! [SV152: $i,SV116: $i,SV57: $i] :
( ( ( SV57
= ( plus @ n0 @ ( times @ SV116 @ SV152 ) ) )
= $false )
| ( ( SV57
= ( plus @ n0 @ ( times @ SV116 @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(618,plain,
! [SV61: $i,SV119: $i] :
( ( ( n1
= ( times @ SV119 @ SV61 ) )
= $false )
| ( ( SV61 = p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(619,plain,
! [SV153: $i,SV120: $i,SV62: $i] :
( ( ( SV62 = SV120 )
= $false )
| ( ( ( plus @ SV153 @ SV62 )
= ( plus @ SV153 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(620,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( less @ n0 @ SV64 )
= $false )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(621,plain,
! [SV166: $i,SV155: $i,SV124: $i,SV68: $i] :
( ( ( SV68
!= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SV166 @ n1 ) ) ) )
= $true )
| ( ( SV68
= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SV166 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(622,plain,
! [SV156: $i,SV125: $i,SV69: $i] :
( ( ( ( plus @ SV69 @ SV125 )
= ( plus @ SV69 @ SV156 ) )
= $false )
| ( ( SV125 = SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(623,plain,
! [SV71: $i,SV126: $i] :
( ( ( n1
= ( times @ SV126 @ SV71 ) )
= $false )
| ( ( less @ n1 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(624,plain,
! [SV157: $i,SV128: $i,SV74: $i] :
( ( ( SV74
= ( plus @ SV128 @ ( times @ SV157 @ p__0 ) ) )
= $false )
| ( ( SV74
= ( plus @ SV128 @ ( times @ SV157 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(625,plain,
! [SV167: $i,SV158: $i,SV129: $i,SV75: $i] :
( ( ( SV75
!= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SV167 @ n1 ) ) ) )
= $true )
| ( ( SV75
= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SV167 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(626,plain,
! [SV159: $i,SV130: $i,SV76: $i] :
( ( ( SV76 = p__0 )
= $false )
| ( ( ( ( times @ SV130 @ SV159 )
!= SV76 )
| ( SV130 = n1 )
| ( SV130 = SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(627,plain,
! [SV160: $i,SV132: $i,SV80: $i] :
( ( ( ( plus @ SV80 @ SV132 )
= ( plus @ SV160 @ SV132 ) )
= $false )
| ( ( SV80 = SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(628,plain,
! [SV171: $i,SV168: $i,SV161: $i,SV133: $i,SV83: $i] :
( ( ~ ( less @ SV83 @ SV133 )
| ~ ( less @ SV83 @ SV161 )
| ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(629,plain,
! [SV162: $i,SV146: $i,SV103: $i,SV35: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ( SV35
!= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
| ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(630,plain,
! [SV163: $i,SV147: $i,SV106: $i,SV42: $i] :
( ( ( SV42
= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SV163 @ n1 ) ) ) )
= $false )
| ( ( SV42
= ( plus @ SV106 @ ( times @ SV147 @ ( plus @ SV163 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(631,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV45 @ n0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(632,plain,
! [SV48: $i,SV110: $i] :
( ( ( SV110 = n1 )
= $false )
| ( ( SV110 = n1 )
= $true )
| ( ( SV48 = p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(633,plain,
! [SV169: $i,SV164: $i,SV149: $i,SV111: $i,SV51: $i] :
( ( ( ~ ( less @ SV51 @ SV111 ) )
= $true )
| ( ( ~ ( less @ SV51 @ SV149 )
| ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(634,plain,
! [SV170: $i,SV165: $i,SV150: $i,SV113: $i,SV54: $i] :
( ( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
!= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SV170 @ n1 ) ) ) )
= $true )
| ( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SV170 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(635,plain,
! [SV151: $i,SV115: $i,SV56: $i] :
( ( ( SV56
!= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
= $true )
| ( ( SV56
= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(636,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(637,plain,
! [SV166: $i,SV155: $i,SV124: $i,SV68: $i] :
( ( ( SV68
= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SV166 @ n1 ) ) ) )
= $false )
| ( ( SV68
= ( plus @ SV124 @ ( times @ SV155 @ ( plus @ SV166 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(638,plain,
! [SV167: $i,SV158: $i,SV129: $i,SV75: $i] :
( ( ( SV75
= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SV167 @ n1 ) ) ) )
