TSTP Solution File: NUM420-1.000 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM420-1.000 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 11:49:34 EDT 2022
% Result : Unsatisfiable 2.38s 2.56s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 104
% Syntax : Number of formulae : 684 ( 422 unt; 12 typ; 0 def)
% Number of atoms : 3061 (1832 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 5500 ( 607 ~; 729 |; 0 &;4164 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 1436 ( 0 ^1436 !; 0 ?;1436 :)
% 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/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(2,axiom,
! [X1: $i,X2: $i] :
( ~ ( less @ n1 @ X1 )
| ( n1
!= ( times @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(3,axiom,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( less @ X1 @ X2 )
| ( less @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(4,axiom,
! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ( X1 != n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(5,axiom,
! [X1: $i] : ( less @ n0 @ ( plus @ X1 @ n1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(7,axiom,
! [X2: $i,X1: $i] :
( ( n1
!= ( times @ X2 @ X1 ) )
| ( X1 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(8,axiom,
! [X1: $i,X2: $i] :
( ( n1
!= ( times @ X1 @ X2 ) )
| ( X1 = n1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(15,axiom,
! [X1: $i] :
( ( times @ n1 @ X1 )
= X1 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(18,axiom,
! [X1: $i] :
( ( times @ X1 @ n1 )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(19,axiom,
! [X1: $i] :
( ( plus @ X1 @ n1 )
!= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(20,axiom,
! [X1: $i,X2: $i] :
( ( times @ X1 @ X2 )
= ( times @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(21,axiom,
! [X1: $i] :
( ( plus @ n1 @ ( plus @ X1 @ n1 ) )
!= n1 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(23,axiom,
! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X2 )
| ( X1 = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(24,axiom,
! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X1 )
| ( X2 = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(25,axiom,
! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X1 @ X2 ) )
| ( X2 = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(26,axiom,
! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X2 @ X1 ) )
| ( X2 = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(27,axiom,
! [X1: $i] :
( ( plus @ n0 @ X1 )
= X1 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(29,axiom,
! [X1: $i,X2: $i] :
( ( plus @ X1 @ X2 )
= ( plus @ X2 @ X1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(33,axiom,
! [X1: $i] :
( ( plus @ X1 @ n0 )
= X1 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_55) ).
thf(40,negated_conjecture,
! [X7: $i,X12: $i] :
( ( X7 != p__0 )
| ( n1
!= ( times @ X12 @ X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_54) ).
thf(41,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( ( s_1 @ X10 )
= p__0 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_52) ).
thf(43,negated_conjecture,
! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_50) ).
thf(45,negated_conjecture,
! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_49) ).
thf(46,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) )
= X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_48) ).
thf(47,negated_conjecture,
! [X7: $i,X10: $i] :
( ( X7 != p__0 )
| ( X10 != n1 )
| ( X10 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_47) ).
thf(48,negated_conjecture,
! [X7: $i] :
( ( X7 != p__0 )
| ( X7 = p__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_46) ).
thf(49,negated_conjecture,
! [X10: $i] :
( ( X10 = n1 )
| ( X10 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_45) ).
thf(50,negated_conjecture,
! [X7: $i] :
( ( X7 != p__0 )
| ( less @ n1 @ X7 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_43) ).
thf(52,negated_conjecture,
p__0 = p__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_42) ).
thf(53,negated_conjecture,
( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_39) ).
thf(56,negated_conjecture,
! [X33: $i] :
( ( X33 != n1 )
| ( X33 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_38) ).
thf(57,negated_conjecture,
! [X33: $i] :
( ( X33 != p__0 )
| ( X33 = p__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_37) ).
thf(58,negated_conjecture,
( ( plus @ n0 @ n1 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_36) ).
thf(59,negated_conjecture,
( ~ ( less @ n1 @ p__0 )
| ( less @ n1 @ p__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35) ).
thf(60,negated_conjecture,
( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 )
| ( less @ n0 @ p__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_34) ).
thf(61,negated_conjecture,
! [X8: $i] :
( ( X8 = n0 )
| ( less @ X8 @ n0 )
| ( less @ n0 @ X8 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_32) ).
thf(63,negated_conjecture,
! [X32: $i] :
( ( X32 != n1 )
| ( X32 = n1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_30) ).
thf(65,negated_conjecture,
! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29) ).
thf(66,negated_conjecture,
! [X23: $i] :
( ( X23 != n1 )
| ( X23 = n1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_26) ).
thf(69,negated_conjecture,
! [X11: $i] :
( ( plus @ n1 @ ( plus @ X11 @ n1 ) )
!= n1 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_20) ).
thf(75,negated_conjecture,
! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_19) ).
thf(76,negated_conjecture,
( ~ ( less @ n0 @ p__0 )
| ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18) ).
thf(77,negated_conjecture,
! [X24: $i] :
( ( X24 != n1 )
| ( X24 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17) ).
thf(78,negated_conjecture,
! [X28: $i] :
( ( X28 != n1 )
| ( X28 = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
thf(79,negated_conjecture,
! [X27: $i] :
( ( X27 != n1 )
| ( X27 = n1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_12) ).
thf(83,negated_conjecture,
n1 = n1,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(85,negated_conjecture,
! [X1: $i,X13: $i] :
~ ( element @ X1 @ X13 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clause_8) ).
thf(87,negated_conjecture,
! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ( X8 != n0 )
| ( X8 = n0 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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,
( ( ! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ! [X2: $i] :
( n1
!= ( times @ X2 @ X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(188,plain,
( ( ! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ( X1 != n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(189,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ! [X4: $i,X5: $i] :
( ( plus @ X1 @ ( times @ X4 @ X3 ) )
!= ( plus @ X2 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(190,plain,
( ( ! [X2: $i,X1: $i] :
( ( n1
!= ( times @ X2 @ X1 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(191,plain,
( ( ! [X1: $i] :
( ! [X2: $i] :
( n1
!= ( times @ X1 @ X2 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(192,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n1 )
!= n0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(193,plain,
( ( ! [X1: $i] :
( ( plus @ n1 @ ( plus @ X1 @ n1 ) )
!= n1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(194,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1 != X2 )
| ! [X3: $i] :
( ( plus @ X3 @ X1 )
= ( plus @ X3 @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(195,plain,
( ( ! [X1: $i] :
( ! [X2: $i] :
( ( plus @ X1 @ X2 )
!= X2 )
| ( X1 = n0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(196,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X1 )
| ( X2 = n0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(197,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X1 @ X2 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(198,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X2 @ X1 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(199,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X1 @ X3 ) )
| ( X2 = X3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(200,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X3 @ X2 ) )
| ( X1 = X3 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(201,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ! [X4: $i,X5: $i] :
( ( plus @ X2 @ ( times @ X4 @ X3 ) )
!= ( plus @ X1 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(202,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[129]) ).
thf(203,plain,
( ( ! [X10: $i,X38: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(204,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ! [X12: $i] :
( ( plus @ n0 @ ( times @ X12 @ X7 ) )
= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(205,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ! [X12: $i] :
( n1
!= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(206,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(207,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(208,plain,
( ( ! [X7: $i] : ( X7 != p__0 )
| ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(209,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( X7 = p__0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(210,plain,
( ( ! [X10: $i] : ( X10 = n1 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(211,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( less @ n1 @ X7 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(212,plain,
( ( ! [X10: $i,X37: $i,X7: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X37 @ X7 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X37 @ X7 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(213,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[144]) ).
thf(214,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[145]) ).
thf(215,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ! [X35: $i] :
( ! [X36: $i] :
( ( times @ X35 @ X36 )
!= X7 )
| ( X35 = n1 )
| ( X35 = X7 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(216,plain,
( ( ! [X33: $i,X34: $i] :
( ( ( times @ X33 @ X34 )
!= p__0 )
| ( ( times @ X33 @ X34 )
= p__0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(217,plain,
( ( ! [X33: $i] :
( ( X33 != n1 )
| ( X33 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(218,plain,
( ( ! [X33: $i] :
( ( X33 != p__0 )
| ( X33 = p__0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(219,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[151]) ).
thf(220,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X7: $i] : ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(221,plain,
( ( ! [X32: $i] :
( ( X32 != n1 )
| ( X32 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(222,plain,
( ( ~ ( less @ n0 @ p__0 )
| $true )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(223,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(224,plain,
( ( ! [X23: $i] :
( ( X23 != n1 )
| ( X23 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(225,plain,
( ( ! [X10: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [X8: $i,X9: $i] :
( ( X10
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X10
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(226,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ ( plus @ X8 @ ( times @ X9 @ p__0 ) ) @ ( times @ X22 @ p__0 ) )
= ( plus @ X8 @ ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(227,plain,
( ( ! [X11: $i] :
( ( plus @ n1 @ ( plus @ X11 @ n1 ) )
!= n1 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(228,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ X8 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(229,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(230,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X7: $i] :
( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(231,plain,
( ( ! [X15: $i,X31: $i] :
( ( X15
!= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) )
| ( X15
= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(232,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(extcnf_combined,[status(esa)],[166]) ).
thf(233,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(234,plain,
( ( ! [X24: $i] :
( ( X24 != n1 )
| ( X24 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(235,plain,
( ( ! [X28: $i] :
( ( X28 != n1 )
| ( X28 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(236,plain,
( ( ! [X27: $i] :
( ( X27 != n1 )
| ( X27 = n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(237,plain,
( ( ! [X8: $i] :
( ~ ( less @ X8 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(238,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(extcnf_combined,[status(esa)],[173]) ).
thf(239,plain,
( ( ! [X7: $i,X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( X7
!= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(240,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[175]) ).
thf(241,plain,
( ( ! [X14: $i,X21: $i] :
( ( X14
!= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) )
| ( X14
= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(242,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X7: $i] :
( ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(243,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X8: $i] :
( ( X8 != n0 )
| ( X8 = n0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(244,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(extcnf_combined,[status(esa)],[180]) ).
thf(245,plain,
( ( ! [X18: $i,X19: $i] :
( ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
!= n1 )
| ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
= n1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(246,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(extcnf_combined,[status(esa)],[182]) ).
thf(247,plain,
( ( ! [X7: $i,X8: $i,X9: $i] :
( ( X7
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(248,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)],[247]) ).
thf(249,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(250,plain,
( ( ! [X10: $i,X12: $i,X13: $i] :
~ ( element @ ( plus @ X10 @ ( plus @ X12 @ n1 ) ) @ X13 ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(251,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)],[246]) ).
thf(252,plain,
( ( ! [X18: $i,X19: $i] :
( ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
!= n1 )
| ( ( plus @ X18 @ ( plus @ X19 @ n1 ) )
= n1 ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(253,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)],[244]) ).
thf(254,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X8: $i] :
( ( X8 != n0 )
| ( X8 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(255,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X7: $i] :
( ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(256,plain,
( ( ! [X1: $i,X13: $i] :
~ ( element @ X1 @ X13 ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(257,plain,
( ( ! [X14: $i,X21: $i] :
( ( X14
!= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) )
| ( X14
= ( plus @ n0 @ ( times @ X21 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(258,plain,
$true = $true,
inference(copy,[status(thm)],[240]) ).
