TSTP Solution File: RNG039-2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG039-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 20:34:02 EDT 2022
% Result : Unsatisfiable 0.44s 0.78s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 85
% Syntax : Number of formulae : 513 ( 332 unt; 10 typ; 0 def)
% Number of atoms : 2673 ( 684 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 5553 ( 605 ~; 802 |; 0 &;4146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 1693 ( 0 ^1693 !; 0 ?;1693 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i > $i > $o ).
thf(1,axiom,
! [A: $i] : ( product @ A @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
thf(2,axiom,
product @ ( add @ a @ b ) @ a @ ( add @ a @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause70) ).
thf(3,axiom,
product @ ( add @ b @ a ) @ a @ ( add @ d @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause69) ).
thf(4,axiom,
product @ ( add @ b @ a ) @ b @ ( add @ b @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause68) ).
thf(5,axiom,
product @ ( add @ a @ b ) @ b @ ( add @ c @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause67) ).
thf(6,axiom,
product @ b @ ( add @ b @ a ) @ ( add @ b @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause66) ).
thf(7,axiom,
product @ b @ ( add @ a @ b ) @ ( add @ d @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause65) ).
thf(8,axiom,
product @ a @ ( add @ a @ b ) @ ( add @ a @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause64) ).
thf(9,axiom,
product @ a @ ( add @ b @ a ) @ ( add @ c @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
thf(10,axiom,
product @ c @ a @ ( multiply @ a @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause60) ).
thf(11,axiom,
product @ ( multiply @ d @ b ) @ a @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause59) ).
thf(12,axiom,
product @ b @ a @ ( multiply @ b @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(13,axiom,
! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause57) ).
thf(14,axiom,
product @ d @ b @ ( multiply @ b @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
thf(15,axiom,
product @ ( multiply @ c @ a ) @ b @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause55) ).
thf(16,axiom,
product @ a @ b @ ( multiply @ a @ c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
thf(17,axiom,
! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause53) ).
thf(18,axiom,
! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause52) ).
thf(19,axiom,
product @ a @ d @ ( multiply @ c @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
thf(20,axiom,
product @ b @ c @ ( multiply @ d @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause50) ).
thf(21,axiom,
product @ b @ ( multiply @ a @ d ) @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause49) ).
thf(22,axiom,
product @ b @ a @ ( multiply @ d @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause48) ).
thf(23,axiom,
! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause47) ).
thf(24,axiom,
product @ a @ ( multiply @ b @ c ) @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause46) ).
thf(25,axiom,
product @ a @ b @ ( multiply @ c @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause45) ).
thf(26,axiom,
! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause44) ).
thf(27,axiom,
! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause43) ).
thf(28,axiom,
product @ d @ a @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause42) ).
thf(29,axiom,
product @ c @ b @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause41) ).
thf(30,axiom,
product @ b @ d @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause40) ).
thf(31,axiom,
product @ a @ c @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause39) ).
thf(32,axiom,
! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause38) ).
thf(33,axiom,
equalish @ ( multiply @ b @ a ) @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(34,axiom,
equalish @ ( multiply @ a @ b ) @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(35,axiom,
! [A: $i] : ( equalish @ ( multiply @ A @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(36,axiom,
! [A: $i] : ( equalish @ ( add @ A @ A ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(37,axiom,
! [A: $i] : ( equalish @ ( add @ A @ additive_identity ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(38,axiom,
! [A: $i] : ( sum @ A @ A @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(39,axiom,
! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion2) ).
thf(40,axiom,
! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorbtion1) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ C )
| ( equalish @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_right_concellation) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ D @ B @ C )
| ( equalish @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_left_cancellation) ).
thf(43,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(44,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(45,axiom,
! [X: $i] : ( product @ X @ additive_identity @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(46,axiom,
! [X: $i] : ( product @ additive_identity @ X @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(47,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
thf(48,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
thf(49,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(50,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ X @ V3 @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(51,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(52,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(53,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(54,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W )
| ( sum @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(55,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W )
| ( sum @ X @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(56,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(57,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(58,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(59,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(60,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(61,axiom,
! [X: $i] : ( equalish @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(62,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
thf(63,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
thf(64,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution1) ).
thf(65,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution2) ).
thf(66,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(67,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
thf(68,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).
thf(69,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution1) ).
thf(70,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution2) ).
thf(71,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_substitution1) ).
thf(72,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(73,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[72]) ).
thf(74,negated_conjecture,
~ ( equalish @ c @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
thf(75,negated_conjecture,
product @ b @ a @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a) ).
thf(76,negated_conjecture,
product @ a @ b @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
thf(77,plain,
$false = $false,
inference(unfold_def,[status(thm)],[73]) ).
thf(78,plain,
( ( ! [A: $i] : ( product @ A @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(79,plain,
( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(80,plain,
( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(81,plain,
( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(82,plain,
( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(83,plain,
( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(84,plain,
( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(85,plain,
( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(86,plain,
( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(87,plain,
( ( product @ c @ a @ ( multiply @ a @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(88,plain,
( ( product @ ( multiply @ d @ b ) @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(89,plain,
( ( product @ b @ a @ ( multiply @ b @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(90,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(91,plain,
( ( product @ d @ b @ ( multiply @ b @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(92,plain,
( ( product @ ( multiply @ c @ a ) @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(93,plain,
( ( product @ a @ b @ ( multiply @ a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(94,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(96,plain,
( ( product @ a @ d @ ( multiply @ c @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(97,plain,
( ( product @ b @ c @ ( multiply @ d @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(98,plain,
( ( product @ b @ ( multiply @ a @ d ) @ d )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(99,plain,
( ( product @ b @ a @ ( multiply @ d @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(100,plain,
( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(101,plain,
( ( product @ a @ ( multiply @ b @ c ) @ c )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(102,plain,
( ( product @ a @ b @ ( multiply @ c @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(105,plain,
( ( product @ d @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(106,plain,
( ( product @ c @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(107,plain,
( ( product @ b @ d @ d )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(108,plain,
( ( product @ a @ c @ c )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(110,plain,