= $false )
| ( ( SV75
= ( plus @ SV129 @ ( times @ SV158 @ ( plus @ SV167 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(639,plain,
! [SV76: $i,SV159: $i,SV130: $i] :
( ( ( ( times @ SV130 @ SV159 )
!= SV76 )
= $true )
| ( ( ( SV130 = n1 )
| ( SV130 = SV76 ) )
= $true )
| ( ( SV76 = p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(640,plain,
! [SV171: $i,SV168: $i,SV161: $i,SV133: $i,SV83: $i] :
( ( ( ~ ( less @ SV83 @ SV133 ) )
= $true )
| ( ( ~ ( less @ SV83 @ SV161 )
| ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(641,plain,
! [SV162: $i,SV146: $i,SV103: $i,SV35: $i] :
( ( ( SV35
!= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
= $true )
| ( ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(642,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ~ ( less @ SV45 @ p__0 )
| ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV45 @ n0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(643,plain,
! [SV169: $i,SV164: $i,SV149: $i,SV111: $i,SV51: $i] :
( ( ( less @ SV51 @ SV111 )
= $false )
| ( ( ~ ( less @ SV51 @ SV149 )
| ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(644,plain,
! [SV170: $i,SV165: $i,SV150: $i,SV113: $i,SV54: $i] :
( ( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SV170 @ n1 ) ) ) )
= $false )
| ( ( ( plus @ SV54 @ ( plus @ SV113 @ n1 ) )
= ( plus @ SV150 @ ( times @ SV165 @ ( plus @ SV170 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(645,plain,
! [SV151: $i,SV115: $i,SV56: $i] :
( ( ( SV56
= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
= $false )
| ( ( SV56
= ( plus @ SV115 @ ( times @ SV151 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(646,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ~ ( less @ SV64 @ p__0 )
| ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(647,plain,
! [SV76: $i,SV159: $i,SV130: $i] :
( ( ( ( times @ SV130 @ SV159 )
= SV76 )
= $false )
| ( ( ( SV130 = n1 )
| ( SV130 = SV76 ) )
= $true )
| ( ( SV76 = p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(648,plain,
! [SV171: $i,SV168: $i,SV161: $i,SV133: $i,SV83: $i] :
( ( ( less @ SV83 @ SV133 )
= $false )
| ( ( ~ ( less @ SV83 @ SV161 )
| ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(649,plain,
! [SV162: $i,SV146: $i,SV103: $i,SV35: $i] :
( ( ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
= $false )
| ( ( SV35
= ( plus @ SV103 @ ( times @ ( plus @ SV146 @ SV162 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(650,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( ~ ( less @ SV45 @ p__0 ) )
= $true )
| ( ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV45 @ n0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(651,plain,
! [SV169: $i,SV164: $i,SV111: $i,SV149: $i,SV51: $i] :
( ( ( ~ ( less @ SV51 @ SV149 ) )
= $true )
| ( ( ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) ) )
= $true )
| ( ( less @ SV51 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(652,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( ~ ( less @ SV64 @ p__0 ) )
= $true )
| ( ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(653,plain,
! [SV159: $i,SV76: $i,SV130: $i] :
( ( ( SV130 = n1 )
= $true )
| ( ( SV130 = SV76 )
= $true )
| ( ( ( times @ SV130 @ SV159 )
= SV76 )
= $false )
| ( ( SV76 = p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(654,plain,
! [SV171: $i,SV168: $i,SV133: $i,SV161: $i,SV83: $i] :
( ( ( ~ ( less @ SV83 @ SV161 ) )
= $true )
| ( ( ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) ) )
= $true )
| ( ( less @ SV83 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(655,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( less @ SV45 @ p__0 )
= $false )
| ( ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV45 @ n0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(656,plain,
! [SV169: $i,SV164: $i,SV111: $i,SV149: $i,SV51: $i] :
( ( ( less @ SV51 @ SV149 )
= $false )
| ( ( ~ ( less @ SV111 @ SV149 )
| ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) ) )
= $true )
| ( ( less @ SV51 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(657,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( less @ SV64 @ p__0 )
= $false )
| ( ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(658,plain,
! [SV171: $i,SV168: $i,SV133: $i,SV161: $i,SV83: $i] :