thf(259,plain,
( ( ! [X7: $i,X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( X7
!= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
| ( X7
= ( plus @ X8 @ ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(260,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)],[238]) ).
thf(261,plain,
( ( ! [X8: $i] :
( ~ ( less @ X8 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(262,plain,
( ( ! [X27: $i] :
( ( X27 != n1 )
| ( X27 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(263,plain,
( ( ! [X28: $i] :
( ( X28 != n1 )
| ( X28 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(264,plain,
( ( ! [X24: $i] :
( ( X24 != n1 )
| ( X24 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(265,plain,
( ( ~ ( less @ n0 @ p__0 )
| ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(266,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(267,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)],[232]) ).
thf(268,plain,
( ( ! [X15: $i,X31: $i] :
( ( X15
!= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) )
| ( X15
= ( plus @ n0 @ ( times @ X31 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(269,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X7: $i] :
( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(270,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(271,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ X8 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ X8 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( plus @ X8 @ ( times @ X9 @ p__0 ) )
!= ( plus @ n0 @ ( times @ X22 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(272,plain,
( ( ! [X11: $i] :
( ( plus @ n1 @ ( plus @ X11 @ n1 ) )
!= n1 ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(273,plain,
( ( ! [X8: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [X9: $i,X22: $i] :
( ( 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)],[226]) ).
thf(274,plain,
( ( ! [X10: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [X8: $i,X9: $i] :
( ( X10
!= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) )
| ( X10
= ( plus @ X8 @ ( times @ X9 @ p__0 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(275,plain,
( ( ! [X23: $i] :
( ( X23 != n1 )
| ( X23 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(276,plain,
( ( ! [X12: $i] :
( ( X12 != n1 )
| ( X12 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(277,plain,
( ( ~ ( less @ n0 @ p__0 )
| $true )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(278,plain,
( ( ! [X32: $i] :
( ( X32 != n1 )
| ( X32 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(279,plain,
( ( ~ ( less @ n0 @ p__0 )
| ! [X7: $i] : ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(280,plain,
( ( ! [X8: $i] :
( ( X8 = n0 )
| ( less @ X8 @ n0 )
| ( less @ n0 @ X8 ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(281,plain,
( ( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 )
| ( less @ n0 @ p__0 ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(282,plain,
$true = $true,
inference(copy,[status(thm)],[219]) ).
thf(283,plain,
( ( ( plus @ n0 @ n1 )
= n1 )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(284,plain,
( ( ! [X33: $i] :
( ( X33 != p__0 )
| ( X33 = p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(285,plain,
( ( ! [X33: $i] :
( ( X33 != n1 )
| ( X33 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(286,plain,
( ( ! [X33: $i,X34: $i] :
( ( ( times @ X33 @ X34 )
!= p__0 )
| ( ( times @ X33 @ X34 )
= p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(287,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ! [X35: $i] :
( ! [X36: $i] :
( ( times @ X35 @ X36 )
!= X7 )
| ( X35 = n1 )
| ( X35 = X7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(288,plain,
$true = $true,
inference(copy,[status(thm)],[214]) ).
thf(289,plain,
$true = $true,
inference(copy,[status(thm)],[213]) ).
thf(290,plain,
( ( ! [X10: $i,X37: $i,X7: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X37 @ X7 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X37 @ X7 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(291,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( less @ n1 @ X7 ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(292,plain,
( ( ! [X10: $i] : ( X10 = n1 )
| $true )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(293,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ( X7 = p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(294,plain,
( ( ! [X7: $i] : ( X7 != p__0 )
| ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(295,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( times @ ( s_1 @ X10 ) @ ( s_4 @ X10 ) )
= X10 ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(296,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(297,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(298,plain,
( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(299,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(300,plain,
( ( ! [X10: $i] :
( ( X10 = n1 )
| ( ( s_1 @ X10 )
= p__0 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(301,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ! [X12: $i] :
( n1
!= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(302,plain,
( ( ! [X7: $i] :
( ( X7 != p__0 )
| ! [X12: $i] :
( ( plus @ n0 @ ( times @ X12 @ X7 ) )
= ( times @ X12 @ X7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(303,plain,
( ( ! [X10: $i,X38: $i] :
( ( X10
!= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) )
| ( X10
= ( plus @ n0 @ ( times @ X38 @ p__0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(304,plain,
$true = $true,
inference(copy,[status(thm)],[202]) ).
thf(305,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ! [X4: $i,X5: $i] :
( ( plus @ X2 @ ( times @ X4 @ X3 ) )
!= ( plus @ X1 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(306,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n0 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(307,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X3 @ X2 ) )
| ( X1 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(308,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ ( plus @ X1 @ X2 ) @ X3 )
= ( plus @ X1 @ ( plus @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(309,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( plus @ X1 @ ( plus @ X2 @ X3 ) )
= ( plus @ ( plus @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(310,plain,
( ( ! [X1: $i,X2: $i] :
( ( plus @ X1 @ X2 )
= ( plus @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(311,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( plus @ X1 @ X2 )
!= ( plus @ X1 @ X3 ) )
| ( X2 = X3 ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(312,plain,
( ( ! [X1: $i] :
( ( plus @ n0 @ X1 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(313,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X2 @ X1 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(314,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1
!= ( plus @ X1 @ X2 ) )
| ( X2 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(315,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( plus @ X1 @ X2 )
!= X1 )
| ( X2 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(316,plain,
( ( ! [X1: $i] :
( ! [X2: $i] :
( ( plus @ X1 @ X2 )
!= X2 )
| ( X1 = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(317,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1 != X2 )
| ! [X3: $i] :
( ( plus @ X3 @ X1 )
= ( plus @ X3 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(318,plain,
( ( ! [X1: $i] :
( ( plus @ n1 @ ( plus @ X1 @ n1 ) )
!= n1 ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(319,plain,
( ( ! [X1: $i,X2: $i] :
( ( times @ X1 @ X2 )
= ( times @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(320,plain,
( ( ! [X1: $i] :
( ( plus @ X1 @ n1 )
!= n0 ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(321,plain,
( ( ! [X1: $i] :
( ( times @ X1 @ n1 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(322,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ X1 @ ( times @ X2 @ X3 ) )
= ( times @ ( times @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(323,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( times @ ( times @ X1 @ X2 ) @ X3 )
= ( times @ X1 @ ( times @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(324,plain,
( ( ! [X1: $i] :
( ( times @ n1 @ X1 )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(325,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(326,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(327,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(328,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(329,plain,
( ( ! [X1: $i,X2: $i] :
( ( plus @ ( times @ X1 @ X2 ) @ X1 )
= ( times @ X1 @ ( plus @ X2 @ n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(330,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(331,plain,
( ( ! [X1: $i] :
( ! [X2: $i] :
( n1
!= ( times @ X1 @ X2 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(332,plain,
( ( ! [X2: $i,X1: $i] :
( ( n1
!= ( times @ X2 @ X1 ) )
| ( X1 = n1 ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(333,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( less @ X1 @ X2 )
| ~ ( less @ X1 @ X3 )
| ~ ( less @ X2 @ X3 )
| ! [X4: $i,X5: $i] :
( ( plus @ X1 @ ( times @ X4 @ X3 ) )
!= ( plus @ X2 @ ( times @ X5 @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(334,plain,
( ( ! [X1: $i] : ( less @ n0 @ ( plus @ X1 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(335,plain,
( ( ! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ( X1 != n1 ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(336,plain,
( ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( less @ X1 @ X2 )
| ( less @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(337,plain,
( ( ! [X1: $i] :
( ~ ( less @ n1 @ X1 )
| ! [X2: $i] :
( n1
!= ( times @ X2 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(338,plain,
( ( ! [X6: $i,X3: $i] :
( ~ ( less @ ( plus @ X6 @ n1 ) @ X3 )
| ( less @ X6 @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(339,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(340,plain,
! [SV1: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( SV1
!= ( plus @ SY171 @ ( times @ SY172 @ p__0 ) ) )
| ( SV1
= ( plus @ SY171 @ ( times @ SY172 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(341,plain,
! [SV2: $i] :
( ( ! [SY173: $i,SY174: $i] :
( ( plus @ SV2 @ ( plus @ ( plus @ ( times @ SY173 @ ( plus @ SY174 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ SY174 @ ( plus @ SV2 @ n1 ) ) ) @ n1 ) )