( ( equalish @ ( multiply @ b @ a ) @ d )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(111,plain,
( ( equalish @ ( multiply @ a @ b ) @ c )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(112,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ A ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(113,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ A ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(114,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ additive_identity ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(115,plain,
( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(118,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ D @ C )
| ( equalish @ D @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(119,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ D @ B @ C )
| ( equalish @ D @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(122,plain,
( ( ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(123,plain,
( ( ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(124,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(125,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(126,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(127,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ X @ V3 @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W )
| ( sum @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W )
| ( sum @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(133,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(134,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(135,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(136,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(137,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(138,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(139,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(140,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(142,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(143,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(144,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(145,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(146,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(147,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(148,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(149,plain,
( ( ~ ( equalish @ c @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(150,plain,
( ( product @ b @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(151,plain,
( ( product @ a @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(152,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[77]) ).
thf(153,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( sum @ A @ B @ C )
| ! [D: $i] :
( ~ ( sum @ A @ D @ C )
| ( equalish @ D @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(154,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( sum @ A @ B @ C )
| ! [D: $i] :
( ~ ( sum @ D @ B @ C )
| ( equalish @ D @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(155,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(156,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(157,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(158,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(159,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(160,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ X @ V3 @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(161,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(162,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(163,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( sum @ X @ V @ W )
| ( sum @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(164,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( sum @ U @ Z @ W )
| ( sum @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(165,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(166,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(167,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(168,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(169,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(170,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(171,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(172,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(173,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(174,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(175,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(176,plain,
( ( product @ a @ b @ c )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(177,plain,
( ( product @ b @ a @ d )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(178,plain,
( ( ~ ( equalish @ c @ d ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(179,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(180,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( add @ W @ X ) @ ( add @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(181,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(182,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(183,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(184,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(185,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i] : ( equalish @ ( multiply @ W @ X ) @ ( multiply @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(186,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(187,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(188,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [W: $i,Z: $i] :
( ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(189,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(190,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(191,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(192,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(193,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(194,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(195,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( sum @ U @ Z @ W )
| ( sum @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(196,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( sum @ X @ V @ W )
| ( sum @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(197,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(198,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(199,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ! [W: $i] :
( ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(200,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ X @ V3 @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(201,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(202,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(203,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(204,plain,
( ( ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(205,plain,
( ( ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(206,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(207,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(208,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( sum @ A @ B @ C )
| ! [D: $i] :
( ~ ( sum @ D @ B @ C )
| ( equalish @ D @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(209,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( sum @ A @ B @ C )
| ! [D: $i] :
( ~ ( sum @ A @ D @ C )
| ( equalish @ D @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(210,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(212,plain,
( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(213,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ additive_identity ) @ A ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(214,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ A ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(215,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(216,plain,
( ( equalish @ ( multiply @ a @ b ) @ c )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(217,plain,
( ( equalish @ ( multiply @ b @ a ) @ d )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(219,plain,
( ( product @ a @ c @ c )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(220,plain,
( ( product @ b @ d @ d )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(221,plain,
( ( product @ c @ b @ c )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(222,plain,
( ( product @ d @ a @ d )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(225,plain,
( ( product @ a @ b @ ( multiply @ c @ b ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(226,plain,
( ( product @ a @ ( multiply @ b @ c ) @ c )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(227,plain,
( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(228,plain,
( ( product @ b @ a @ ( multiply @ d @ a ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(229,plain,
( ( product @ b @ ( multiply @ a @ d ) @ d )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(230,plain,
( ( product @ b @ c @ ( multiply @ d @ b ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(231,plain,
( ( product @ a @ d @ ( multiply @ c @ a ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(233,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(234,plain,
( ( product @ a @ b @ ( multiply @ a @ c ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(235,plain,
( ( product @ ( multiply @ c @ a ) @ b @ c )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(236,plain,
( ( product @ d @ b @ ( multiply @ b @ c ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(237,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(238,plain,
( ( product @ b @ a @ ( multiply @ b @ d ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(239,plain,
( ( product @ ( multiply @ d @ b ) @ a @ d )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(240,plain,
( ( product @ c @ a @ ( multiply @ a @ d ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(241,plain,
( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(242,plain,
( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(243,plain,
( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(244,plain,
( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(245,plain,
( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(246,plain,
( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(247,plain,
( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(248,plain,
( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(249,plain,
( ( ! [A: $i] : ( product @ A @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(250,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(251,plain,
( ( equalish @ c @ d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(252,plain,
! [SV1: $i] :
( ( ! [SY139: $i] :
( ~ ( equalish @ SV1 @ SY139 )
| ! [SY140: $i] : ( equalish @ ( add @ SV1 @ SY140 ) @ ( add @ SY139 @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(253,plain,
! [SV2: $i] :
( ( ! [SY141: $i] :
( ~ ( equalish @ SV2 @ SY141 )
| ! [SY142: $i] : ( equalish @ ( add @ SY142 @ SV2 ) @ ( add @ SY142 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(254,plain,
! [SV3: $i] :
( ( ! [SY143: $i] :
( ~ ( equalish @ SV3 @ SY143 )
| ! [SY144: $i,SY145: $i] :
( ~ ( sum @ SV3 @ SY144 @ SY145 )
| ( sum @ SY143 @ SY144 @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(255,plain,
! [SV4: $i] :
( ( ! [SY146: $i] :
( ~ ( equalish @ SV4 @ SY146 )
| ! [SY147: $i,SY148: $i] :
( ~ ( sum @ SY147 @ SV4 @ SY148 )
| ( sum @ SY147 @ SY146 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(256,plain,
! [SV5: $i] :
( ( ! [SY149: $i] :
( ~ ( equalish @ SV5 @ SY149 )
| ! [SY150: $i,SY151: $i] :
( ~ ( sum @ SY150 @ SY151 @ SV5 )
| ( sum @ SY150 @ SY151 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(257,plain,
! [SV6: $i] :
( ( ! [SY152: $i] :
( ~ ( equalish @ SV6 @ SY152 )
| ! [SY153: $i] : ( equalish @ ( multiply @ SV6 @ SY153 ) @ ( multiply @ SY152 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(258,plain,
! [SV7: $i] :
( ( ! [SY154: $i] :
( ~ ( equalish @ SV7 @ SY154 )
| ! [SY155: $i] : ( equalish @ ( multiply @ SY155 @ SV7 ) @ ( multiply @ SY155 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(259,plain,
! [SV8: $i] :
( ( ! [SY156: $i] :
( ~ ( equalish @ SV8 @ SY156 )
| ! [SY157: $i,SY158: $i] :
( ~ ( product @ SV8 @ SY157 @ SY158 )
| ( product @ SY156 @ SY157 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(260,plain,
! [SV9: $i] :
( ( ! [SY159: $i] :
( ~ ( equalish @ SV9 @ SY159 )
| ! [SY160: $i,SY161: $i] :
( ~ ( product @ SY160 @ SV9 @ SY161 )
| ( product @ SY160 @ SY159 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(261,plain,
! [SV10: $i] :
( ( ! [SY162: $i] :
( ~ ( equalish @ SV10 @ SY162 )
| ! [SY163: $i,SY164: $i] :
( ~ ( product @ SY163 @ SY164 @ SV10 )
| ( product @ SY163 @ SY164 @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(262,plain,
! [SV11: $i] :
( ( equalish @ SV11 @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(263,plain,
! [SV12: $i] :
( ( ! [SY165: $i] :
( ~ ( equalish @ SV12 @ SY165 )
| ! [SY166: $i] :
( ~ ( equalish @ SY165 @ SY166 )
| ( equalish @ SV12 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(264,plain,
! [SV13: $i] :
( ( sum @ additive_identity @ SV13 @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(265,plain,
! [SV14: $i] :
( ( sum @ SV14 @ additive_identity @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(266,plain,
! [SV15: $i] :
( ( ! [SY167: $i] : ( product @ SV15 @ SY167 @ ( multiply @ SV15 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(267,plain,
! [SV16: $i] :
( ( ! [SY168: $i] : ( sum @ SV16 @ SY168 @ ( add @ SV16 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(268,plain,
! [SV17: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i] :
( ~ ( sum @ SV17 @ SY169 @ SY170 )
| ! [SY172: $i] :
( ~ ( sum @ SY169 @ SY171 @ SY172 )
| ! [SY173: $i] :
( ~ ( sum @ SY170 @ SY171 @ SY173 )
| ( sum @ SV17 @ SY172 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(269,plain,
! [SV18: $i] :
( ( ! [SY174: $i,SY175: $i,SY176: $i] :
( ~ ( sum @ SV18 @ SY174 @ SY175 )
| ! [SY177: $i] :
( ~ ( sum @ SY174 @ SY176 @ SY177 )
| ! [SY178: $i] :
( ~ ( sum @ SV18 @ SY177 @ SY178 )
| ( sum @ SY175 @ SY176 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(270,plain,
! [SV19: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( sum @ SV19 @ SY179 @ SY180 )
| ( sum @ SY179 @ SV19 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(271,plain,
! [SV20: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i] :
( ~ ( product @ SV20 @ SY181 @ SY182 )
| ! [SY184: $i] :
( ~ ( product @ SY181 @ SY183 @ SY184 )
| ! [SY185: $i] :
( ~ ( product @ SY182 @ SY183 @ SY185 )
| ( product @ SV20 @ SY184 @ SY185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(272,plain,
! [SV21: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i] :
( ~ ( product @ SV21 @ SY186 @ SY187 )
| ! [SY189: $i] :
( ~ ( product @ SY186 @ SY188 @ SY189 )
| ! [SY190: $i] :
( ~ ( product @ SV21 @ SY189 @ SY190 )
| ( product @ SY187 @ SY188 @ SY190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(273,plain,
! [SV22: $i] :
( ( ! [SY191: $i,SY192: $i,SY193: $i,SY194: $i] :
( ~ ( product @ SV22 @ SY191 @ SY192 )
| ~ ( product @ SV22 @ SY193 @ SY194 )
| ! [SY195: $i] :
( ~ ( sum @ SY191 @ SY193 @ SY195 )
| ! [SY196: $i] :
( ~ ( product @ SV22 @ SY195 @ SY196 )
| ( sum @ SY192 @ SY194 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(274,plain,
! [SV23: $i] :
( ( ! [SY197: $i,SY198: $i,SY199: $i,SY200: $i] :
( ~ ( product @ SV23 @ SY197 @ SY198 )
| ~ ( product @ SV23 @ SY199 @ SY200 )
| ! [SY201: $i] :
( ~ ( sum @ SY197 @ SY199 @ SY201 )
| ! [SY202: $i] :
( ~ ( sum @ SY198 @ SY200 @ SY202 )
| ( product @ SV23 @ SY201 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(275,plain,
! [SV24: $i] :
( ( ! [SY203: $i,SY204: $i,SY205: $i,SY206: $i] :
( ~ ( product @ SV24 @ SY203 @ SY204 )
| ~ ( product @ SY205 @ SY203 @ SY206 )
| ! [SY207: $i] :
( ~ ( sum @ SV24 @ SY205 @ SY207 )
| ! [V4: $i] :
( ~ ( product @ SY207 @ SY203 @ V4 )
| ( sum @ SY204 @ SY206 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(276,plain,
! [SV25: $i] :
( ( ! [SY209: $i,SY210: $i,SY211: $i,SY212: $i] :
( ~ ( product @ SV25 @ SY209 @ SY210 )
| ~ ( product @ SY211 @ SY209 @ SY212 )
| ! [SY213: $i] :
( ~ ( sum @ SV25 @ SY211 @ SY213 )
| ! [V4: $i] :
( ~ ( sum @ SY210 @ SY212 @ V4 )
| ( product @ SY213 @ SY209 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(277,plain,
! [SV26: $i] :
( ( product @ additive_identity @ SV26 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(278,plain,
! [SV27: $i] :
( ( product @ SV27 @ additive_identity @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(279,plain,
! [SV28: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ( sum @ SV28 @ SY215 @ SY216 )
| ! [SY217: $i] :
( ~ ( sum @ SV28 @ SY215 @ SY217 )
| ( equalish @ SY216 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(280,plain,
! [SV29: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ~ ( product @ SV29 @ SY218 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV29 @ SY218 @ SY220 )
| ( equalish @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(281,plain,
! [SV30: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ~ ( sum @ SV30 @ SY221 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SY223 @ SY221 @ SY222 )
| ( equalish @ SY223 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(282,plain,
! [SV31: $i] :
( ( ! [SY224: $i,SY225: $i] :
( ~ ( sum @ SV31 @ SY224 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV31 @ SY226 @ SY225 )
| ( equalish @ SY226 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(283,plain,
! [SV32: $i] :
( ( ! [SY227: $i] : ( sum @ SV32 @ ( add @ SV32 @ SY227 ) @ SY227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(284,plain,
! [SV33: $i] :
( ( ! [SY228: $i] : ( sum @ ( add @ SV33 @ SY228 ) @ SY228 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(285,plain,
! [SV34: $i] :
( ( sum @ SV34 @ SV34 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(286,plain,
! [SV35: $i] :
( ( equalish @ ( add @ SV35 @ additive_identity ) @ SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(287,plain,
! [SV36: $i] :
( ( equalish @ ( add @ SV36 @ SV36 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(288,plain,
! [SV37: $i] :
( ( equalish @ ( multiply @ SV37 @ SV37 ) @ SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(289,plain,
! [SV38: $i] :
( ( ! [SY229: $i] : ( sum @ SV38 @ SY229 @ ( add @ SY229 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(290,plain,
! [SV39: $i] :
( ( ! [SY230: $i] : ( product @ SV39 @ ( multiply @ SV39 @ SY230 ) @ ( multiply @ SV39 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(291,plain,
! [SV40: $i] :
( ( ! [SY231: $i] : ( product @ a @ ( multiply @ b @ SV40 ) @ ( multiply @ SY231 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(292,plain,
! [SV41: $i] :
( ( product @ b @ ( multiply @ a @ SV41 ) @ ( multiply @ d @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(293,plain,
! [SV42: $i] :
( ( ! [SY232: $i] : ( product @ ( multiply @ SV42 @ SY232 ) @ SY232 @ ( multiply @ SV42 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(294,plain,
! [SV43: $i] :
( ( product @ ( multiply @ SV43 @ a ) @ b @ ( multiply @ SV43 @ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(295,plain,
! [SV44: $i] :
( ( product @ ( multiply @ SV44 @ b ) @ a @ ( multiply @ SV44 @ d ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(296,plain,
! [SV45: $i] :
( ( product @ SV45 @ SV45 @ SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(297,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(298,plain,
! [SV46: $i,SV1: $i] :
( ( ~ ( equalish @ SV1 @ SV46 )
| ! [SY233: $i] : ( equalish @ ( add @ SV1 @ SY233 ) @ ( add @ SV46 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(299,plain,