( ( ( less @ SV83 @ SV161 )
= $false )
| ( ( ~ ( less @ SV133 @ SV161 )
| ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) ) )
= $true )
| ( ( less @ SV83 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(659,plain,
! [SV148: $i,SV107: $i,SV45: $i] :
( ( ( ( plus @ SV45 @ ( times @ SV107 @ p__0 ) )
= ( plus @ n0 @ ( times @ SV148 @ p__0 ) ) )
= $false )
| ( ( less @ SV45 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV45 @ n0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(660,plain,
! [SV169: $i,SV51: $i,SV164: $i,SV149: $i,SV111: $i] :
( ( ( ~ ( less @ SV111 @ SV149 ) )
= $true )
| ( ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) )
= $true )
| ( ( less @ SV51 @ SV149 )
= $false )
| ( ( less @ SV51 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(661,plain,
! [SV154: $i,SV122: $i,SV64: $i] :
( ( ( ( plus @ SV64 @ ( times @ SV122 @ p__0 ) )
= ( plus @ n0 @ ( times @ SV154 @ p__0 ) ) )
= $false )
| ( ( less @ SV64 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(662,plain,
! [SV171: $i,SV168: $i,SV83: $i,SV161: $i,SV133: $i] :
( ( ( ~ ( less @ SV133 @ SV161 ) )
= $true )
| ( ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) )
= $true )
| ( ( less @ SV83 @ SV161 )
= $false )
| ( ( less @ SV83 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(663,plain,
! [SV169: $i,SV51: $i,SV164: $i,SV149: $i,SV111: $i] :
( ( ( less @ SV111 @ SV149 )
= $false )
| ( ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
!= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) )
= $true )
| ( ( less @ SV51 @ SV149 )
= $false )
| ( ( less @ SV51 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(664,plain,
! [SV171: $i,SV168: $i,SV83: $i,SV161: $i,SV133: $i] :
( ( ( less @ SV133 @ SV161 )
= $false )
| ( ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
!= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) )
= $true )
| ( ( less @ SV83 @ SV161 )
= $false )
| ( ( less @ SV83 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(665,plain,
! [SV169: $i,SV51: $i,SV149: $i,SV164: $i,SV111: $i] :
( ( ( ( plus @ SV111 @ ( times @ SV164 @ SV149 ) )
= ( plus @ SV51 @ ( times @ SV169 @ SV149 ) ) )
= $false )
| ( ( less @ SV111 @ SV149 )
= $false )
| ( ( less @ SV51 @ SV149 )
= $false )
| ( ( less @ SV51 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(666,plain,
! [SV171: $i,SV133: $i,SV161: $i,SV168: $i,SV83: $i] :
( ( ( ( plus @ SV83 @ ( times @ SV168 @ SV161 ) )
= ( plus @ SV133 @ ( times @ SV171 @ SV161 ) ) )
= $false )
| ( ( less @ SV133 @ SV161 )
= $false )
| ( ( less @ SV83 @ SV161 )
= $false )
| ( ( less @ SV83 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(667,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[197,666,665,661,659,653,649,645,644,638,637,632,630,627,624,623,622,619,618,617,613,609,607,606,603,599,595,593,590,589,586,584,581,579,578,574,573,571,570,567,566,564,563,560,555,553,550,544,529,528,526,525,523,519,516,515,514,513,512,511,510,509,508,507,506,502,501,499,492,480,468,445,438,437,434,433,432,431,430,429,428,427,420,366,363,356,353,351,347,243,228,222]) ).
thf(668,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM420-1.000 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 13:15:39 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 89.85/15.26
% 89.85/15.26 No.of.Axioms: 91
% 89.85/15.26
% 89.85/15.26 Length.of.Defs: 0
% 89.85/15.26
% 89.85/15.26 Contains.Choice.Funs: false
% 89.85/15.26 .....................
% 89.85/15.26
% 89.85/15.26 ********************************
% 89.85/15.26 * All subproblems solved! *
% 89.85/15.26 ********************************
% 89.85/15.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:91,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:667,loop_count:0,foatp_calls:1,translation:fof_full)
% 89.85/15.26
% 89.85/15.26 %**** Beginning of derivation protocol ****
% 89.85/15.26 % SZS output start CNFRefutation
% See solution above
% 89.85/15.26
% 89.85/15.26 %**** End of derivation protocol ****
% 89.85/15.26 %**** no. of clauses in derivation: 668 ****
% 89.85/15.26 %**** clause counter: 667 ****
% 89.85/15.26
% 89.85/15.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:91,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:667,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------