= ( plus @ SY173 @ ( times @ ( plus @ SY173 @ ( plus @ SV2 @ n1 ) ) @ ( plus @ SY174 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(342,plain,
! [SV3: $i] :
( ( ! [SY175: $i,SY176: $i] :
~ ( element @ ( plus @ SV3 @ ( plus @ SY175 @ n1 ) ) @ SY176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(343,plain,
! [SV4: $i] :
( ( ! [SY177: $i,SY178: $i,SY179: $i] :
( ( SV4
!= ( plus @ SY177 @ ( times @ SY178 @ ( plus @ SY179 @ n1 ) ) ) )
| ( SV4
= ( plus @ SY177 @ ( times @ SY178 @ ( plus @ SY179 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(344,plain,
! [SV5: $i] :
( ( ! [SY180: $i] :
( ( ( plus @ SV5 @ ( plus @ SY180 @ n1 ) )
!= n1 )
| ( ( plus @ SV5 @ ( plus @ SY180 @ n1 ) )
= n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(345,plain,
! [SV6: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i] :
( ( ( plus @ SV6 @ ( plus @ SY181 @ n1 ) )
!= ( plus @ SY182 @ ( times @ SY183 @ ( plus @ SY184 @ n1 ) ) ) )
| ( ( plus @ SV6 @ ( plus @ SY181 @ n1 ) )
= ( plus @ SY182 @ ( times @ SY183 @ ( plus @ SY184 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(346,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [X8: $i] :
( ( X8 != n0 )
| ( X8 = n0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(347,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [X7: $i] :
( ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(348,plain,
! [SV7: $i] :
( ( ! [SY185: $i] :
~ ( element @ SV7 @ SY185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(349,plain,
! [SV8: $i] :
( ( ! [SY186: $i] :
( ( SV8
!= ( plus @ n0 @ ( times @ SY186 @ p__0 ) ) )
| ( SV8
= ( plus @ n0 @ ( times @ SY186 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(350,plain,
! [SV9: $i] :
( ( ! [SY187: $i] :
( ~ ( less @ n0 @ p__0 )
| ! [SY188: $i,SY189: $i] :
( ( SV9
!= ( plus @ SY187 @ ( times @ ( plus @ SY188 @ SY189 ) @ p__0 ) ) )
| ( SV9
= ( plus @ SY187 @ ( times @ ( plus @ SY188 @ SY189 ) @ p__0 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(351,plain,
! [SV10: $i] :
( ( ! [SY190: $i,SY191: $i,SY192: $i] :
( ( SV10
!= ( plus @ SY190 @ ( times @ SY191 @ ( plus @ SY192 @ n1 ) ) ) )
| ( SV10
= ( plus @ SY190 @ ( times @ SY191 @ ( plus @ SY192 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(352,plain,
! [SV11: $i] :
( ( ~ ( less @ SV11 @ n0 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV11 @ p__0 )
| ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(353,plain,
! [SV12: $i] :
( ( ( SV12 != n1 )
| ( SV12 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(354,plain,
! [SV13: $i] :
( ( ( SV13 != n1 )
| ( SV13 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(355,plain,
! [SV14: $i] :
( ( ( SV14 != n1 )
| ( SV14 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(356,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(357,plain,
! [SV15: $i] :
( ( ( SV15 != n1 )
| ( SV15 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(358,plain,
! [SV16: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ( SV16
!= ( plus @ SY195 @ ( times @ SY196 @ ( plus @ SY197 @ n1 ) ) ) )
| ( SV16
= ( plus @ SY195 @ ( times @ SY196 @ ( plus @ SY197 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(359,plain,
! [SV17: $i] :
( ( ! [SY198: $i] :
( ( SV17
!= ( plus @ n0 @ ( times @ SY198 @ p__0 ) ) )
| ( SV17
= ( plus @ n0 @ ( times @ SY198 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(360,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [X7: $i] :
( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(361,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [X9: $i,X22: $i] :
( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(362,plain,
! [SV18: $i] :
( ( ~ ( less @ n0 @ SV18 )
| ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV18 @ p__0 )
| ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(363,plain,
! [SV19: $i] :
( ( ( ( plus @ n1 @ ( plus @ SV19 @ n1 ) )
!= n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(364,plain,
! [SV20: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ! [SY201: $i,SY202: $i] :
( ( plus @ ( plus @ SV20 @ ( times @ SY201 @ p__0 ) ) @ ( times @ SY202 @ p__0 ) )
= ( plus @ SV20 @ ( plus @ ( times @ SY201 @ p__0 ) @ ( times @ SY202 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(365,plain,
! [SV21: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ! [SY203: $i,SY204: $i] :
( ( SV21
!= ( plus @ SY203 @ ( times @ SY204 @ p__0 ) ) )
| ( SV21
= ( plus @ SY203 @ ( times @ SY204 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(366,plain,
! [SV22: $i] :
( ( ( SV22 != n1 )
| ( SV22 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(367,plain,
! [SV23: $i] :
( ( ( SV23 != n1 )
| ( SV23 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(368,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(369,plain,
! [SV24: $i] :
( ( ( SV24 != n1 )
| ( SV24 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(370,plain,
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [X7: $i] : ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(371,plain,
! [SV25: $i] :
( ( ( SV25 = n0 )
| ( less @ SV25 @ n0 )
| ( less @ n0 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(372,plain,
( ( ( ~ ( less @ ( plus @ n0 @ n1 ) @ p__0 ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(373,plain,
! [SV26: $i] :
( ( ( SV26 != p__0 )
| ( SV26 = p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(374,plain,
! [SV27: $i] :
( ( ( SV27 != n1 )
| ( SV27 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(375,plain,
! [SV28: $i] :
( ( ! [SY205: $i] :
( ( ( times @ SV28 @ SY205 )
!= p__0 )
| ( ( times @ SV28 @ SY205 )
= p__0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(376,plain,
! [SV29: $i] :
( ( ( SV29 != p__0 )
| ! [SY206: $i] :
( ! [SY207: $i] :
( ( times @ SY206 @ SY207 )
!= SV29 )
| ( SY206 = n1 )
| ( SY206 = SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(377,plain,
! [SV30: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ( SV30
!= ( plus @ n0 @ ( times @ SY208 @ SY209 ) ) )
| ( SV30
= ( plus @ n0 @ ( times @ SY208 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(378,plain,
! [SV31: $i] :
( ( ( SV31 != p__0 )
| ( less @ n1 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(379,plain,
( ( ( ! [X10: $i] : ( X10 = n1 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(380,plain,
! [SV32: $i] :
( ( ( SV32 != p__0 )
| ( SV32 = p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(381,plain,
( ( ( ! [X7: $i] : ( X7 != p__0 ) )
= $true )
| ( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(382,plain,
! [SV33: $i] :
( ( ( SV33 = n1 )
| ( ( times @ ( s_1 @ SV33 ) @ ( s_4 @ SV33 ) )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(383,plain,
! [SV34: $i] :
( ( ( SV34 != n1 )
| ( SV34 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(384,plain,
! [SV35: $i] :
( ( ( SV35 = n1 )
| ( ( times @ ( s_4 @ SV35 ) @ ( s_1 @ SV35 ) )
= ( times @ ( s_1 @ SV35 ) @ ( s_4 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(385,plain,
! [SV36: $i] :
( ( ( SV36 != n1 )
| ( SV36 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(386,plain,
! [SV37: $i] :
( ( ( SV37 = n1 )
| ( ( plus @ n0 @ ( times @ ( s_4 @ SV37 ) @ ( s_1 @ SV37 ) ) )
= ( times @ ( s_4 @ SV37 ) @ ( s_1 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(387,plain,
! [SV38: $i] :
( ( ( SV38 = n1 )
| ( ( s_1 @ SV38 )
= p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(388,plain,
! [SV39: $i] :
( ( ( SV39 != p__0 )
| ! [SY210: $i] :
( n1
!= ( times @ SY210 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(389,plain,
! [SV40: $i] :
( ( ( SV40 != p__0 )
| ! [SY211: $i] :
( ( plus @ n0 @ ( times @ SY211 @ SV40 ) )
= ( times @ SY211 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(390,plain,
! [SV41: $i] :
( ( ! [SY212: $i] :
( ( SV41
!= ( plus @ n0 @ ( times @ SY212 @ p__0 ) ) )
| ( SV41
= ( plus @ n0 @ ( times @ SY212 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(391,plain,
! [SV42: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ~ ( less @ SV42 @ SY213 )
| ~ ( less @ SV42 @ SY214 )
| ~ ( less @ SY213 @ SY214 )
| ! [SY215: $i,SY216: $i] :
( ( plus @ SY213 @ ( times @ SY215 @ SY214 ) )
!= ( plus @ SV42 @ ( times @ SY216 @ SY214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(392,plain,
! [SV43: $i] :
( ( ( plus @ SV43 @ n0 )
= SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(393,plain,
! [SV44: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ( ( plus @ SV44 @ SY217 )
!= ( plus @ SY218 @ SY217 ) )
| ( SV44 = SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(394,plain,
! [SV45: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ( plus @ ( plus @ SV45 @ SY219 ) @ SY220 )
= ( plus @ SV45 @ ( plus @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(395,plain,
! [SV46: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ( plus @ SV46 @ ( plus @ SY221 @ SY222 ) )
= ( plus @ ( plus @ SV46 @ SY221 ) @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(396,plain,
! [SV47: $i] :
( ( ! [SY223: $i] :
( ( plus @ SV47 @ SY223 )
= ( plus @ SY223 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(397,plain,
! [SV48: $i] :
( ( ! [SY224: $i,SY225: $i] :
( ( ( plus @ SV48 @ SY224 )
!= ( plus @ SV48 @ SY225 ) )
| ( SY224 = SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(398,plain,
! [SV49: $i] :
( ( ( plus @ n0 @ SV49 )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(399,plain,
! [SV50: $i] :
( ( ! [SY226: $i] :
( ( SV50
!= ( plus @ SY226 @ SV50 ) )
| ( SY226 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(400,plain,
! [SV51: $i] :
( ( ! [SY227: $i] :
( ( SV51
!= ( plus @ SV51 @ SY227 ) )
| ( SY227 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(401,plain,
! [SV52: $i] :
( ( ! [SY228: $i] :
( ( ( plus @ SV52 @ SY228 )
!= SV52 )
| ( SY228 = n0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(402,plain,
! [SV53: $i] :
( ( ! [SY229: $i] :
( ( plus @ SV53 @ SY229 )
!= SY229 )
| ( SV53 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(403,plain,
! [SV54: $i] :
( ( ! [SY230: $i] :
( ( SV54 != SY230 )
| ! [SY231: $i] :
( ( plus @ SY231 @ SV54 )
= ( plus @ SY231 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(404,plain,
! [SV55: $i] :
( ( ( ( plus @ n1 @ ( plus @ SV55 @ n1 ) )
!= n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(405,plain,
! [SV56: $i] :
( ( ! [SY232: $i] :
( ( times @ SV56 @ SY232 )
= ( times @ SY232 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(406,plain,
! [SV57: $i] :
( ( ( ( plus @ SV57 @ n1 )