! [SV47: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV47 )
| ! [SY234: $i] : ( equalish @ ( add @ SY234 @ SV2 ) @ ( add @ SY234 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(300,plain,
! [SV48: $i,SV3: $i] :
( ( ~ ( equalish @ SV3 @ SV48 )
| ! [SY235: $i,SY236: $i] :
( ~ ( sum @ SV3 @ SY235 @ SY236 )
| ( sum @ SV48 @ SY235 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(301,plain,
! [SV49: $i,SV4: $i] :
( ( ~ ( equalish @ SV4 @ SV49 )
| ! [SY237: $i,SY238: $i] :
( ~ ( sum @ SY237 @ SV4 @ SY238 )
| ( sum @ SY237 @ SV49 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(302,plain,
! [SV50: $i,SV5: $i] :
( ( ~ ( equalish @ SV5 @ SV50 )
| ! [SY239: $i,SY240: $i] :
( ~ ( sum @ SY239 @ SY240 @ SV5 )
| ( sum @ SY239 @ SY240 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(303,plain,
! [SV51: $i,SV6: $i] :
( ( ~ ( equalish @ SV6 @ SV51 )
| ! [SY241: $i] : ( equalish @ ( multiply @ SV6 @ SY241 ) @ ( multiply @ SV51 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(304,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV52 )
| ! [SY242: $i] : ( equalish @ ( multiply @ SY242 @ SV7 ) @ ( multiply @ SY242 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(305,plain,
! [SV53: $i,SV8: $i] :
( ( ~ ( equalish @ SV8 @ SV53 )
| ! [SY243: $i,SY244: $i] :
( ~ ( product @ SV8 @ SY243 @ SY244 )
| ( product @ SV53 @ SY243 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(306,plain,
! [SV54: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV54 )
| ! [SY245: $i,SY246: $i] :
( ~ ( product @ SY245 @ SV9 @ SY246 )
| ( product @ SY245 @ SV54 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(307,plain,
! [SV55: $i,SV10: $i] :
( ( ~ ( equalish @ SV10 @ SV55 )
| ! [SY247: $i,SY248: $i] :
( ~ ( product @ SY247 @ SY248 @ SV10 )
| ( product @ SY247 @ SY248 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(308,plain,
! [SV56: $i,SV12: $i] :
( ( ~ ( equalish @ SV12 @ SV56 )
| ! [SY249: $i] :
( ~ ( equalish @ SV56 @ SY249 )
| ( equalish @ SV12 @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(309,plain,
! [SV57: $i,SV15: $i] :
( ( product @ SV15 @ SV57 @ ( multiply @ SV15 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(310,plain,
! [SV58: $i,SV16: $i] :
( ( sum @ SV16 @ SV58 @ ( add @ SV16 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(311,plain,
! [SV59: $i,SV17: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( sum @ SV17 @ SV59 @ SY250 )
| ! [SY252: $i] :
( ~ ( sum @ SV59 @ SY251 @ SY252 )
| ! [SY173: $i] :
( ~ ( sum @ SY250 @ SY251 @ SY173 )
| ( sum @ SV17 @ SY252 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(312,plain,
! [SV60: $i,SV18: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ~ ( sum @ SV18 @ SV60 @ SY254 )
| ! [SY256: $i] :
( ~ ( sum @ SV60 @ SY255 @ SY256 )
| ! [SY178: $i] :
( ~ ( sum @ SV18 @ SY256 @ SY178 )
| ( sum @ SY254 @ SY255 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(313,plain,
! [SV61: $i,SV19: $i] :
( ( ! [SY258: $i] :
( ~ ( sum @ SV19 @ SV61 @ SY258 )
| ( sum @ SV61 @ SV19 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(314,plain,
! [SV62: $i,SV20: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ~ ( product @ SV20 @ SV62 @ SY259 )
| ! [SY261: $i] :
( ~ ( product @ SV62 @ SY260 @ SY261 )
| ! [SY185: $i] :
( ~ ( product @ SY259 @ SY260 @ SY185 )
| ( product @ SV20 @ SY261 @ SY185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(315,plain,
! [SV63: $i,SV21: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( product @ SV21 @ SV63 @ SY263 )
| ! [SY265: $i] :
( ~ ( product @ SV63 @ SY264 @ SY265 )
| ! [SY190: $i] :
( ~ ( product @ SV21 @ SY265 @ SY190 )
| ( product @ SY263 @ SY264 @ SY190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(316,plain,
! [SV64: $i,SV22: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i] :
( ~ ( product @ SV22 @ SV64 @ SY267 )
| ~ ( product @ SV22 @ SY268 @ SY269 )
| ! [SY270: $i] :
( ~ ( sum @ SV64 @ SY268 @ SY270 )
| ! [SY196: $i] :
( ~ ( product @ SV22 @ SY270 @ SY196 )
| ( sum @ SY267 @ SY269 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(317,plain,
! [SV65: $i,SV23: $i] :
( ( ! [SY272: $i,SY273: $i,SY274: $i] :
( ~ ( product @ SV23 @ SV65 @ SY272 )
| ~ ( product @ SV23 @ SY273 @ SY274 )
| ! [SY275: $i] :
( ~ ( sum @ SV65 @ SY273 @ SY275 )
| ! [SY202: $i] :
( ~ ( sum @ SY272 @ SY274 @ SY202 )
| ( product @ SV23 @ SY275 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(318,plain,
! [SV66: $i,SV24: $i] :
( ( ! [SY277: $i,SY278: $i,SY279: $i] :
( ~ ( product @ SV24 @ SV66 @ SY277 )
| ~ ( product @ SY278 @ SV66 @ SY279 )
| ! [SY280: $i] :
( ~ ( sum @ SV24 @ SY278 @ SY280 )
| ! [SY281: $i] :
( ~ ( product @ SY280 @ SV66 @ SY281 )
| ( sum @ SY277 @ SY279 @ SY281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(319,plain,
! [SV67: $i,SV25: $i] :
( ( ! [SY282: $i,SY283: $i,SY284: $i] :
( ~ ( product @ SV25 @ SV67 @ SY282 )
| ~ ( product @ SY283 @ SV67 @ SY284 )
| ! [SY285: $i] :
( ~ ( sum @ SV25 @ SY283 @ SY285 )
| ! [SY286: $i] :
( ~ ( sum @ SY282 @ SY284 @ SY286 )
| ( product @ SY285 @ SV67 @ SY286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(320,plain,
! [SV68: $i,SV28: $i] :
( ( ! [SY287: $i] :
( ~ ( sum @ SV28 @ SV68 @ SY287 )
| ! [SY288: $i] :
( ~ ( sum @ SV28 @ SV68 @ SY288 )
| ( equalish @ SY287 @ SY288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(321,plain,
! [SV69: $i,SV29: $i] :
( ( ! [SY289: $i] :
( ~ ( product @ SV29 @ SV69 @ SY289 )
| ! [SY290: $i] :
( ~ ( product @ SV29 @ SV69 @ SY290 )
| ( equalish @ SY289 @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(322,plain,
! [SV70: $i,SV30: $i] :
( ( ! [SY291: $i] :
( ~ ( sum @ SV30 @ SV70 @ SY291 )
| ! [SY292: $i] :
( ~ ( sum @ SY292 @ SV70 @ SY291 )
| ( equalish @ SY292 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(323,plain,
! [SV71: $i,SV31: $i] :
( ( ! [SY293: $i] :
( ~ ( sum @ SV31 @ SV71 @ SY293 )
| ! [SY294: $i] :
( ~ ( sum @ SV31 @ SY294 @ SY293 )
| ( equalish @ SY294 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(324,plain,
! [SV72: $i,SV32: $i] :
( ( sum @ SV32 @ ( add @ SV32 @ SV72 ) @ SV72 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(325,plain,
! [SV73: $i,SV33: $i] :
( ( sum @ ( add @ SV33 @ SV73 ) @ SV73 @ SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(326,plain,
! [SV74: $i,SV38: $i] :
( ( sum @ SV38 @ SV74 @ ( add @ SV74 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(327,plain,
! [SV75: $i,SV39: $i] :
( ( product @ SV39 @ ( multiply @ SV39 @ SV75 ) @ ( multiply @ SV39 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(328,plain,
! [SV76: $i,SV40: $i] :
( ( product @ a @ ( multiply @ b @ SV40 ) @ ( multiply @ SV76 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(329,plain,
! [SV77: $i,SV42: $i] :
( ( product @ ( multiply @ SV42 @ SV77 ) @ SV77 @ ( multiply @ SV42 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(330,plain,
! [SV46: $i,SV1: $i] :
( ( ( ~ ( equalish @ SV1 @ SV46 ) )
= $true )
| ( ( ! [SY233: $i] : ( equalish @ ( add @ SV1 @ SY233 ) @ ( add @ SV46 @ SY233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(331,plain,
! [SV47: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV47 ) )
= $true )
| ( ( ! [SY234: $i] : ( equalish @ ( add @ SY234 @ SV2 ) @ ( add @ SY234 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(332,plain,
! [SV48: $i,SV3: $i] :
( ( ( ~ ( equalish @ SV3 @ SV48 ) )
= $true )
| ( ( ! [SY235: $i,SY236: $i] :
( ~ ( sum @ SV3 @ SY235 @ SY236 )
| ( sum @ SV48 @ SY235 @ SY236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(333,plain,
! [SV49: $i,SV4: $i] :
( ( ( ~ ( equalish @ SV4 @ SV49 ) )
= $true )
| ( ( ! [SY237: $i,SY238: $i] :
( ~ ( sum @ SY237 @ SV4 @ SY238 )
| ( sum @ SY237 @ SV49 @ SY238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(334,plain,
! [SV50: $i,SV5: $i] :
( ( ( ~ ( equalish @ SV5 @ SV50 ) )
= $true )
| ( ( ! [SY239: $i,SY240: $i] :
( ~ ( sum @ SY239 @ SY240 @ SV5 )
| ( sum @ SY239 @ SY240 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(335,plain,
! [SV51: $i,SV6: $i] :
( ( ( ~ ( equalish @ SV6 @ SV51 ) )
= $true )
| ( ( ! [SY241: $i] : ( equalish @ ( multiply @ SV6 @ SY241 ) @ ( multiply @ SV51 @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(336,plain,
! [SV52: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV52 ) )
= $true )
| ( ( ! [SY242: $i] : ( equalish @ ( multiply @ SY242 @ SV7 ) @ ( multiply @ SY242 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(337,plain,
! [SV53: $i,SV8: $i] :
( ( ( ~ ( equalish @ SV8 @ SV53 ) )
= $true )
| ( ( ! [SY243: $i,SY244: $i] :
( ~ ( product @ SV8 @ SY243 @ SY244 )
| ( product @ SV53 @ SY243 @ SY244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(338,plain,
! [SV54: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV54 ) )
= $true )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( product @ SY245 @ SV9 @ SY246 )
| ( product @ SY245 @ SV54 @ SY246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(339,plain,
! [SV55: $i,SV10: $i] :
( ( ( ~ ( equalish @ SV10 @ SV55 ) )
= $true )
| ( ( ! [SY247: $i,SY248: $i] :
( ~ ( product @ SY247 @ SY248 @ SV10 )
| ( product @ SY247 @ SY248 @ SV55 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(340,plain,
! [SV56: $i,SV12: $i] :
( ( ( ~ ( equalish @ SV12 @ SV56 ) )
= $true )
| ( ( ! [SY249: $i] :
( ~ ( equalish @ SV56 @ SY249 )
| ( equalish @ SV12 @ SY249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(341,plain,
! [SV78: $i,SV59: $i,SV17: $i] :
( ( ! [SY295: $i] :
( ~ ( sum @ SV17 @ SV59 @ SV78 )
| ! [SY296: $i] :
( ~ ( sum @ SV59 @ SY295 @ SY296 )
| ! [SY297: $i] :
( ~ ( sum @ SV78 @ SY295 @ SY297 )
| ( sum @ SV17 @ SY296 @ SY297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(342,plain,
! [SV79: $i,SV60: $i,SV18: $i] :
( ( ! [SY298: $i] :
( ~ ( sum @ SV18 @ SV60 @ SV79 )
| ! [SY299: $i] :
( ~ ( sum @ SV60 @ SY298 @ SY299 )
| ! [SY300: $i] :
( ~ ( sum @ SV18 @ SY299 @ SY300 )