!= n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(407,plain,
! [SV58: $i] :
( ( ( times @ SV58 @ n1 )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(408,plain,
! [SV59: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ( times @ SV59 @ ( times @ SY233 @ SY234 ) )
= ( times @ ( times @ SV59 @ SY233 ) @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(409,plain,
! [SV60: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ( times @ ( times @ SV60 @ SY235 ) @ SY236 )
= ( times @ SV60 @ ( times @ SY235 @ SY236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(410,plain,
! [SV61: $i] :
( ( ( times @ n1 @ SV61 )
= SV61 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(411,plain,
! [SV62: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ( times @ SV62 @ ( plus @ SY237 @ SY238 ) )
= ( plus @ ( times @ SV62 @ SY237 ) @ ( times @ SV62 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(412,plain,
! [SV63: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( plus @ ( times @ SV63 @ SY239 ) @ ( times @ SV63 @ SY240 ) )
= ( times @ SV63 @ ( plus @ SY240 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(413,plain,
! [SV64: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ( times @ ( plus @ SV64 @ SY241 ) @ SY242 )
= ( plus @ ( times @ SV64 @ SY242 ) @ ( times @ SY241 @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(414,plain,
! [SV65: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ( plus @ ( times @ SV65 @ SY243 ) @ ( times @ SY244 @ SY243 ) )
= ( times @ ( plus @ SV65 @ SY244 ) @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(415,plain,
! [SV66: $i] :
( ( ! [SY245: $i] :
( ( plus @ ( times @ SV66 @ SY245 ) @ SV66 )
= ( times @ SV66 @ ( plus @ SY245 @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(416,plain,
! [SV67: $i] :
( ( ! [SY246: $i,SY247: $i] :
( ( times @ ( plus @ SV67 @ SY246 ) @ SY247 )
= ( plus @ ( times @ SY246 @ SY247 ) @ ( times @ SV67 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(417,plain,
! [SV68: $i] :
( ( ! [SY248: $i] :
( n1
!= ( times @ SV68 @ SY248 ) )
| ( SV68 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(418,plain,
! [SV69: $i] :
( ( ! [SY249: $i] :
( ( n1
!= ( times @ SV69 @ SY249 ) )
| ( SY249 = n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(419,plain,
! [SV70: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( less @ SV70 @ SY250 )
| ~ ( less @ SV70 @ SY251 )
| ~ ( less @ SY250 @ SY251 )
| ! [SY252: $i,SY253: $i] :
( ( plus @ SV70 @ ( times @ SY252 @ SY251 ) )
!= ( plus @ SY250 @ ( times @ SY253 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(420,plain,
! [SV71: $i] :
( ( less @ n0 @ ( plus @ SV71 @ n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(421,plain,
! [SV72: $i] :
( ( ~ ( less @ n1 @ SV72 )
| ( SV72 != n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(422,plain,
! [SV73: $i] :
( ( ! [SY254: $i] :
( ( SV73 = SY254 )
| ( less @ SV73 @ SY254 )
| ( less @ SY254 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(423,plain,
! [SV74: $i] :
( ( ~ ( less @ n1 @ SV74 )
| ! [SY255: $i] :
( n1
!= ( times @ SY255 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(424,plain,
! [SV75: $i] :
( ( ! [SY256: $i] :
( ~ ( less @ ( plus @ SV75 @ n1 ) @ SY256 )
| ( less @ SV75 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(425,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(426,plain,
! [SV76: $i,SV1: $i] :
( ( ! [SY257: $i] :
( ( SV1
!= ( plus @ SV76 @ ( times @ SY257 @ p__0 ) ) )
| ( SV1
= ( plus @ SV76 @ ( times @ SY257 @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(427,plain,
! [SV77: $i,SV2: $i] :
( ( ! [SY258: $i] :
( ( plus @ SV2 @ ( plus @ ( plus @ ( times @ SV77 @ ( plus @ SY258 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ SY258 @ ( plus @ SV2 @ n1 ) ) ) @ n1 ) )
= ( plus @ SV77 @ ( times @ ( plus @ SV77 @ ( plus @ SV2 @ n1 ) ) @ ( plus @ SY258 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(428,plain,
! [SV78: $i,SV3: $i] :
( ( ! [SY259: $i] :
~ ( element @ ( plus @ SV3 @ ( plus @ SV78 @ n1 ) ) @ SY259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(429,plain,
! [SV79: $i,SV4: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ( SV4
!= ( plus @ SV79 @ ( times @ SY260 @ ( plus @ SY261 @ n1 ) ) ) )
| ( SV4
= ( plus @ SV79 @ ( times @ SY260 @ ( plus @ SY261 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(430,plain,
! [SV80: $i,SV5: $i] :
( ( ( ( plus @ SV5 @ ( plus @ SV80 @ n1 ) )
!= n1 )
| ( ( plus @ SV5 @ ( plus @ SV80 @ n1 ) )
= n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(431,plain,
! [SV81: $i,SV6: $i] :
( ( ! [SY262: $i,SY263: $i,SY264: $i] :
( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
!= ( plus @ SY262 @ ( times @ SY263 @ ( plus @ SY264 @ n1 ) ) ) )
| ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SY262 @ ( times @ SY263 @ ( plus @ SY264 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(432,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [X8: $i] :
( ( X8 != n0 )
| ( X8 = n0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(433,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [X7: $i] :
( ( ( s_5 @ p__0 @ X7 )
!= n0 )
| ( X7
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(434,plain,
! [SV82: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(435,plain,
! [SV83: $i,SV8: $i] :
( ( ( SV8
!= ( plus @ n0 @ ( times @ SV83 @ p__0 ) ) )
| ( SV8
= ( plus @ n0 @ ( times @ SV83 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(436,plain,
! [SV84: $i,SV9: $i] :
( ( ~ ( less @ n0 @ p__0 )
| ! [SY265: $i,SY266: $i] :
( ( SV9
!= ( plus @ SV84 @ ( times @ ( plus @ SY265 @ SY266 ) @ p__0 ) ) )
| ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SY265 @ SY266 ) @ p__0 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(437,plain,
! [SV85: $i,SV10: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ( SV10
!= ( plus @ SV85 @ ( times @ SY267 @ ( plus @ SY268 @ n1 ) ) ) )
| ( SV10
= ( plus @ SV85 @ ( times @ SY267 @ ( plus @ SY268 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(438,plain,
! [SV11: $i] :
( ( ( ~ ( less @ SV11 @ n0 ) )
= $true )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV11 @ p__0 )
| ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(439,plain,
! [SV12: $i] :
( ( ( ( SV12 != n1 ) )
= $true )
| ( ( SV12 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(440,plain,
! [SV13: $i] :
( ( ( ( SV13 != n1 ) )
= $true )
| ( ( SV13 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(441,plain,
! [SV14: $i] :
( ( ( ( SV14 != n1 ) )
= $true )
| ( ( SV14 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(442,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( p__0
= ( plus @ ( s_7 @ p__0 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(443,plain,
! [SV15: $i] :
( ( ( ( SV15 != n1 ) )
= $true )
| ( ( SV15 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(444,plain,
! [SV86: $i,SV16: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ( SV16
!= ( plus @ SV86 @ ( times @ SY269 @ ( plus @ SY270 @ n1 ) ) ) )
| ( SV16
= ( plus @ SV86 @ ( times @ SY269 @ ( plus @ SY270 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(445,plain,
! [SV87: $i,SV17: $i] :
( ( ( SV17
!= ( plus @ n0 @ ( times @ SV87 @ p__0 ) ) )
| ( SV17
= ( plus @ n0 @ ( times @ SV87 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(446,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [X7: $i] :
( X7
= ( plus @ ( s_5 @ p__0 @ X7 ) @ ( times @ ( s_6 @ p__0 @ X7 ) @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(447,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [X9: $i,X22: $i] :
( ( plus @ ( times @ X9 @ p__0 ) @ ( times @ X22 @ p__0 ) )
= ( times @ ( plus @ X9 @ X22 ) @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(448,plain,
! [SV18: $i] :
( ( ( ~ ( less @ n0 @ SV18 ) )
= $true )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV18 @ p__0 )
| ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(449,plain,
! [SV19: $i] :
( ( ( plus @ n1 @ ( plus @ SV19 @ n1 ) )
= n1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(450,plain,
! [SV20: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [SY201: $i,SY202: $i] :
( ( plus @ ( plus @ SV20 @ ( times @ SY201 @ p__0 ) ) @ ( times @ SY202 @ p__0 ) )
= ( plus @ SV20 @ ( plus @ ( times @ SY201 @ p__0 ) @ ( times @ SY202 @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(451,plain,
! [SV21: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [SY203: $i,SY204: $i] :
( ( SV21
!= ( plus @ SY203 @ ( times @ SY204 @ p__0 ) ) )
| ( SV21
= ( plus @ SY203 @ ( times @ SY204 @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(452,plain,
! [SV22: $i] :
( ( ( ( SV22 != n1 ) )
= $true )
| ( ( SV22 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(453,plain,
! [SV23: $i] :
( ( ( ( SV23 != n1 ) )
= $true )
| ( ( SV23 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(454,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(455,plain,
! [SV24: $i] :
( ( ( ( SV24 != n1 ) )
= $true )
| ( ( SV24 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(456,plain,
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [X7: $i] : ( less @ ( s_5 @ p__0 @ X7 ) @ p__0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(457,plain,
! [SV25: $i] :
( ( ( SV25 = n0 )
= $true )
| ( ( ( less @ SV25 @ n0 )
| ( less @ n0 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(458,plain,
( ( ( less @ ( plus @ n0 @ n1 ) @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(459,plain,
! [SV26: $i] :
( ( ( ( SV26 != p__0 ) )
= $true )
| ( ( SV26 = p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(460,plain,
! [SV27: $i] :
( ( ( ( SV27 != n1 ) )
= $true )
| ( ( SV27 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(461,plain,
! [SV88: $i,SV28: $i] :
( ( ( ( times @ SV28 @ SV88 )
!= p__0 )
| ( ( times @ SV28 @ SV88 )
= p__0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(462,plain,
! [SV29: $i] :
( ( ( ( SV29 != p__0 ) )
= $true )
| ( ( ! [SY206: $i] :
( ! [SY207: $i] :
( ( times @ SY206 @ SY207 )
!= SV29 )
| ( SY206 = n1 )
| ( SY206 = SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(463,plain,
! [SV89: $i,SV30: $i] :
( ( ! [SY271: $i] :
( ( SV30
!= ( plus @ n0 @ ( times @ SV89 @ SY271 ) ) )
| ( SV30
= ( plus @ n0 @ ( times @ SV89 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(464,plain,
! [SV31: $i] :
( ( ( ( SV31 != p__0 ) )
= $true )
| ( ( less @ n1 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(465,plain,
! [SV90: $i] :
( ( ( SV90 = n1 )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(466,plain,
! [SV32: $i] :