| ( sum @ SV79 @ SY298 @ SY300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(343,plain,
! [SV80: $i,SV61: $i,SV19: $i] :
( ( ~ ( sum @ SV19 @ SV61 @ SV80 )
| ( sum @ SV61 @ SV19 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(344,plain,
! [SV81: $i,SV62: $i,SV20: $i] :
( ( ! [SY301: $i] :
( ~ ( product @ SV20 @ SV62 @ SV81 )
| ! [SY302: $i] :
( ~ ( product @ SV62 @ SY301 @ SY302 )
| ! [SY303: $i] :
( ~ ( product @ SV81 @ SY301 @ SY303 )
| ( product @ SV20 @ SY302 @ SY303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(345,plain,
! [SV82: $i,SV63: $i,SV21: $i] :
( ( ! [SY304: $i] :
( ~ ( product @ SV21 @ SV63 @ SV82 )
| ! [SY305: $i] :
( ~ ( product @ SV63 @ SY304 @ SY305 )
| ! [SY306: $i] :
( ~ ( product @ SV21 @ SY305 @ SY306 )
| ( product @ SV82 @ SY304 @ SY306 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(346,plain,
! [SV83: $i,SV64: $i,SV22: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ~ ( product @ SV22 @ SV64 @ SV83 )
| ~ ( product @ SV22 @ SY307 @ SY308 )
| ! [SY309: $i] :
( ~ ( sum @ SV64 @ SY307 @ SY309 )
| ! [SY310: $i] :
( ~ ( product @ SV22 @ SY309 @ SY310 )
| ( sum @ SV83 @ SY308 @ SY310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(347,plain,
! [SV84: $i,SV65: $i,SV23: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( product @ SV23 @ SV65 @ SV84 )
| ~ ( product @ SV23 @ SY311 @ SY312 )
| ! [SY313: $i] :
( ~ ( sum @ SV65 @ SY311 @ SY313 )
| ! [SY314: $i] :
( ~ ( sum @ SV84 @ SY312 @ SY314 )
| ( product @ SV23 @ SY313 @ SY314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(348,plain,
! [SV85: $i,SV66: $i,SV24: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ( product @ SV24 @ SV66 @ SV85 )
| ~ ( product @ SY315 @ SV66 @ SY316 )
| ! [SY317: $i] :
( ~ ( sum @ SV24 @ SY315 @ SY317 )
| ! [SY318: $i] :
( ~ ( product @ SY317 @ SV66 @ SY318 )
| ( sum @ SV85 @ SY316 @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(349,plain,
! [SV86: $i,SV67: $i,SV25: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ( product @ SV25 @ SV67 @ SV86 )
| ~ ( product @ SY319 @ SV67 @ SY320 )
| ! [SY321: $i] :
( ~ ( sum @ SV25 @ SY319 @ SY321 )
| ! [SY322: $i] :
( ~ ( sum @ SV86 @ SY320 @ SY322 )
| ( product @ SY321 @ SV67 @ SY322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(350,plain,
! [SV87: $i,SV68: $i,SV28: $i] :
( ( ~ ( sum @ SV28 @ SV68 @ SV87 )
| ! [SY323: $i] :
( ~ ( sum @ SV28 @ SV68 @ SY323 )
| ( equalish @ SV87 @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(351,plain,
! [SV88: $i,SV69: $i,SV29: $i] :
( ( ~ ( product @ SV29 @ SV69 @ SV88 )
| ! [SY324: $i] :
( ~ ( product @ SV29 @ SV69 @ SY324 )
| ( equalish @ SV88 @ SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(352,plain,
! [SV89: $i,SV70: $i,SV30: $i] :
( ( ~ ( sum @ SV30 @ SV70 @ SV89 )
| ! [SY325: $i] :
( ~ ( sum @ SY325 @ SV70 @ SV89 )
| ( equalish @ SY325 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(353,plain,
! [SV90: $i,SV71: $i,SV31: $i] :
( ( ~ ( sum @ SV31 @ SV71 @ SV90 )
| ! [SY326: $i] :
( ~ ( sum @ SV31 @ SY326 @ SV90 )
| ( equalish @ SY326 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(354,plain,
! [SV46: $i,SV1: $i] :
( ( ( equalish @ SV1 @ SV46 )
= $false )
| ( ( ! [SY233: $i] : ( equalish @ ( add @ SV1 @ SY233 ) @ ( add @ SV46 @ SY233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(355,plain,
! [SV47: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV47 )
= $false )
| ( ( ! [SY234: $i] : ( equalish @ ( add @ SY234 @ SV2 ) @ ( add @ SY234 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(356,plain,
! [SV48: $i,SV3: $i] :
( ( ( equalish @ SV3 @ SV48 )
= $false )
| ( ( ! [SY235: $i,SY236: $i] :
( ~ ( sum @ SV3 @ SY235 @ SY236 )
| ( sum @ SV48 @ SY235 @ SY236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(357,plain,
! [SV49: $i,SV4: $i] :
( ( ( equalish @ SV4 @ SV49 )
= $false )
| ( ( ! [SY237: $i,SY238: $i] :
( ~ ( sum @ SY237 @ SV4 @ SY238 )
| ( sum @ SY237 @ SV49 @ SY238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(358,plain,
! [SV50: $i,SV5: $i] :
( ( ( equalish @ SV5 @ SV50 )
= $false )
| ( ( ! [SY239: $i,SY240: $i] :
( ~ ( sum @ SY239 @ SY240 @ SV5 )
| ( sum @ SY239 @ SY240 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(359,plain,
! [SV51: $i,SV6: $i] :
( ( ( equalish @ SV6 @ SV51 )
= $false )
| ( ( ! [SY241: $i] : ( equalish @ ( multiply @ SV6 @ SY241 ) @ ( multiply @ SV51 @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(360,plain,
! [SV52: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV52 )
= $false )
| ( ( ! [SY242: $i] : ( equalish @ ( multiply @ SY242 @ SV7 ) @ ( multiply @ SY242 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(361,plain,
! [SV53: $i,SV8: $i] :
( ( ( equalish @ SV8 @ SV53 )
= $false )
| ( ( ! [SY243: $i,SY244: $i] :
( ~ ( product @ SV8 @ SY243 @ SY244 )
| ( product @ SV53 @ SY243 @ SY244 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(362,plain,
! [SV54: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV54 )
= $false )
| ( ( ! [SY245: $i,SY246: $i] :
( ~ ( product @ SY245 @ SV9 @ SY246 )
| ( product @ SY245 @ SV54 @ SY246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(363,plain,
! [SV55: $i,SV10: $i] :
( ( ( equalish @ SV10 @ SV55 )
= $false )
| ( ( ! [SY247: $i,SY248: $i] :
( ~ ( product @ SY247 @ SY248 @ SV10 )
| ( product @ SY247 @ SY248 @ SV55 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(364,plain,
! [SV56: $i,SV12: $i] :
( ( ( equalish @ SV12 @ SV56 )
= $false )
| ( ( ! [SY249: $i] :
( ~ ( equalish @ SV56 @ SY249 )
| ( equalish @ SV12 @ SY249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(365,plain,
! [SV91: $i,SV78: $i,SV59: $i,SV17: $i] :
( ( ~ ( sum @ SV17 @ SV59 @ SV78 )
| ! [SY327: $i] :
( ~ ( sum @ SV59 @ SV91 @ SY327 )
| ! [SY328: $i] :
( ~ ( sum @ SV78 @ SV91 @ SY328 )
| ( sum @ SV17 @ SY327 @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(366,plain,
! [SV92: $i,SV79: $i,SV60: $i,SV18: $i] :
( ( ~ ( sum @ SV18 @ SV60 @ SV79 )
| ! [SY329: $i] :
( ~ ( sum @ SV60 @ SV92 @ SY329 )
| ! [SY330: $i] :
( ~ ( sum @ SV18 @ SY329 @ SY330 )
| ( sum @ SV79 @ SV92 @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(367,plain,
! [SV80: $i,SV61: $i,SV19: $i] :
( ( ( ~ ( sum @ SV19 @ SV61 @ SV80 ) )
= $true )
| ( ( sum @ SV61 @ SV19 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(368,plain,
! [SV93: $i,SV81: $i,SV62: $i,SV20: $i] :
( ( ~ ( product @ SV20 @ SV62 @ SV81 )
| ! [SY331: $i] :
( ~ ( product @ SV62 @ SV93 @ SY331 )
| ! [SY332: $i] :
( ~ ( product @ SV81 @ SV93 @ SY332 )
| ( product @ SV20 @ SY331 @ SY332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(369,plain,
! [SV94: $i,SV82: $i,SV63: $i,SV21: $i] :
( ( ~ ( product @ SV21 @ SV63 @ SV82 )
| ! [SY333: $i] :
( ~ ( product @ SV63 @ SV94 @ SY333 )
| ! [SY334: $i] :
( ~ ( product @ SV21 @ SY333 @ SY334 )
| ( product @ SV82 @ SV94 @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(370,plain,
! [SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
( ( ! [SY335: $i] :
( ~ ( product @ SV22 @ SV64 @ SV83 )
| ~ ( product @ SV22 @ SV95 @ SY335 )
| ! [SY336: $i] :
( ~ ( sum @ SV64 @ SV95 @ SY336 )
| ! [SY310: $i] :
( ~ ( product @ SV22 @ SY336 @ SY310 )
| ( sum @ SV83 @ SY335 @ SY310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(371,plain,
! [SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
( ( ! [SY338: $i] :
( ~ ( product @ SV23 @ SV65 @ SV84 )
| ~ ( product @ SV23 @ SV96 @ SY338 )
| ! [SY339: $i] :
( ~ ( sum @ SV65 @ SV96 @ SY339 )
| ! [SY314: $i] :
( ~ ( sum @ SV84 @ SY338 @ SY314 )
| ( product @ SV23 @ SY339 @ SY314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(372,plain,
! [SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
( ( ! [SY341: $i] :
( ~ ( product @ SV24 @ SV66 @ SV85 )
| ~ ( product @ SV97 @ SV66 @ SY341 )
| ! [SY342: $i] :
( ~ ( sum @ SV24 @ SV97 @ SY342 )
| ! [SY318: $i] :
( ~ ( product @ SY342 @ SV66 @ SY318 )
| ( sum @ SV85 @ SY341 @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(373,plain,
! [SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
( ( ! [SY344: $i] :
( ~ ( product @ SV25 @ SV67 @ SV86 )
| ~ ( product @ SV98 @ SV67 @ SY344 )
| ! [SY345: $i] :
( ~ ( sum @ SV25 @ SV98 @ SY345 )
| ! [SY322: $i] :
( ~ ( sum @ SV86 @ SY344 @ SY322 )
| ( product @ SY345 @ SV67 @ SY322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(374,plain,
! [SV87: $i,SV68: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV68 @ SV87 ) )
= $true )
| ( ( ! [SY323: $i] :
( ~ ( sum @ SV28 @ SV68 @ SY323 )
| ( equalish @ SV87 @ SY323 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(375,plain,
! [SV88: $i,SV69: $i,SV29: $i] :
( ( ( ~ ( product @ SV29 @ SV69 @ SV88 ) )
= $true )
| ( ( ! [SY324: $i] :
( ~ ( product @ SV29 @ SV69 @ SY324 )
| ( equalish @ SV88 @ SY324 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(376,plain,
! [SV89: $i,SV70: $i,SV30: $i] :
( ( ( ~ ( sum @ SV30 @ SV70 @ SV89 ) )
= $true )
| ( ( ! [SY325: $i] :
( ~ ( sum @ SY325 @ SV70 @ SV89 )
| ( equalish @ SY325 @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(377,plain,
! [SV90: $i,SV71: $i,SV31: $i] :
( ( ( ~ ( sum @ SV31 @ SV71 @ SV90 ) )
= $true )
| ( ( ! [SY326: $i] :
( ~ ( sum @ SV31 @ SY326 @ SV90 )
| ( equalish @ SY326 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(378,plain,
! [SV46: $i,SV99: $i,SV1: $i] :
( ( ( equalish @ ( add @ SV1 @ SV99 ) @ ( add @ SV46 @ SV99 ) )
= $true )
| ( ( equalish @ SV1 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(379,plain,
! [SV47: $i,SV2: $i,SV100: $i] :
( ( ( equalish @ ( add @ SV100 @ SV2 ) @ ( add @ SV100 @ SV47 ) )
= $true )
| ( ( equalish @ SV2 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(380,plain,
! [SV48: $i,SV101: $i,SV3: $i] :
( ( ( ! [SY347: $i] :
( ~ ( sum @ SV3 @ SV101 @ SY347 )
| ( sum @ SV48 @ SV101 @ SY347 ) ) )
= $true )
| ( ( equalish @ SV3 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(381,plain,
! [SV49: $i,SV4: $i,SV102: $i] :
( ( ( ! [SY348: $i] :
( ~ ( sum @ SV102 @ SV4 @ SY348 )
| ( sum @ SV102 @ SV49 @ SY348 ) ) )
= $true )
| ( ( equalish @ SV4 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(382,plain,
! [SV50: $i,SV5: $i,SV103: $i] :
( ( ( ! [SY349: $i] :
( ~ ( sum @ SV103 @ SY349 @ SV5 )
| ( sum @ SV103 @ SY349 @ SV50 ) ) )
= $true )
| ( ( equalish @ SV5 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(383,plain,
! [SV51: $i,SV104: $i,SV6: $i] :
( ( ( equalish @ ( multiply @ SV6 @ SV104 ) @ ( multiply @ SV51 @ SV104 ) )
= $true )
| ( ( equalish @ SV6 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(384,plain,
! [SV52: $i,SV7: $i,SV105: $i] :
( ( ( equalish @ ( multiply @ SV105 @ SV7 ) @ ( multiply @ SV105 @ SV52 ) )
= $true )
| ( ( equalish @ SV7 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(385,plain,
! [SV53: $i,SV106: $i,SV8: $i] :
( ( ( ! [SY350: $i] :
( ~ ( product @ SV8 @ SV106 @ SY350 )
| ( product @ SV53 @ SV106 @ SY350 ) ) )
= $true )
| ( ( equalish @ SV8 @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(386,plain,
! [SV54: $i,SV9: $i,SV107: $i] :
( ( ( ! [SY351: $i] :
( ~ ( product @ SV107 @ SV9 @ SY351 )
| ( product @ SV107 @ SV54 @ SY351 ) ) )
= $true )
| ( ( equalish @ SV9 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(387,plain,
! [SV55: $i,SV10: $i,SV108: $i] :
( ( ( ! [SY352: $i] :
( ~ ( product @ SV108 @ SY352 @ SV10 )
| ( product @ SV108 @ SY352 @ SV55 ) ) )
= $true )
| ( ( equalish @ SV10 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(388,plain,
! [SV12: $i,SV109: $i,SV56: $i] :
( ( ( ~ ( equalish @ SV56 @ SV109 )
| ( equalish @ SV12 @ SV109 ) )
= $true )
| ( ( equalish @ SV12 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(389,plain,
! [SV91: $i,SV78: $i,SV59: $i,SV17: $i] :
( ( ( ~ ( sum @ SV17 @ SV59 @ SV78 ) )
= $true )
| ( ( ! [SY327: $i] :
( ~ ( sum @ SV59 @ SV91 @ SY327 )
| ! [SY328: $i] :
( ~ ( sum @ SV78 @ SV91 @ SY328 )
| ( sum @ SV17 @ SY327 @ SY328 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(390,plain,
! [SV92: $i,SV79: $i,SV60: $i,SV18: $i] :
( ( ( ~ ( sum @ SV18 @ SV60 @ SV79 ) )
= $true )
| ( ( ! [SY329: $i] :
( ~ ( sum @ SV60 @ SV92 @ SY329 )
| ! [SY330: $i] :
( ~ ( sum @ SV18 @ SY329 @ SY330 )
| ( sum @ SV79 @ SV92 @ SY330 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(391,plain,
! [SV80: $i,SV61: $i,SV19: $i] :
( ( ( sum @ SV19 @ SV61 @ SV80 )
= $false )
| ( ( sum @ SV61 @ SV19 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(392,plain,
! [SV93: $i,SV81: $i,SV62: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV62 @ SV81 ) )
= $true )
| ( ( ! [SY331: $i] :
( ~ ( product @ SV62 @ SV93 @ SY331 )
| ! [SY332: $i] :
( ~ ( product @ SV81 @ SV93 @ SY332 )
| ( product @ SV20 @ SY331 @ SY332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(393,plain,
! [SV94: $i,SV82: $i,SV63: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV63 @ SV82 ) )
= $true )
| ( ( ! [SY333: $i] :
( ~ ( product @ SV63 @ SV94 @ SY333 )
| ! [SY334: $i] :
( ~ ( product @ SV21 @ SY333 @ SY334 )
| ( product @ SV82 @ SV94 @ SY334 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(394,plain,
! [SV110: $i,SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
( ( ~ ( product @ SV22 @ SV64 @ SV83 )
| ~ ( product @ SV22 @ SV95 @ SV110 )
| ! [SY353: $i] :
( ~ ( sum @ SV64 @ SV95 @ SY353 )
| ! [SY354: $i] :
( ~ ( product @ SV22 @ SY353 @ SY354 )
| ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(395,plain,
! [SV111: $i,SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
( ( ~ ( product @ SV23 @ SV65 @ SV84 )
| ~ ( product @ SV23 @ SV96 @ SV111 )
| ! [SY355: $i] :
( ~ ( sum @ SV65 @ SV96 @ SY355 )
| ! [SY356: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY356 )
| ( product @ SV23 @ SY355 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(396,plain,
! [SV112: $i,SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
( ( ~ ( product @ SV24 @ SV66 @ SV85 )
| ~ ( product @ SV97 @ SV66 @ SV112 )
| ! [SY357: $i] :
( ~ ( sum @ SV24 @ SV97 @ SY357 )
| ! [SY358: $i] :
( ~ ( product @ SY357 @ SV66 @ SY358 )
| ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(397,plain,
! [SV113: $i,SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
( ( ~ ( product @ SV25 @ SV67 @ SV86 )
| ~ ( product @ SV98 @ SV67 @ SV113 )
| ! [SY359: $i] :
( ~ ( sum @ SV25 @ SV98 @ SY359 )
| ! [SY360: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY360 )
| ( product @ SY359 @ SV67 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(398,plain,
! [SV87: $i,SV68: $i,SV28: $i] :
( ( ( sum @ SV28 @ SV68 @ SV87 )
= $false )
| ( ( ! [SY323: $i] :
( ~ ( sum @ SV28 @ SV68 @ SY323 )
| ( equalish @ SV87 @ SY323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(399,plain,
! [SV88: $i,SV69: $i,SV29: $i] :
( ( ( product @ SV29 @ SV69 @ SV88 )
= $false )
| ( ( ! [SY324: $i] :
( ~ ( product @ SV29 @ SV69 @ SY324 )
| ( equalish @ SV88 @ SY324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(400,plain,
! [SV89: $i,SV70: $i,SV30: $i] :
( ( ( sum @ SV30 @ SV70 @ SV89 )
= $false )
| ( ( ! [SY325: $i] :
( ~ ( sum @ SY325 @ SV70 @ SV89 )
| ( equalish @ SY325 @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(401,plain,
! [SV90: $i,SV71: $i,SV31: $i] :
( ( ( sum @ SV31 @ SV71 @ SV90 )
= $false )
| ( ( ! [SY326: $i] :
( ~ ( sum @ SV31 @ SY326 @ SV90 )
| ( equalish @ SY326 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(402,plain,
! [SV48: $i,SV114: $i,SV101: $i,SV3: $i] :
( ( ( ~ ( sum @ SV3 @ SV101 @ SV114 )
| ( sum @ SV48 @ SV101 @ SV114 ) )
= $true )
| ( ( equalish @ SV3 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(403,plain,
! [SV49: $i,SV115: $i,SV4: $i,SV102: $i] :
( ( ( ~ ( sum @ SV102 @ SV4 @ SV115 )
| ( sum @ SV102 @ SV49 @ SV115 ) )
= $true )
| ( ( equalish @ SV4 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(404,plain,
! [SV50: $i,SV5: $i,SV116: $i,SV103: $i] :
( ( ( ~ ( sum @ SV103 @ SV116 @ SV5 )
| ( sum @ SV103 @ SV116 @ SV50 ) )
= $true )
| ( ( equalish @ SV5 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(405,plain,
! [SV53: $i,SV117: $i,SV106: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV106 @ SV117 )
| ( product @ SV53 @ SV106 @ SV117 ) )
= $true )
| ( ( equalish @ SV8 @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(406,plain,
! [SV54: $i,SV118: $i,SV9: $i,SV107: $i] :
( ( ( ~ ( product @ SV107 @ SV9 @ SV118 )
| ( product @ SV107 @ SV54 @ SV118 ) )
= $true )
| ( ( equalish @ SV9 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(407,plain,
! [SV55: $i,SV10: $i,SV119: $i,SV108: $i] :
( ( ( ~ ( product @ SV108 @ SV119 @ SV10 )
| ( product @ SV108 @ SV119 @ SV55 ) )
= $true )
| ( ( equalish @ SV10 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(408,plain,
! [SV12: $i,SV109: $i,SV56: $i] :
( ( ( ~ ( equalish @ SV56 @ SV109 ) )
= $true )
| ( ( equalish @ SV12 @ SV109 )
= $true )
| ( ( equalish @ SV12 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(409,plain,
! [SV91: $i,SV78: $i,SV59: $i,SV17: $i] :
( ( ( sum @ SV17 @ SV59 @ SV78 )
= $false )
| ( ( ! [SY327: $i] :
( ~ ( sum @ SV59 @ SV91 @ SY327 )
| ! [SY328: $i] :
( ~ ( sum @ SV78 @ SV91 @ SY328 )
| ( sum @ SV17 @ SY327 @ SY328 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(410,plain,
! [SV92: $i,SV79: $i,SV60: $i,SV18: $i] :
( ( ( sum @ SV18 @ SV60 @ SV79 )
= $false )
| ( ( ! [SY329: $i] :
( ~ ( sum @ SV60 @ SV92 @ SY329 )
| ! [SY330: $i] :
( ~ ( sum @ SV18 @ SY329 @ SY330 )
| ( sum @ SV79 @ SV92 @ SY330 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(411,plain,
! [SV93: $i,SV81: $i,SV62: $i,SV20: $i] :
( ( ( product @ SV20 @ SV62 @ SV81 )
= $false )
| ( ( ! [SY331: $i] :
( ~ ( product @ SV62 @ SV93 @ SY331 )
| ! [SY332: $i] :
( ~ ( product @ SV81 @ SV93 @ SY332 )
| ( product @ SV20 @ SY331 @ SY332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(412,plain,
! [SV94: $i,SV82: $i,SV63: $i,SV21: $i] :
( ( ( product @ SV21 @ SV63 @ SV82 )
= $false )
| ( ( ! [SY333: $i] :
( ~ ( product @ SV63 @ SV94 @ SY333 )
| ! [SY334: $i] :
( ~ ( product @ SV21 @ SY333 @ SY334 )
| ( product @ SV82 @ SV94 @ SY334 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(413,plain,
! [SV110: $i,SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV64 @ SV83 ) )
= $true )
| ( ( ~ ( product @ SV22 @ SV95 @ SV110 )
| ! [SY353: $i] :
( ~ ( sum @ SV64 @ SV95 @ SY353 )
| ! [SY354: $i] :
( ~ ( product @ SV22 @ SY353 @ SY354 )
| ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(414,plain,
! [SV111: $i,SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
( ( ( ~ ( product @ SV23 @ SV65 @ SV84 ) )
= $true )
| ( ( ~ ( product @ SV23 @ SV96 @ SV111 )
| ! [SY355: $i] :
( ~ ( sum @ SV65 @ SV96 @ SY355 )
| ! [SY356: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY356 )
| ( product @ SV23 @ SY355 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(415,plain,
! [SV112: $i,SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
( ( ( ~ ( product @ SV24 @ SV66 @ SV85 ) )
= $true )
| ( ( ~ ( product @ SV97 @ SV66 @ SV112 )
| ! [SY357: $i] :
( ~ ( sum @ SV24 @ SV97 @ SY357 )
| ! [SY358: $i] :
( ~ ( product @ SY357 @ SV66 @ SY358 )
| ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(416,plain,
! [SV113: $i,SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
( ( ( ~ ( product @ SV25 @ SV67 @ SV86 ) )
= $true )
| ( ( ~ ( product @ SV98 @ SV67 @ SV113 )
| ! [SY359: $i] :
( ~ ( sum @ SV25 @ SV98 @ SY359 )
| ! [SY360: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY360 )
| ( product @ SY359 @ SV67 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(417,plain,
! [SV87: $i,SV120: $i,SV68: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV68 @ SV120 )
| ( equalish @ SV87 @ SV120 ) )
= $true )
| ( ( sum @ SV28 @ SV68 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(418,plain,
! [SV88: $i,SV121: $i,SV69: $i,SV29: $i] :
( ( ( ~ ( product @ SV29 @ SV69 @ SV121 )
| ( equalish @ SV88 @ SV121 ) )
= $true )
| ( ( product @ SV29 @ SV69 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(419,plain,