( ( ( ( SV32 != p__0 ) )
= $true )
| ( ( SV32 = p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(467,plain,
! [SV91: $i] :
( ( ( ( SV91 != p__0 ) )
= $true )
| ( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(468,plain,
! [SV33: $i] :
( ( ( SV33 = n1 )
= $true )
| ( ( ( times @ ( s_1 @ SV33 ) @ ( s_4 @ SV33 ) )
= SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(469,plain,
! [SV34: $i] :
( ( ( ( SV34 != n1 ) )
= $true )
| ( ( SV34 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(470,plain,
! [SV35: $i] :
( ( ( SV35 = n1 )
= $true )
| ( ( ( times @ ( s_4 @ SV35 ) @ ( s_1 @ SV35 ) )
= ( times @ ( s_1 @ SV35 ) @ ( s_4 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(471,plain,
! [SV36: $i] :
( ( ( ( SV36 != n1 ) )
= $true )
| ( ( SV36 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(472,plain,
! [SV37: $i] :
( ( ( SV37 = n1 )
= $true )
| ( ( ( plus @ n0 @ ( times @ ( s_4 @ SV37 ) @ ( s_1 @ SV37 ) ) )
= ( times @ ( s_4 @ SV37 ) @ ( s_1 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(473,plain,
! [SV38: $i] :
( ( ( SV38 = n1 )
= $true )
| ( ( ( s_1 @ SV38 )
= p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(474,plain,
! [SV39: $i] :
( ( ( ( SV39 != p__0 ) )
= $true )
| ( ( ! [SY210: $i] :
( n1
!= ( times @ SY210 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(475,plain,
! [SV40: $i] :
( ( ( ( SV40 != p__0 ) )
= $true )
| ( ( ! [SY211: $i] :
( ( plus @ n0 @ ( times @ SY211 @ SV40 ) )
= ( times @ SY211 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(476,plain,
! [SV92: $i,SV41: $i] :
( ( ( SV41
!= ( plus @ n0 @ ( times @ SV92 @ p__0 ) ) )
| ( SV41
= ( plus @ n0 @ ( times @ SV92 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(477,plain,
! [SV93: $i,SV42: $i] :
( ( ! [SY272: $i] :
( ~ ( less @ SV42 @ SV93 )
| ~ ( less @ SV42 @ SY272 )
| ~ ( less @ SV93 @ SY272 )
| ! [SY273: $i,SY274: $i] :
( ( plus @ SV93 @ ( times @ SY273 @ SY272 ) )
!= ( plus @ SV42 @ ( times @ SY274 @ SY272 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(478,plain,
! [SV94: $i,SV44: $i] :
( ( ! [SY275: $i] :
( ( ( plus @ SV44 @ SV94 )
!= ( plus @ SY275 @ SV94 ) )
| ( SV44 = SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(479,plain,
! [SV95: $i,SV45: $i] :
( ( ! [SY276: $i] :
( ( plus @ ( plus @ SV45 @ SV95 ) @ SY276 )
= ( plus @ SV45 @ ( plus @ SV95 @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(480,plain,
! [SV96: $i,SV46: $i] :
( ( ! [SY277: $i] :
( ( plus @ SV46 @ ( plus @ SV96 @ SY277 ) )
= ( plus @ ( plus @ SV46 @ SV96 ) @ SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(481,plain,
! [SV97: $i,SV47: $i] :
( ( ( plus @ SV47 @ SV97 )
= ( plus @ SV97 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(482,plain,
! [SV98: $i,SV48: $i] :
( ( ! [SY278: $i] :
( ( ( plus @ SV48 @ SV98 )
!= ( plus @ SV48 @ SY278 ) )
| ( SV98 = SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(483,plain,
! [SV99: $i,SV50: $i] :
( ( ( SV50
!= ( plus @ SV99 @ SV50 ) )
| ( SV99 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(484,plain,
! [SV100: $i,SV51: $i] :
( ( ( SV51
!= ( plus @ SV51 @ SV100 ) )
| ( SV100 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(485,plain,
! [SV101: $i,SV52: $i] :
( ( ( ( plus @ SV52 @ SV101 )
!= SV52 )
| ( SV101 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(486,plain,
! [SV53: $i] :
( ( ( ! [SY229: $i] :
( ( plus @ SV53 @ SY229 )
!= SY229 ) )
= $true )
| ( ( SV53 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(487,plain,
! [SV102: $i,SV54: $i] :
( ( ( SV54 != SV102 )
| ! [SY279: $i] :
( ( plus @ SY279 @ SV54 )
= ( plus @ SY279 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(488,plain,
! [SV55: $i] :
( ( ( plus @ n1 @ ( plus @ SV55 @ n1 ) )
= n1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(489,plain,
! [SV103: $i,SV56: $i] :
( ( ( times @ SV56 @ SV103 )
= ( times @ SV103 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(490,plain,
! [SV57: $i] :
( ( ( plus @ SV57 @ n1 )
= n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(491,plain,
! [SV104: $i,SV59: $i] :
( ( ! [SY280: $i] :
( ( times @ SV59 @ ( times @ SV104 @ SY280 ) )
= ( times @ ( times @ SV59 @ SV104 ) @ SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(492,plain,
! [SV105: $i,SV60: $i] :
( ( ! [SY281: $i] :
( ( times @ ( times @ SV60 @ SV105 ) @ SY281 )
= ( times @ SV60 @ ( times @ SV105 @ SY281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(493,plain,
! [SV106: $i,SV62: $i] :
( ( ! [SY282: $i] :
( ( times @ SV62 @ ( plus @ SV106 @ SY282 ) )
= ( plus @ ( times @ SV62 @ SV106 ) @ ( times @ SV62 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(494,plain,
! [SV107: $i,SV63: $i] :
( ( ! [SY283: $i] :
( ( plus @ ( times @ SV63 @ SV107 ) @ ( times @ SV63 @ SY283 ) )
= ( times @ SV63 @ ( plus @ SY283 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(495,plain,
! [SV108: $i,SV64: $i] :
( ( ! [SY284: $i] :
( ( times @ ( plus @ SV64 @ SV108 ) @ SY284 )
= ( plus @ ( times @ SV64 @ SY284 ) @ ( times @ SV108 @ SY284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(496,plain,
! [SV109: $i,SV65: $i] :
( ( ! [SY285: $i] :
( ( plus @ ( times @ SV65 @ SV109 ) @ ( times @ SY285 @ SV109 ) )
= ( times @ ( plus @ SV65 @ SY285 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(497,plain,
! [SV110: $i,SV66: $i] :
( ( ( plus @ ( times @ SV66 @ SV110 ) @ SV66 )
= ( times @ SV66 @ ( plus @ SV110 @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(498,plain,
! [SV111: $i,SV67: $i] :
( ( ! [SY286: $i] :
( ( times @ ( plus @ SV67 @ SV111 ) @ SY286 )
= ( plus @ ( times @ SV111 @ SY286 ) @ ( times @ SV67 @ SY286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(499,plain,
! [SV68: $i] :
( ( ( ! [SY248: $i] :
( n1
!= ( times @ SV68 @ SY248 ) ) )
= $true )
| ( ( SV68 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(500,plain,
! [SV112: $i,SV69: $i] :
( ( ( n1
!= ( times @ SV69 @ SV112 ) )
| ( SV112 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(501,plain,
! [SV113: $i,SV70: $i] :
( ( ! [SY287: $i] :
( ~ ( less @ SV70 @ SV113 )
| ~ ( less @ SV70 @ SY287 )
| ~ ( less @ SV113 @ SY287 )
| ! [SY288: $i,SY289: $i] :
( ( plus @ SV70 @ ( times @ SY288 @ SY287 ) )
!= ( plus @ SV113 @ ( times @ SY289 @ SY287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(502,plain,
! [SV72: $i] :
( ( ( ~ ( less @ n1 @ SV72 ) )
= $true )
| ( ( ( SV72 != n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(503,plain,
! [SV114: $i,SV73: $i] :
( ( ( SV73 = SV114 )
| ( less @ SV73 @ SV114 )
| ( less @ SV114 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(504,plain,
! [SV74: $i] :
( ( ( ~ ( less @ n1 @ SV74 ) )
= $true )
| ( ( ! [SY255: $i] :
( n1
!= ( times @ SY255 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(505,plain,
! [SV115: $i,SV75: $i] :
( ( ~ ( less @ ( plus @ SV75 @ n1 ) @ SV115 )
| ( less @ SV75 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(506,plain,
! [SV116: $i,SV76: $i,SV1: $i] :
( ( ( SV1
!= ( plus @ SV76 @ ( times @ SV116 @ p__0 ) ) )
| ( SV1
= ( plus @ SV76 @ ( times @ SV116 @ p__0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(507,plain,
! [SV117: $i,SV77: $i,SV2: $i] :
( ( ( plus @ SV2 @ ( plus @ ( plus @ ( times @ SV77 @ ( plus @ SV117 @ ( plus @ n1 @ n1 ) ) ) @ ( times @ SV117 @ ( plus @ SV2 @ n1 ) ) ) @ n1 ) )
= ( plus @ SV77 @ ( times @ ( plus @ SV77 @ ( plus @ SV2 @ n1 ) ) @ ( plus @ SV117 @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(508,plain,
! [SV118: $i,SV78: $i,SV3: $i] :
( ( ~ ( element @ ( plus @ SV3 @ ( plus @ SV78 @ n1 ) ) @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(509,plain,
! [SV119: $i,SV79: $i,SV4: $i] :
( ( ! [SY290: $i] :
( ( SV4
!= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SY290 @ n1 ) ) ) )
| ( SV4
= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SY290 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(510,plain,
! [SV80: $i,SV5: $i] :
( ( ( ( ( plus @ SV5 @ ( plus @ SV80 @ n1 ) )
!= n1 ) )
= $true )
| ( ( ( plus @ SV5 @ ( plus @ SV80 @ n1 ) )
= n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(511,plain,
! [SV120: $i,SV81: $i,SV6: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
!= ( plus @ SV120 @ ( times @ SY291 @ ( plus @ SY292 @ n1 ) ) ) )
| ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SV120 @ ( times @ SY291 @ ( plus @ SY292 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(512,plain,
! [SV121: $i] :
( ( ( ( SV121 != n0 )
| ( SV121 = n0 ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(513,plain,
! [SV122: $i] :
( ( ( ( ( s_5 @ p__0 @ SV122 )
!= n0 )
| ( SV122
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV122 ) @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(514,plain,
! [SV82: $i,SV7: $i] :
( ( element @ SV7 @ SV82 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(515,plain,
! [SV83: $i,SV8: $i] :
( ( ( ( SV8
!= ( plus @ n0 @ ( times @ SV83 @ p__0 ) ) ) )
= $true )
| ( ( SV8
= ( plus @ n0 @ ( times @ SV83 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(516,plain,
! [SV84: $i,SV9: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ! [SY265: $i,SY266: $i] :
( ( SV9
!= ( plus @ SV84 @ ( times @ ( plus @ SY265 @ SY266 ) @ p__0 ) ) )
| ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SY265 @ SY266 ) @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(517,plain,
! [SV123: $i,SV85: $i,SV10: $i] :
( ( ! [SY293: $i] :
( ( SV10
!= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SY293 @ n1 ) ) ) )
| ( SV10
= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SY293 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(518,plain,
! [SV11: $i] :
( ( ( less @ SV11 @ n0 )
= $false )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV11 @ p__0 )
| ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(519,plain,
! [SV12: $i] :
( ( ( SV12 = n1 )
= $false )
| ( ( SV12 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(520,plain,
! [SV13: $i] :
( ( ( SV13 = n1 )
= $false )
| ( ( SV13 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(521,plain,
! [SV14: $i] :
( ( ( SV14 = n1 )
= $false )
| ( ( SV14 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(522,plain,
! [SV15: $i] :
( ( ( SV15 = n1 )
= $false )
| ( ( SV15 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(523,plain,
! [SV124: $i,SV86: $i,SV16: $i] :
( ( ! [SY294: $i] :
( ( SV16
!= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SY294 @ n1 ) ) ) )
| ( SV16
= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SY294 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(524,plain,