! [SV30: $i,SV89: $i,SV70: $i,SV122: $i] :
( ( ( ~ ( sum @ SV122 @ SV70 @ SV89 )
| ( equalish @ SV122 @ SV30 ) )
= $true )
| ( ( sum @ SV30 @ SV70 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(420,plain,
! [SV71: $i,SV90: $i,SV123: $i,SV31: $i] :
( ( ( ~ ( sum @ SV31 @ SV123 @ SV90 )
| ( equalish @ SV123 @ SV71 ) )
= $true )
| ( ( sum @ SV31 @ SV71 @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(421,plain,
! [SV48: $i,SV114: $i,SV101: $i,SV3: $i] :
( ( ( ~ ( sum @ SV3 @ SV101 @ SV114 ) )
= $true )
| ( ( sum @ SV48 @ SV101 @ SV114 )
= $true )
| ( ( equalish @ SV3 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(422,plain,
! [SV49: $i,SV115: $i,SV4: $i,SV102: $i] :
( ( ( ~ ( sum @ SV102 @ SV4 @ SV115 ) )
= $true )
| ( ( sum @ SV102 @ SV49 @ SV115 )
= $true )
| ( ( equalish @ SV4 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(423,plain,
! [SV50: $i,SV5: $i,SV116: $i,SV103: $i] :
( ( ( ~ ( sum @ SV103 @ SV116 @ SV5 ) )
= $true )
| ( ( sum @ SV103 @ SV116 @ SV50 )
= $true )
| ( ( equalish @ SV5 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(424,plain,
! [SV53: $i,SV117: $i,SV106: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV106 @ SV117 ) )
= $true )
| ( ( product @ SV53 @ SV106 @ SV117 )
= $true )
| ( ( equalish @ SV8 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(425,plain,
! [SV54: $i,SV118: $i,SV9: $i,SV107: $i] :
( ( ( ~ ( product @ SV107 @ SV9 @ SV118 ) )
= $true )
| ( ( product @ SV107 @ SV54 @ SV118 )
= $true )
| ( ( equalish @ SV9 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(426,plain,
! [SV55: $i,SV10: $i,SV119: $i,SV108: $i] :
( ( ( ~ ( product @ SV108 @ SV119 @ SV10 ) )
= $true )
| ( ( product @ SV108 @ SV119 @ SV55 )
= $true )
| ( ( equalish @ SV10 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(427,plain,
! [SV12: $i,SV109: $i,SV56: $i] :
( ( ( equalish @ SV56 @ SV109 )
= $false )
| ( ( equalish @ SV12 @ SV109 )
= $true )
| ( ( equalish @ SV12 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(428,plain,
! [SV17: $i,SV78: $i,SV124: $i,SV91: $i,SV59: $i] :
( ( ( ~ ( sum @ SV59 @ SV91 @ SV124 )
| ! [SY361: $i] :
( ~ ( sum @ SV78 @ SV91 @ SY361 )
| ( sum @ SV17 @ SV124 @ SY361 ) ) )
= $true )
| ( ( sum @ SV17 @ SV59 @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(429,plain,
! [SV79: $i,SV18: $i,SV125: $i,SV92: $i,SV60: $i] :
( ( ( ~ ( sum @ SV60 @ SV92 @ SV125 )
| ! [SY362: $i] :
( ~ ( sum @ SV18 @ SV125 @ SY362 )
| ( sum @ SV79 @ SV92 @ SY362 ) ) )
= $true )
| ( ( sum @ SV18 @ SV60 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(430,plain,
! [SV20: $i,SV81: $i,SV126: $i,SV93: $i,SV62: $i] :
( ( ( ~ ( product @ SV62 @ SV93 @ SV126 )
| ! [SY363: $i] :
( ~ ( product @ SV81 @ SV93 @ SY363 )
| ( product @ SV20 @ SV126 @ SY363 ) ) )
= $true )
| ( ( product @ SV20 @ SV62 @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(431,plain,
! [SV82: $i,SV21: $i,SV127: $i,SV94: $i,SV63: $i] :
( ( ( ~ ( product @ SV63 @ SV94 @ SV127 )
| ! [SY364: $i] :
( ~ ( product @ SV21 @ SV127 @ SY364 )
| ( product @ SV82 @ SV94 @ SY364 ) ) )
= $true )
| ( ( product @ SV21 @ SV63 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(432,plain,
! [SV110: $i,SV95: $i,SV83: $i,SV64: $i,SV22: $i] :
( ( ( product @ SV22 @ SV64 @ SV83 )
= $false )
| ( ( ~ ( product @ SV22 @ SV95 @ SV110 )
| ! [SY353: $i] :
( ~ ( sum @ SV64 @ SV95 @ SY353 )
| ! [SY354: $i] :
( ~ ( product @ SV22 @ SY353 @ SY354 )
| ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(433,plain,
! [SV111: $i,SV96: $i,SV84: $i,SV65: $i,SV23: $i] :
( ( ( product @ SV23 @ SV65 @ SV84 )
= $false )
| ( ( ~ ( product @ SV23 @ SV96 @ SV111 )
| ! [SY355: $i] :
( ~ ( sum @ SV65 @ SV96 @ SY355 )
| ! [SY356: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY356 )
| ( product @ SV23 @ SY355 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(434,plain,
! [SV112: $i,SV97: $i,SV85: $i,SV66: $i,SV24: $i] :
( ( ( product @ SV24 @ SV66 @ SV85 )
= $false )
| ( ( ~ ( product @ SV97 @ SV66 @ SV112 )
| ! [SY357: $i] :
( ~ ( sum @ SV24 @ SV97 @ SY357 )
| ! [SY358: $i] :
( ~ ( product @ SY357 @ SV66 @ SY358 )
| ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(435,plain,
! [SV113: $i,SV98: $i,SV86: $i,SV67: $i,SV25: $i] :
( ( ( product @ SV25 @ SV67 @ SV86 )
= $false )
| ( ( ~ ( product @ SV98 @ SV67 @ SV113 )
| ! [SY359: $i] :
( ~ ( sum @ SV25 @ SV98 @ SY359 )
| ! [SY360: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY360 )
| ( product @ SY359 @ SV67 @ SY360 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(436,plain,
! [SV87: $i,SV120: $i,SV68: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV68 @ SV120 ) )
= $true )
| ( ( equalish @ SV87 @ SV120 )
= $true )
| ( ( sum @ SV28 @ SV68 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(437,plain,
! [SV88: $i,SV121: $i,SV69: $i,SV29: $i] :
( ( ( ~ ( product @ SV29 @ SV69 @ SV121 ) )
= $true )
| ( ( equalish @ SV88 @ SV121 )
= $true )
| ( ( product @ SV29 @ SV69 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(438,plain,
! [SV30: $i,SV89: $i,SV70: $i,SV122: $i] :
( ( ( ~ ( sum @ SV122 @ SV70 @ SV89 ) )
= $true )
| ( ( equalish @ SV122 @ SV30 )
= $true )
| ( ( sum @ SV30 @ SV70 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(439,plain,
! [SV71: $i,SV90: $i,SV123: $i,SV31: $i] :
( ( ( ~ ( sum @ SV31 @ SV123 @ SV90 ) )
= $true )
| ( ( equalish @ SV123 @ SV71 )
= $true )
| ( ( sum @ SV31 @ SV71 @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(440,plain,
! [SV48: $i,SV114: $i,SV101: $i,SV3: $i] :
( ( ( sum @ SV3 @ SV101 @ SV114 )
= $false )
| ( ( sum @ SV48 @ SV101 @ SV114 )
= $true )
| ( ( equalish @ SV3 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(441,plain,
! [SV49: $i,SV115: $i,SV4: $i,SV102: $i] :
( ( ( sum @ SV102 @ SV4 @ SV115 )
= $false )
| ( ( sum @ SV102 @ SV49 @ SV115 )
= $true )
| ( ( equalish @ SV4 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(442,plain,
! [SV50: $i,SV5: $i,SV116: $i,SV103: $i] :
( ( ( sum @ SV103 @ SV116 @ SV5 )
= $false )
| ( ( sum @ SV103 @ SV116 @ SV50 )
= $true )
| ( ( equalish @ SV5 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(443,plain,
! [SV53: $i,SV117: $i,SV106: $i,SV8: $i] :
( ( ( product @ SV8 @ SV106 @ SV117 )
= $false )
| ( ( product @ SV53 @ SV106 @ SV117 )
= $true )
| ( ( equalish @ SV8 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(444,plain,
! [SV54: $i,SV118: $i,SV9: $i,SV107: $i] :
( ( ( product @ SV107 @ SV9 @ SV118 )
= $false )
| ( ( product @ SV107 @ SV54 @ SV118 )
= $true )
| ( ( equalish @ SV9 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(445,plain,
! [SV55: $i,SV10: $i,SV119: $i,SV108: $i] :
( ( ( product @ SV108 @ SV119 @ SV10 )
= $false )
| ( ( product @ SV108 @ SV119 @ SV55 )
= $true )
| ( ( equalish @ SV10 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(446,plain,
! [SV17: $i,SV78: $i,SV124: $i,SV91: $i,SV59: $i] :
( ( ( ~ ( sum @ SV59 @ SV91 @ SV124 ) )
= $true )
| ( ( ! [SY361: $i] :
( ~ ( sum @ SV78 @ SV91 @ SY361 )
| ( sum @ SV17 @ SV124 @ SY361 ) ) )
= $true )
| ( ( sum @ SV17 @ SV59 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(447,plain,
! [SV79: $i,SV18: $i,SV125: $i,SV92: $i,SV60: $i] :
( ( ( ~ ( sum @ SV60 @ SV92 @ SV125 ) )
= $true )
| ( ( ! [SY362: $i] :
( ~ ( sum @ SV18 @ SV125 @ SY362 )
| ( sum @ SV79 @ SV92 @ SY362 ) ) )
= $true )
| ( ( sum @ SV18 @ SV60 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(448,plain,
! [SV20: $i,SV81: $i,SV126: $i,SV93: $i,SV62: $i] :
( ( ( ~ ( product @ SV62 @ SV93 @ SV126 ) )
= $true )
| ( ( ! [SY363: $i] :
( ~ ( product @ SV81 @ SV93 @ SY363 )
| ( product @ SV20 @ SV126 @ SY363 ) ) )
= $true )
| ( ( product @ SV20 @ SV62 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(449,plain,
! [SV82: $i,SV21: $i,SV127: $i,SV94: $i,SV63: $i] :
( ( ( ~ ( product @ SV63 @ SV94 @ SV127 ) )
= $true )
| ( ( ! [SY364: $i] :
( ~ ( product @ SV21 @ SV127 @ SY364 )
| ( product @ SV82 @ SV94 @ SY364 ) ) )
= $true )
| ( ( product @ SV21 @ SV63 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(450,plain,
! [SV83: $i,SV64: $i,SV110: $i,SV95: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV95 @ SV110 ) )
= $true )
| ( ( ! [SY353: $i] :
( ~ ( sum @ SV64 @ SV95 @ SY353 )
| ! [SY354: $i] :
( ~ ( product @ SV22 @ SY353 @ SY354 )
| ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
= $true )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(451,plain,
! [SV84: $i,SV65: $i,SV111: $i,SV96: $i,SV23: $i] :
( ( ( ~ ( product @ SV23 @ SV96 @ SV111 ) )
= $true )
| ( ( ! [SY355: $i] :
( ~ ( sum @ SV65 @ SV96 @ SY355 )
| ! [SY356: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY356 )
| ( product @ SV23 @ SY355 @ SY356 ) ) ) )
= $true )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(452,plain,
! [SV85: $i,SV24: $i,SV112: $i,SV66: $i,SV97: $i] :
( ( ( ~ ( product @ SV97 @ SV66 @ SV112 ) )
= $true )
| ( ( ! [SY357: $i] :
( ~ ( sum @ SV24 @ SV97 @ SY357 )
| ! [SY358: $i] :
( ~ ( product @ SY357 @ SV66 @ SY358 )
| ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
= $true )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(453,plain,
! [SV86: $i,SV25: $i,SV113: $i,SV67: $i,SV98: $i] :
( ( ( ~ ( product @ SV98 @ SV67 @ SV113 ) )
= $true )
| ( ( ! [SY359: $i] :
( ~ ( sum @ SV25 @ SV98 @ SY359 )
| ! [SY360: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY360 )
| ( product @ SY359 @ SV67 @ SY360 ) ) ) )
= $true )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(454,plain,
! [SV87: $i,SV120: $i,SV68: $i,SV28: $i] :
( ( ( sum @ SV28 @ SV68 @ SV120 )
= $false )
| ( ( equalish @ SV87 @ SV120 )
= $true )
| ( ( sum @ SV28 @ SV68 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(455,plain,
! [SV88: $i,SV121: $i,SV69: $i,SV29: $i] :
( ( ( product @ SV29 @ SV69 @ SV121 )
= $false )
| ( ( equalish @ SV88 @ SV121 )
= $true )
| ( ( product @ SV29 @ SV69 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(456,plain,