! [SV87: $i,SV17: $i] :
( ( ( ( SV17
!= ( plus @ n0 @ ( times @ SV87 @ p__0 ) ) ) )
= $true )
| ( ( SV17
= ( plus @ n0 @ ( times @ SV87 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(525,plain,
! [SV125: $i] :
( ( ( SV125
= ( plus @ ( s_5 @ p__0 @ SV125 ) @ ( times @ ( s_6 @ p__0 @ SV125 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(526,plain,
! [SV126: $i] :
( ( ( ! [SY295: $i] :
( ( plus @ ( times @ SV126 @ p__0 ) @ ( times @ SY295 @ p__0 ) )
= ( times @ ( plus @ SV126 @ SY295 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(527,plain,
! [SV18: $i] :
( ( ( less @ n0 @ SV18 )
= $false )
| ( ( ~ ( less @ n0 @ p__0 )
| ~ ( less @ SV18 @ p__0 )
| ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(528,plain,
! [SV20: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [SY201: $i,SY202: $i] :
( ( plus @ ( plus @ SV20 @ ( times @ SY201 @ p__0 ) ) @ ( times @ SY202 @ p__0 ) )
= ( plus @ SV20 @ ( plus @ ( times @ SY201 @ p__0 ) @ ( times @ SY202 @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(529,plain,
! [SV21: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [SY203: $i,SY204: $i] :
( ( SV21
!= ( plus @ SY203 @ ( times @ SY204 @ p__0 ) ) )
| ( SV21
= ( plus @ SY203 @ ( times @ SY204 @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(530,plain,
! [SV22: $i] :
( ( ( SV22 = n1 )
= $false )
| ( ( SV22 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(531,plain,
! [SV23: $i] :
( ( ( SV23 = n1 )
= $false )
| ( ( SV23 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(532,plain,
! [SV24: $i] :
( ( ( SV24 = n1 )
= $false )
| ( ( SV24 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(533,plain,
! [SV127: $i] :
( ( ( less @ ( s_5 @ p__0 @ SV127 ) @ p__0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(534,plain,
! [SV25: $i] :
( ( ( less @ SV25 @ n0 )
= $true )
| ( ( less @ n0 @ SV25 )
= $true )
| ( ( SV25 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(535,plain,
! [SV26: $i] :
( ( ( SV26 = p__0 )
= $false )
| ( ( SV26 = p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(536,plain,
! [SV27: $i] :
( ( ( SV27 = n1 )
= $false )
| ( ( SV27 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(537,plain,
! [SV88: $i,SV28: $i] :
( ( ( ( ( times @ SV28 @ SV88 )
!= p__0 ) )
= $true )
| ( ( ( times @ SV28 @ SV88 )
= p__0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(538,plain,
! [SV29: $i] :
( ( ( SV29 = p__0 )
= $false )
| ( ( ! [SY206: $i] :
( ! [SY207: $i] :
( ( times @ SY206 @ SY207 )
!= SV29 )
| ( SY206 = n1 )
| ( SY206 = SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(539,plain,
! [SV128: $i,SV89: $i,SV30: $i] :
( ( ( SV30
!= ( plus @ n0 @ ( times @ SV89 @ SV128 ) ) )
| ( SV30
= ( plus @ n0 @ ( times @ SV89 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(540,plain,
! [SV31: $i] :
( ( ( SV31 = p__0 )
= $false )
| ( ( less @ n1 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(541,plain,
! [SV32: $i] :
( ( ( SV32 = p__0 )
= $false )
| ( ( SV32 = p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(542,plain,
! [SV91: $i] :
( ( ( SV91 = p__0 )
= $false )
| ( ( ! [X10: $i] :
( ( X10 != n1 )
| ( X10 = n1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(543,plain,
! [SV34: $i] :
( ( ( SV34 = n1 )
= $false )
| ( ( SV34 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(544,plain,
! [SV36: $i] :
( ( ( SV36 = n1 )
= $false )
| ( ( SV36 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(545,plain,
! [SV39: $i] :
( ( ( SV39 = p__0 )
= $false )
| ( ( ! [SY210: $i] :
( n1
!= ( times @ SY210 @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(546,plain,
! [SV40: $i] :
( ( ( SV40 = p__0 )
= $false )
| ( ( ! [SY211: $i] :
( ( plus @ n0 @ ( times @ SY211 @ SV40 ) )
= ( times @ SY211 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(547,plain,
! [SV92: $i,SV41: $i] :
( ( ( ( SV41
!= ( plus @ n0 @ ( times @ SV92 @ p__0 ) ) ) )
= $true )
| ( ( SV41
= ( plus @ n0 @ ( times @ SV92 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(548,plain,
! [SV129: $i,SV93: $i,SV42: $i] :
( ( ~ ( less @ SV42 @ SV93 )
| ~ ( less @ SV42 @ SV129 )
| ~ ( less @ SV93 @ SV129 )
| ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(549,plain,
! [SV130: $i,SV94: $i,SV44: $i] :
( ( ( ( plus @ SV44 @ SV94 )
!= ( plus @ SV130 @ SV94 ) )
| ( SV44 = SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(550,plain,
! [SV131: $i,SV95: $i,SV45: $i] :
( ( ( plus @ ( plus @ SV45 @ SV95 ) @ SV131 )
= ( plus @ SV45 @ ( plus @ SV95 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(551,plain,
! [SV132: $i,SV96: $i,SV46: $i] :
( ( ( plus @ SV46 @ ( plus @ SV96 @ SV132 ) )
= ( plus @ ( plus @ SV46 @ SV96 ) @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(552,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ( ( plus @ SV48 @ SV98 )
!= ( plus @ SV48 @ SV133 ) )
| ( SV98 = SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(553,plain,
! [SV99: $i,SV50: $i] :
( ( ( ( SV50
!= ( plus @ SV99 @ SV50 ) ) )
= $true )
| ( ( SV99 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(554,plain,
! [SV100: $i,SV51: $i] :
( ( ( ( SV51
!= ( plus @ SV51 @ SV100 ) ) )
= $true )
| ( ( SV100 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(555,plain,
! [SV101: $i,SV52: $i] :
( ( ( ( ( plus @ SV52 @ SV101 )
!= SV52 ) )
= $true )
| ( ( SV101 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(556,plain,
! [SV134: $i,SV53: $i] :
( ( ( ( ( plus @ SV53 @ SV134 )
!= SV134 ) )
= $true )
| ( ( SV53 = n0 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(557,plain,
! [SV102: $i,SV54: $i] :
( ( ( ( SV54 != SV102 ) )
= $true )
| ( ( ! [SY279: $i] :
( ( plus @ SY279 @ SV54 )
= ( plus @ SY279 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(558,plain,
! [SV135: $i,SV104: $i,SV59: $i] :
( ( ( times @ SV59 @ ( times @ SV104 @ SV135 ) )
= ( times @ ( times @ SV59 @ SV104 ) @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(559,plain,
! [SV136: $i,SV105: $i,SV60: $i] :
( ( ( times @ ( times @ SV60 @ SV105 ) @ SV136 )
= ( times @ SV60 @ ( times @ SV105 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(560,plain,
! [SV137: $i,SV106: $i,SV62: $i] :
( ( ( times @ SV62 @ ( plus @ SV106 @ SV137 ) )
= ( plus @ ( times @ SV62 @ SV106 ) @ ( times @ SV62 @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(561,plain,
! [SV138: $i,SV107: $i,SV63: $i] :
( ( ( plus @ ( times @ SV63 @ SV107 ) @ ( times @ SV63 @ SV138 ) )
= ( times @ SV63 @ ( plus @ SV138 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(562,plain,
! [SV139: $i,SV108: $i,SV64: $i] :
( ( ( times @ ( plus @ SV64 @ SV108 ) @ SV139 )
= ( plus @ ( times @ SV64 @ SV139 ) @ ( times @ SV108 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(563,plain,
! [SV140: $i,SV109: $i,SV65: $i] :
( ( ( plus @ ( times @ SV65 @ SV109 ) @ ( times @ SV140 @ SV109 ) )
= ( times @ ( plus @ SV65 @ SV140 ) @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(564,plain,
! [SV141: $i,SV111: $i,SV67: $i] :
( ( ( times @ ( plus @ SV67 @ SV111 ) @ SV141 )
= ( plus @ ( times @ SV111 @ SV141 ) @ ( times @ SV67 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(565,plain,
! [SV142: $i,SV68: $i] :
( ( ( ( n1
!= ( times @ SV68 @ SV142 ) ) )
= $true )
| ( ( SV68 = n1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(566,plain,
! [SV112: $i,SV69: $i] :
( ( ( ( n1
!= ( times @ SV69 @ SV112 ) ) )
= $true )
| ( ( SV112 = n1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(567,plain,
! [SV143: $i,SV113: $i,SV70: $i] :
( ( ~ ( less @ SV70 @ SV113 )
| ~ ( less @ SV70 @ SV143 )
| ~ ( less @ SV113 @ SV143 )
| ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(568,plain,
! [SV72: $i] :
( ( ( less @ n1 @ SV72 )
= $false )
| ( ( ( SV72 != n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(569,plain,
! [SV114: $i,SV73: $i] :
( ( ( SV73 = SV114 )
= $true )
| ( ( ( less @ SV73 @ SV114 )
| ( less @ SV114 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(570,plain,
! [SV74: $i] :
( ( ( less @ n1 @ SV74 )
= $false )
| ( ( ! [SY255: $i] :
( n1
!= ( times @ SY255 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(571,plain,
! [SV115: $i,SV75: $i] :
( ( ( ~ ( less @ ( plus @ SV75 @ n1 ) @ SV115 ) )
= $true )
| ( ( less @ SV75 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(572,plain,
! [SV116: $i,SV76: $i,SV1: $i] :
( ( ( ( SV1
!= ( plus @ SV76 @ ( times @ SV116 @ p__0 ) ) ) )
= $true )
| ( ( SV1
= ( plus @ SV76 @ ( times @ SV116 @ p__0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(573,plain,
! [SV118: $i,SV78: $i,SV3: $i] :
( ( element @ ( plus @ SV3 @ ( plus @ SV78 @ n1 ) ) @ SV118 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(574,plain,
! [SV144: $i,SV119: $i,SV79: $i,SV4: $i] :
( ( ( SV4
!= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SV144 @ n1 ) ) ) )
| ( SV4
= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SV144 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(575,plain,
! [SV80: $i,SV5: $i] :
( ( ( ( plus @ SV5 @ ( plus @ SV80 @ n1 ) )
= n1 )
= $false )
| ( ( ( plus @ SV5 @ ( plus @ SV80 @ n1 ) )
= n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(576,plain,
! [SV145: $i,SV120: $i,SV81: $i,SV6: $i] :
( ( ! [SY300: $i] :
( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
!= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SY300 @ n1 ) ) ) )
| ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SY300 @ n1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(577,plain,
! [SV121: $i] :
( ( ( ( SV121 != n0 ) )
= $true )
| ( ( SV121 = n0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(578,plain,
! [SV122: $i] :
( ( ( ( ( s_5 @ p__0 @ SV122 )
!= n0 ) )
= $true )
| ( ( SV122
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV122 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(579,plain,
! [SV83: $i,SV8: $i] :
( ( ( SV8
= ( plus @ n0 @ ( times @ SV83 @ p__0 ) ) )
= $false )
| ( ( SV8
= ( plus @ n0 @ ( times @ SV83 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(580,plain,
! [SV84: $i,SV9: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ! [SY265: $i,SY266: $i] :
( ( SV9
!= ( plus @ SV84 @ ( times @ ( plus @ SY265 @ SY266 ) @ p__0 ) ) )
| ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SY265 @ SY266 ) @ p__0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(581,plain,
! [SV146: $i,SV123: $i,SV85: $i,SV10: $i] :
( ( ( SV10
!= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SV146 @ n1 ) ) ) )
| ( SV10
= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SV146 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(582,plain,
! [SV11: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ~ ( less @ SV11 @ p__0 )
| ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(583,plain,
! [SV147: $i,SV124: $i,SV86: $i,SV16: $i] :
( ( ( SV16
!= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SV147 @ n1 ) ) ) )
| ( SV16
= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SV147 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(584,plain,
! [SV87: $i,SV17: $i] :
( ( ( SV17
= ( plus @ n0 @ ( times @ SV87 @ p__0 ) ) )
= $false )
| ( ( SV17
= ( plus @ n0 @ ( times @ SV87 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(585,plain,
! [SV148: $i,SV126: $i] :
( ( ( ( plus @ ( times @ SV126 @ p__0 ) @ ( times @ SV148 @ p__0 ) )
= ( times @ ( plus @ SV126 @ SV148 ) @ p__0 ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(586,plain,
! [SV18: $i] :
( ( ( ~ ( less @ n0 @ p__0 ) )
= $true )
| ( ( ~ ( less @ SV18 @ p__0 )
| ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(587,plain,
! [SV149: $i,SV20: $i] :
( ( ( ! [SY301: $i] :
( ( plus @ ( plus @ SV20 @ ( times @ SV149 @ p__0 ) ) @ ( times @ SY301 @ p__0 ) )
= ( plus @ SV20 @ ( plus @ ( times @ SV149 @ p__0 ) @ ( times @ SY301 @ p__0 ) ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(588,plain,
! [SV150: $i,SV21: $i] :
( ( ( ! [SY302: $i] :
( ( SV21
!= ( plus @ SV150 @ ( times @ SY302 @ p__0 ) ) )
| ( SV21
= ( plus @ SV150 @ ( times @ SY302 @ p__0 ) ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(589,plain,
! [SV88: $i,SV28: $i] :
( ( ( ( times @ SV28 @ SV88 )
= p__0 )
= $false )
| ( ( ( times @ SV28 @ SV88 )
= p__0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(590,plain,
! [SV29: $i,SV151: $i] :
( ( ( ! [SY303: $i] :
( ( times @ SV151 @ SY303 )
!= SV29 )
| ( SV151 = n1 )
| ( SV151 = SV29 ) )
= $true )
| ( ( SV29 = p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(591,plain,
! [SV128: $i,SV89: $i,SV30: $i] :
( ( ( ( SV30
!= ( plus @ n0 @ ( times @ SV89 @ SV128 ) ) ) )
= $true )
| ( ( SV30
= ( plus @ n0 @ ( times @ SV89 @ SV128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(592,plain,
! [SV91: $i,SV152: $i] :
( ( ( ( SV152 != n1 )
| ( SV152 = n1 ) )
= $true )
| ( ( SV91 = p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(593,plain,
! [SV39: $i,SV153: $i] :
( ( ( ( n1
!= ( times @ SV153 @ SV39 ) ) )
= $true )
| ( ( SV39 = p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(594,plain,
! [SV40: $i,SV154: $i] :
( ( ( ( plus @ n0 @ ( times @ SV154 @ SV40 ) )
= ( times @ SV154 @ SV40 ) )
= $true )
| ( ( SV40 = p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(595,plain,
! [SV92: $i,SV41: $i] :
( ( ( SV41
= ( plus @ n0 @ ( times @ SV92 @ p__0 ) ) )
= $false )
| ( ( SV41
= ( plus @ n0 @ ( times @ SV92 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(596,plain,
! [SV129: $i,SV93: $i,SV42: $i] :
( ( ( ~ ( less @ SV42 @ SV93 ) )
= $true )
| ( ( ~ ( less @ SV42 @ SV129 )
| ~ ( less @ SV93 @ SV129 )
| ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(597,plain,
! [SV130: $i,SV94: $i,SV44: $i] :
( ( ( ( ( plus @ SV44 @ SV94 )
!= ( plus @ SV130 @ SV94 ) ) )
= $true )
| ( ( SV44 = SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(598,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ( ( ( plus @ SV48 @ SV98 )
!= ( plus @ SV48 @ SV133 ) ) )
= $true )
| ( ( SV98 = SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(599,plain,
! [SV99: $i,SV50: $i] :
( ( ( SV50
= ( plus @ SV99 @ SV50 ) )
= $false )
| ( ( SV99 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(600,plain,
! [SV100: $i,SV51: $i] :
( ( ( SV51
= ( plus @ SV51 @ SV100 ) )
= $false )
| ( ( SV100 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(601,plain,
! [SV101: $i,SV52: $i] :
( ( ( ( plus @ SV52 @ SV101 )
= SV52 )
= $false )
| ( ( SV101 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(602,plain,
! [SV134: $i,SV53: $i] :
( ( ( ( plus @ SV53 @ SV134 )
= SV134 )
= $false )
| ( ( SV53 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(603,plain,
! [SV102: $i,SV54: $i] :
( ( ( SV54 = SV102 )
= $false )
| ( ( ! [SY279: $i] :
( ( plus @ SY279 @ SV54 )
= ( plus @ SY279 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(604,plain,
! [SV142: $i,SV68: $i] :
( ( ( n1
= ( times @ SV68 @ SV142 ) )
= $false )
| ( ( SV68 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(605,plain,
! [SV112: $i,SV69: $i] :
( ( ( n1
= ( times @ SV69 @ SV112 ) )
= $false )
| ( ( SV112 = n1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(606,plain,
! [SV143: $i,SV113: $i,SV70: $i] :
( ( ( ~ ( less @ SV70 @ SV113 ) )
= $true )
| ( ( ~ ( less @ SV70 @ SV143 )
| ~ ( less @ SV113 @ SV143 )
| ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(607,plain,
! [SV72: $i] :
( ( ( SV72 = n1 )
= $false )
| ( ( less @ n1 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(608,plain,
! [SV114: $i,SV73: $i] :
( ( ( less @ SV73 @ SV114 )
= $true )
| ( ( less @ SV114 @ SV73 )
= $true )
| ( ( SV73 = SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(609,plain,
! [SV74: $i,SV155: $i] :
( ( ( ( n1
!= ( times @ SV155 @ SV74 ) ) )
= $true )
| ( ( less @ n1 @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(610,plain,
! [SV115: $i,SV75: $i] :
( ( ( less @ ( plus @ SV75 @ n1 ) @ SV115 )
= $false )
| ( ( less @ SV75 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(611,plain,
! [SV116: $i,SV76: $i,SV1: $i] :
( ( ( SV1
= ( plus @ SV76 @ ( times @ SV116 @ p__0 ) ) )
= $false )
| ( ( SV1
= ( plus @ SV76 @ ( times @ SV116 @ p__0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(612,plain,
! [SV144: $i,SV119: $i,SV79: $i,SV4: $i] :
( ( ( ( SV4
!= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SV144 @ n1 ) ) ) ) )
= $true )
| ( ( SV4
= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SV144 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(613,plain,
! [SV156: $i,SV145: $i,SV120: $i,SV81: $i,SV6: $i] :
( ( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
!= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SV156 @ n1 ) ) ) )
| ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SV156 @ n1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(614,plain,
! [SV121: $i] :
( ( ( SV121 = n0 )
= $false )
| ( ( SV121 = n0 )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(615,plain,
! [SV122: $i] :
( ( ( ( s_5 @ p__0 @ SV122 )
= n0 )
= $false )
| ( ( SV122
= ( plus @ n0 @ ( times @ ( s_6 @ p__0 @ SV122 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(616,plain,
! [SV157: $i,SV84: $i,SV9: $i] :
( ( ( ! [SY304: $i] :
( ( SV9
!= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SY304 ) @ p__0 ) ) )
| ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SY304 ) @ p__0 ) ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(617,plain,
! [SV146: $i,SV123: $i,SV85: $i,SV10: $i] :
( ( ( ( SV10
!= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SV146 @ n1 ) ) ) ) )
= $true )
| ( ( SV10
= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SV146 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(618,plain,
! [SV11: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ~ ( less @ SV11 @ p__0 )
| ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(619,plain,
! [SV147: $i,SV124: $i,SV86: $i,SV16: $i] :
( ( ( ( SV16
!= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SV147 @ n1 ) ) ) ) )
= $true )
| ( ( SV16
= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SV147 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(620,plain,
! [SV18: $i] :
( ( ( less @ n0 @ p__0 )
= $false )
| ( ( ~ ( less @ SV18 @ p__0 )
| ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(621,plain,
! [SV158: $i,SV149: $i,SV20: $i] :
( ( ( ( plus @ ( plus @ SV20 @ ( times @ SV149 @ p__0 ) ) @ ( times @ SV158 @ p__0 ) )
= ( plus @ SV20 @ ( plus @ ( times @ SV149 @ p__0 ) @ ( times @ SV158 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(622,plain,
! [SV159: $i,SV150: $i,SV21: $i] :
( ( ( ( SV21
!= ( plus @ SV150 @ ( times @ SV159 @ p__0 ) ) )
| ( SV21
= ( plus @ SV150 @ ( times @ SV159 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(623,plain,
! [SV29: $i,SV151: $i] :
( ( ( ! [SY303: $i] :
( ( times @ SV151 @ SY303 )
!= SV29 ) )
= $true )
| ( ( ( SV151 = n1 )
| ( SV151 = SV29 ) )
= $true )
| ( ( SV29 = p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(624,plain,
! [SV128: $i,SV89: $i,SV30: $i] :
( ( ( SV30
= ( plus @ n0 @ ( times @ SV89 @ SV128 ) ) )
= $false )
| ( ( SV30
= ( plus @ n0 @ ( times @ SV89 @ SV128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(625,plain,
! [SV91: $i,SV152: $i] :
( ( ( ( SV152 != n1 ) )
= $true )
| ( ( SV152 = n1 )
= $true )
| ( ( SV91 = p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(626,plain,
! [SV39: $i,SV153: $i] :
( ( ( n1
= ( times @ SV153 @ SV39 ) )
= $false )
| ( ( SV39 = p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(627,plain,
! [SV129: $i,SV93: $i,SV42: $i] :
( ( ( less @ SV42 @ SV93 )
= $false )
| ( ( ~ ( less @ SV42 @ SV129 )
| ~ ( less @ SV93 @ SV129 )
| ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(628,plain,
! [SV130: $i,SV94: $i,SV44: $i] :
( ( ( ( plus @ SV44 @ SV94 )
= ( plus @ SV130 @ SV94 ) )
= $false )
| ( ( SV44 = SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(629,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ( ( plus @ SV48 @ SV98 )
= ( plus @ SV48 @ SV133 ) )
= $false )
| ( ( SV98 = SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(630,plain,
! [SV102: $i,SV54: $i,SV160: $i] :
( ( ( ( plus @ SV160 @ SV54 )
= ( plus @ SV160 @ SV102 ) )
= $true )
| ( ( SV54 = SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(631,plain,
! [SV143: $i,SV113: $i,SV70: $i] :
( ( ( less @ SV70 @ SV113 )
= $false )
| ( ( ~ ( less @ SV70 @ SV143 )
| ~ ( less @ SV113 @ SV143 )
| ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(632,plain,
! [SV74: $i,SV155: $i] :
( ( ( n1
= ( times @ SV155 @ SV74 ) )
= $false )
| ( ( less @ n1 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(633,plain,
! [SV144: $i,SV119: $i,SV79: $i,SV4: $i] :
( ( ( SV4
= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SV144 @ n1 ) ) ) )
= $false )
| ( ( SV4
= ( plus @ SV79 @ ( times @ SV119 @ ( plus @ SV144 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(634,plain,
! [SV156: $i,SV145: $i,SV120: $i,SV81: $i,SV6: $i] :
( ( ( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
!= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SV156 @ n1 ) ) ) ) )
= $true )
| ( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SV156 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(635,plain,
! [SV161: $i,SV157: $i,SV84: $i,SV9: $i] :
( ( ( ( SV9
!= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SV161 ) @ p__0 ) ) )
| ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SV161 ) @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(636,plain,
! [SV146: $i,SV123: $i,SV85: $i,SV10: $i] :
( ( ( SV10
= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SV146 @ n1 ) ) ) )
= $false )
| ( ( SV10
= ( plus @ SV85 @ ( times @ SV123 @ ( plus @ SV146 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(637,plain,
! [SV11: $i] :
( ( ( ~ ( less @ SV11 @ p__0 ) )
= $true )
| ( ( ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(638,plain,
! [SV147: $i,SV124: $i,SV86: $i,SV16: $i] :
( ( ( SV16
= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SV147 @ n1 ) ) ) )
= $false )
| ( ( SV16
= ( plus @ SV86 @ ( times @ SV124 @ ( plus @ SV147 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(639,plain,
! [SV18: $i] :
( ( ( ~ ( less @ SV18 @ p__0 ) )
= $true )
| ( ( ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(640,plain,
! [SV159: $i,SV150: $i,SV21: $i] :
( ( ( ( SV21
!= ( plus @ SV150 @ ( times @ SV159 @ p__0 ) ) ) )
= $true )
| ( ( SV21
= ( plus @ SV150 @ ( times @ SV159 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(641,plain,
! [SV29: $i,SV162: $i,SV151: $i] :
( ( ( ( ( times @ SV151 @ SV162 )
!= SV29 ) )
= $true )
| ( ( ( SV151 = n1 )
| ( SV151 = SV29 ) )
= $true )
| ( ( SV29 = p__0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(642,plain,
! [SV91: $i,SV152: $i] :
( ( ( SV152 = n1 )
= $false )
| ( ( SV152 = n1 )
= $true )
| ( ( SV91 = p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(643,plain,
! [SV93: $i,SV129: $i,SV42: $i] :
( ( ( ~ ( less @ SV42 @ SV129 ) )
= $true )
| ( ( ~ ( less @ SV93 @ SV129 )
| ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(644,plain,
! [SV113: $i,SV143: $i,SV70: $i] :
( ( ( ~ ( less @ SV70 @ SV143 ) )
= $true )
| ( ( ~ ( less @ SV113 @ SV143 )
| ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(645,plain,
! [SV156: $i,SV145: $i,SV120: $i,SV81: $i,SV6: $i] :
( ( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SV156 @ n1 ) ) ) )
= $false )
| ( ( ( plus @ SV6 @ ( plus @ SV81 @ n1 ) )
= ( plus @ SV120 @ ( times @ SV145 @ ( plus @ SV156 @ n1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(646,plain,
! [SV161: $i,SV157: $i,SV84: $i,SV9: $i] :
( ( ( ( SV9
!= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SV161 ) @ p__0 ) ) ) )
= $true )
| ( ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SV161 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(647,plain,
! [SV11: $i] :
( ( ( less @ SV11 @ p__0 )
= $false )
| ( ( ! [SY193: $i,SY194: $i] :
( ( plus @ SV11 @ ( times @ SY193 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY194 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(648,plain,
! [SV18: $i] :
( ( ( less @ SV18 @ p__0 )
= $false )
| ( ( ! [SY199: $i,SY200: $i] :
( ( plus @ SV18 @ ( times @ SY199 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY200 @ p__0 ) ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(649,plain,
! [SV159: $i,SV150: $i,SV21: $i] :
( ( ( SV21
= ( plus @ SV150 @ ( times @ SV159 @ p__0 ) ) )
= $false )
| ( ( SV21
= ( plus @ SV150 @ ( times @ SV159 @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(650,plain,
! [SV29: $i,SV162: $i,SV151: $i] :
( ( ( ( times @ SV151 @ SV162 )
= SV29 )
= $false )
| ( ( ( SV151 = n1 )
| ( SV151 = SV29 ) )
= $true )
| ( ( SV29 = p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(651,plain,
! [SV93: $i,SV129: $i,SV42: $i] :
( ( ( less @ SV42 @ SV129 )
= $false )
| ( ( ~ ( less @ SV93 @ SV129 )
| ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(652,plain,
! [SV113: $i,SV143: $i,SV70: $i] :
( ( ( less @ SV70 @ SV143 )
= $false )
| ( ( ~ ( less @ SV113 @ SV143 )
| ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(653,plain,
! [SV161: $i,SV157: $i,SV84: $i,SV9: $i] :
( ( ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SV161 ) @ p__0 ) ) )
= $false )
| ( ( SV9
= ( plus @ SV84 @ ( times @ ( plus @ SV157 @ SV161 ) @ p__0 ) ) )
= $true )
| ( ( less @ n0 @ p__0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(654,plain,
! [SV163: $i,SV11: $i] :
( ( ( ! [SY305: $i] :
( ( plus @ SV11 @ ( times @ SV163 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY305 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV11 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(655,plain,
! [SV164: $i,SV18: $i] :
( ( ( ! [SY306: $i] :
( ( plus @ SV18 @ ( times @ SV164 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SY306 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV18 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(656,plain,
! [SV162: $i,SV29: $i,SV151: $i] :
( ( ( SV151 = n1 )
= $true )
| ( ( SV151 = SV29 )
= $true )
| ( ( ( times @ SV151 @ SV162 )
= SV29 )
= $false )
| ( ( SV29 = p__0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(657,plain,
! [SV42: $i,SV129: $i,SV93: $i] :
( ( ( ~ ( less @ SV93 @ SV129 ) )
= $true )
| ( ( ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true )
| ( ( less @ SV42 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(658,plain,
! [SV70: $i,SV143: $i,SV113: $i] :
( ( ( ~ ( less @ SV113 @ SV143 ) )
= $true )
| ( ( ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true )
| ( ( less @ SV70 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(659,plain,
! [SV165: $i,SV163: $i,SV11: $i] :
( ( ( ( ( plus @ SV11 @ ( times @ SV163 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV165 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV11 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(660,plain,
! [SV166: $i,SV164: $i,SV18: $i] :
( ( ( ( ( plus @ SV18 @ ( times @ SV164 @ p__0 ) )
!= ( plus @ n0 @ ( times @ SV166 @ p__0 ) ) ) )
= $true )
| ( ( less @ SV18 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(661,plain,
! [SV42: $i,SV129: $i,SV93: $i] :
( ( ( less @ SV93 @ SV129 )
= $false )
| ( ( ! [SY296: $i,SY297: $i] :
( ( plus @ SV93 @ ( times @ SY296 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY297 @ SV129 ) ) ) )
= $true )
| ( ( less @ SV42 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(662,plain,
! [SV70: $i,SV143: $i,SV113: $i] :
( ( ( less @ SV113 @ SV143 )
= $false )
| ( ( ! [SY298: $i,SY299: $i] :
( ( plus @ SV70 @ ( times @ SY298 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY299 @ SV143 ) ) ) )
= $true )
| ( ( less @ SV70 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(663,plain,
! [SV165: $i,SV163: $i,SV11: $i] :
( ( ( ( plus @ SV11 @ ( times @ SV163 @ p__0 ) )
= ( plus @ n0 @ ( times @ SV165 @ p__0 ) ) )
= $false )
| ( ( less @ SV11 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ SV11 @ n0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(664,plain,
! [SV166: $i,SV164: $i,SV18: $i] :
( ( ( ( plus @ SV18 @ ( times @ SV164 @ p__0 ) )
= ( plus @ n0 @ ( times @ SV166 @ p__0 ) ) )
= $false )
| ( ( less @ SV18 @ p__0 )
= $false )
| ( ( less @ n0 @ p__0 )
= $false )
| ( ( less @ n0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(665,plain,
! [SV42: $i,SV129: $i,SV167: $i,SV93: $i] :
( ( ( ! [SY307: $i] :
( ( plus @ SV93 @ ( times @ SV167 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SY307 @ SV129 ) ) ) )
= $true )
| ( ( less @ SV93 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(666,plain,
! [SV113: $i,SV143: $i,SV168: $i,SV70: $i] :
( ( ( ! [SY308: $i] :
( ( plus @ SV70 @ ( times @ SV168 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SY308 @ SV143 ) ) ) )
= $true )
| ( ( less @ SV113 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(667,plain,
! [SV169: $i,SV42: $i,SV129: $i,SV167: $i,SV93: $i] :
( ( ( ( ( plus @ SV93 @ ( times @ SV167 @ SV129 ) )
!= ( plus @ SV42 @ ( times @ SV169 @ SV129 ) ) ) )
= $true )
| ( ( less @ SV93 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(668,plain,
! [SV170: $i,SV113: $i,SV143: $i,SV168: $i,SV70: $i] :
( ( ( ( ( plus @ SV70 @ ( times @ SV168 @ SV143 ) )
!= ( plus @ SV113 @ ( times @ SV170 @ SV143 ) ) ) )
= $true )
| ( ( less @ SV113 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(669,plain,
! [SV169: $i,SV42: $i,SV129: $i,SV167: $i,SV93: $i] :
( ( ( ( plus @ SV93 @ ( times @ SV167 @ SV129 ) )
= ( plus @ SV42 @ ( times @ SV169 @ SV129 ) ) )
= $false )
| ( ( less @ SV93 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV129 )
= $false )
| ( ( less @ SV42 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(670,plain,
! [SV170: $i,SV113: $i,SV143: $i,SV168: $i,SV70: $i] :
( ( ( ( plus @ SV70 @ ( times @ SV168 @ SV143 ) )
= ( plus @ SV113 @ ( times @ SV170 @ SV143 ) ) )
= $false )
| ( ( less @ SV113 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV143 )
= $false )
| ( ( less @ SV70 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(671,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[258,670,669,664,663,656,653,649,645,642,638,636,633,632,630,629,628,626,624,621,615,614,611,610,608,607,605,604,602,601,600,599,595,594,589,585,584,579,575,573,564,563,562,561,560,559,558,551,550,544,543,541,540,536,535,534,533,532,531,530,525,522,521,520,519,514,507,497,490,489,488,481,473,472,470,468,465,458,454,449,442,425,420,410,407,398,392,304,289,288,283,282]) ).
thf(672,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM420-1.000 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 15:09:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36 ..
% 0.18/0.39
% 0.18/0.39 No.of.Axioms: 91
% 0.18/0.39
% 0.18/0.39 Length.of.Defs: 0
% 0.18/0.39
% 0.18/0.39 Contains.Choice.Funs: false
% 0.18/0.41 ..
% 0.18/0.45 (rf:0,axioms:91,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:93,loop_count:0,foatp_calls:0,translation:fof_full).................................
% 2.38/2.56
% 2.38/2.56 ********************************
% 2.38/2.56 * All subproblems solved! *
% 2.38/2.56 ********************************
% 2.38/2.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:91,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:671,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.54/2.72
% 2.54/2.72 %**** Beginning of derivation protocol ****
% 2.54/2.72 % SZS output start CNFRefutation
% See solution above
% 2.54/2.73
% 2.54/2.73 %**** End of derivation protocol ****
% 2.54/2.73 %**** no. of clauses in derivation: 672 ****
% 2.54/2.73 %**** clause counter: 671 ****
% 2.54/2.73
% 2.54/2.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:91,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:671,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------