! [SV30: $i,SV89: $i,SV70: $i,SV122: $i] :
( ( ( sum @ SV122 @ SV70 @ SV89 )
= $false )
| ( ( equalish @ SV122 @ SV30 )
= $true )
| ( ( sum @ SV30 @ SV70 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(457,plain,
! [SV71: $i,SV90: $i,SV123: $i,SV31: $i] :
( ( ( sum @ SV31 @ SV123 @ SV90 )
= $false )
| ( ( equalish @ SV123 @ SV71 )
= $true )
| ( ( sum @ SV31 @ SV71 @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(458,plain,
! [SV17: $i,SV78: $i,SV124: $i,SV91: $i,SV59: $i] :
( ( ( sum @ SV59 @ SV91 @ SV124 )
= $false )
| ( ( ! [SY361: $i] :
( ~ ( sum @ SV78 @ SV91 @ SY361 )
| ( sum @ SV17 @ SV124 @ SY361 ) ) )
= $true )
| ( ( sum @ SV17 @ SV59 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(459,plain,
! [SV79: $i,SV18: $i,SV125: $i,SV92: $i,SV60: $i] :
( ( ( sum @ SV60 @ SV92 @ SV125 )
= $false )
| ( ( ! [SY362: $i] :
( ~ ( sum @ SV18 @ SV125 @ SY362 )
| ( sum @ SV79 @ SV92 @ SY362 ) ) )
= $true )
| ( ( sum @ SV18 @ SV60 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(460,plain,
! [SV20: $i,SV81: $i,SV126: $i,SV93: $i,SV62: $i] :
( ( ( product @ SV62 @ SV93 @ SV126 )
= $false )
| ( ( ! [SY363: $i] :
( ~ ( product @ SV81 @ SV93 @ SY363 )
| ( product @ SV20 @ SV126 @ SY363 ) ) )
= $true )
| ( ( product @ SV20 @ SV62 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(461,plain,
! [SV82: $i,SV21: $i,SV127: $i,SV94: $i,SV63: $i] :
( ( ( product @ SV63 @ SV94 @ SV127 )
= $false )
| ( ( ! [SY364: $i] :
( ~ ( product @ SV21 @ SV127 @ SY364 )
| ( product @ SV82 @ SV94 @ SY364 ) ) )
= $true )
| ( ( product @ SV21 @ SV63 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(462,plain,
! [SV83: $i,SV64: $i,SV110: $i,SV95: $i,SV22: $i] :
( ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( ! [SY353: $i] :
( ~ ( sum @ SV64 @ SV95 @ SY353 )
| ! [SY354: $i] :
( ~ ( product @ SV22 @ SY353 @ SY354 )
| ( sum @ SV83 @ SV110 @ SY354 ) ) ) )
= $true )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(463,plain,
! [SV84: $i,SV65: $i,SV111: $i,SV96: $i,SV23: $i] :
( ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( ! [SY355: $i] :
( ~ ( sum @ SV65 @ SV96 @ SY355 )
| ! [SY356: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY356 )
| ( product @ SV23 @ SY355 @ SY356 ) ) ) )
= $true )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(464,plain,
! [SV85: $i,SV24: $i,SV112: $i,SV66: $i,SV97: $i] :
( ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( ! [SY357: $i] :
( ~ ( sum @ SV24 @ SV97 @ SY357 )
| ! [SY358: $i] :
( ~ ( product @ SY357 @ SV66 @ SY358 )
| ( sum @ SV85 @ SV112 @ SY358 ) ) ) )
= $true )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(465,plain,
! [SV86: $i,SV25: $i,SV113: $i,SV67: $i,SV98: $i] :
( ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( ! [SY359: $i] :
( ~ ( sum @ SV25 @ SV98 @ SY359 )
| ! [SY360: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY360 )
| ( product @ SY359 @ SV67 @ SY360 ) ) ) )
= $true )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(466,plain,
! [SV59: $i,SV124: $i,SV17: $i,SV128: $i,SV91: $i,SV78: $i] :
( ( ( ~ ( sum @ SV78 @ SV91 @ SV128 )
| ( sum @ SV17 @ SV124 @ SV128 ) )
= $true )
| ( ( sum @ SV59 @ SV91 @ SV124 )
= $false )
| ( ( sum @ SV17 @ SV59 @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(467,plain,
! [SV60: $i,SV92: $i,SV79: $i,SV129: $i,SV125: $i,SV18: $i] :
( ( ( ~ ( sum @ SV18 @ SV125 @ SV129 )
| ( sum @ SV79 @ SV92 @ SV129 ) )
= $true )
| ( ( sum @ SV60 @ SV92 @ SV125 )
= $false )
| ( ( sum @ SV18 @ SV60 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(468,plain,
! [SV62: $i,SV126: $i,SV20: $i,SV130: $i,SV93: $i,SV81: $i] :
( ( ( ~ ( product @ SV81 @ SV93 @ SV130 )
| ( product @ SV20 @ SV126 @ SV130 ) )
= $true )
| ( ( product @ SV62 @ SV93 @ SV126 )
= $false )
| ( ( product @ SV20 @ SV62 @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(469,plain,
! [SV63: $i,SV94: $i,SV82: $i,SV131: $i,SV127: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV127 @ SV131 )
| ( product @ SV82 @ SV94 @ SV131 ) )
= $true )
| ( ( product @ SV63 @ SV94 @ SV127 )
= $false )
| ( ( product @ SV21 @ SV63 @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(470,plain,
! [SV110: $i,SV83: $i,SV22: $i,SV132: $i,SV95: $i,SV64: $i] :
( ( ( ~ ( sum @ SV64 @ SV95 @ SV132 )
| ! [SY365: $i] :
( ~ ( product @ SV22 @ SV132 @ SY365 )
| ( sum @ SV83 @ SV110 @ SY365 ) ) )
= $true )
| ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(471,plain,
! [SV23: $i,SV111: $i,SV84: $i,SV133: $i,SV96: $i,SV65: $i] :
( ( ( ~ ( sum @ SV65 @ SV96 @ SV133 )
| ! [SY366: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY366 )
| ( product @ SV23 @ SV133 @ SY366 ) ) )
= $true )
| ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(472,plain,
! [SV112: $i,SV85: $i,SV66: $i,SV134: $i,SV97: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV97 @ SV134 )
| ! [SY367: $i] :
( ~ ( product @ SV134 @ SV66 @ SY367 )
| ( sum @ SV85 @ SV112 @ SY367 ) ) )
= $true )
| ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(473,plain,
! [SV67: $i,SV113: $i,SV86: $i,SV135: $i,SV98: $i,SV25: $i] :
( ( ( ~ ( sum @ SV25 @ SV98 @ SV135 )
| ! [SY368: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY368 )
| ( product @ SV135 @ SV67 @ SY368 ) ) )
= $true )
| ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(474,plain,
! [SV59: $i,SV124: $i,SV17: $i,SV128: $i,SV91: $i,SV78: $i] :
( ( ( ~ ( sum @ SV78 @ SV91 @ SV128 ) )
= $true )
| ( ( sum @ SV17 @ SV124 @ SV128 )
= $true )
| ( ( sum @ SV59 @ SV91 @ SV124 )
= $false )
| ( ( sum @ SV17 @ SV59 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(475,plain,
! [SV60: $i,SV92: $i,SV79: $i,SV129: $i,SV125: $i,SV18: $i] :
( ( ( ~ ( sum @ SV18 @ SV125 @ SV129 ) )
= $true )
| ( ( sum @ SV79 @ SV92 @ SV129 )
= $true )
| ( ( sum @ SV60 @ SV92 @ SV125 )
= $false )
| ( ( sum @ SV18 @ SV60 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(476,plain,
! [SV62: $i,SV126: $i,SV20: $i,SV130: $i,SV93: $i,SV81: $i] :
( ( ( ~ ( product @ SV81 @ SV93 @ SV130 ) )
= $true )
| ( ( product @ SV20 @ SV126 @ SV130 )
= $true )
| ( ( product @ SV62 @ SV93 @ SV126 )
= $false )
| ( ( product @ SV20 @ SV62 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(477,plain,
! [SV63: $i,SV94: $i,SV82: $i,SV131: $i,SV127: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV127 @ SV131 ) )
= $true )
| ( ( product @ SV82 @ SV94 @ SV131 )
= $true )
| ( ( product @ SV63 @ SV94 @ SV127 )
= $false )
| ( ( product @ SV21 @ SV63 @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(478,plain,
! [SV110: $i,SV83: $i,SV22: $i,SV132: $i,SV95: $i,SV64: $i] :
( ( ( ~ ( sum @ SV64 @ SV95 @ SV132 ) )
= $true )
| ( ( ! [SY365: $i] :
( ~ ( product @ SV22 @ SV132 @ SY365 )
| ( sum @ SV83 @ SV110 @ SY365 ) ) )
= $true )
| ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(479,plain,
! [SV23: $i,SV111: $i,SV84: $i,SV133: $i,SV96: $i,SV65: $i] :
( ( ( ~ ( sum @ SV65 @ SV96 @ SV133 ) )
= $true )
| ( ( ! [SY366: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY366 )
| ( product @ SV23 @ SV133 @ SY366 ) ) )
= $true )
| ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(480,plain,
! [SV112: $i,SV85: $i,SV66: $i,SV134: $i,SV97: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV97 @ SV134 ) )
= $true )
| ( ( ! [SY367: $i] :
( ~ ( product @ SV134 @ SV66 @ SY367 )
| ( sum @ SV85 @ SV112 @ SY367 ) ) )
= $true )
| ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(481,plain,
! [SV67: $i,SV113: $i,SV86: $i,SV135: $i,SV98: $i,SV25: $i] :
( ( ( ~ ( sum @ SV25 @ SV98 @ SV135 ) )
= $true )
| ( ( ! [SY368: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY368 )
| ( product @ SV135 @ SV67 @ SY368 ) ) )
= $true )
| ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(482,plain,
! [SV59: $i,SV124: $i,SV17: $i,SV128: $i,SV91: $i,SV78: $i] :
( ( ( sum @ SV78 @ SV91 @ SV128 )
= $false )
| ( ( sum @ SV17 @ SV124 @ SV128 )
= $true )
| ( ( sum @ SV59 @ SV91 @ SV124 )
= $false )
| ( ( sum @ SV17 @ SV59 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(483,plain,
! [SV60: $i,SV92: $i,SV79: $i,SV129: $i,SV125: $i,SV18: $i] :
( ( ( sum @ SV18 @ SV125 @ SV129 )
= $false )
| ( ( sum @ SV79 @ SV92 @ SV129 )
= $true )
| ( ( sum @ SV60 @ SV92 @ SV125 )
= $false )
| ( ( sum @ SV18 @ SV60 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(484,plain,
! [SV62: $i,SV126: $i,SV20: $i,SV130: $i,SV93: $i,SV81: $i] :
( ( ( product @ SV81 @ SV93 @ SV130 )
= $false )
| ( ( product @ SV20 @ SV126 @ SV130 )
= $true )
| ( ( product @ SV62 @ SV93 @ SV126 )
= $false )
| ( ( product @ SV20 @ SV62 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(485,plain,
! [SV63: $i,SV94: $i,SV82: $i,SV131: $i,SV127: $i,SV21: $i] :
( ( ( product @ SV21 @ SV127 @ SV131 )
= $false )
| ( ( product @ SV82 @ SV94 @ SV131 )
= $true )
| ( ( product @ SV63 @ SV94 @ SV127 )
= $false )
| ( ( product @ SV21 @ SV63 @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(486,plain,
! [SV110: $i,SV83: $i,SV22: $i,SV132: $i,SV95: $i,SV64: $i] :
( ( ( sum @ SV64 @ SV95 @ SV132 )
= $false )
| ( ( ! [SY365: $i] :
( ~ ( product @ SV22 @ SV132 @ SY365 )
| ( sum @ SV83 @ SV110 @ SY365 ) ) )
= $true )
| ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(487,plain,
! [SV23: $i,SV111: $i,SV84: $i,SV133: $i,SV96: $i,SV65: $i] :
( ( ( sum @ SV65 @ SV96 @ SV133 )
= $false )
| ( ( ! [SY366: $i] :
( ~ ( sum @ SV84 @ SV111 @ SY366 )
| ( product @ SV23 @ SV133 @ SY366 ) ) )
= $true )
| ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(488,plain,
! [SV112: $i,SV85: $i,SV66: $i,SV134: $i,SV97: $i,SV24: $i] :
( ( ( sum @ SV24 @ SV97 @ SV134 )
= $false )
| ( ( ! [SY367: $i] :
( ~ ( product @ SV134 @ SV66 @ SY367 )
| ( sum @ SV85 @ SV112 @ SY367 ) ) )
= $true )
| ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(489,plain,
! [SV67: $i,SV113: $i,SV86: $i,SV135: $i,SV98: $i,SV25: $i] :
( ( ( sum @ SV25 @ SV98 @ SV135 )
= $false )
| ( ( ! [SY368: $i] :
( ~ ( sum @ SV86 @ SV113 @ SY368 )
| ( product @ SV135 @ SV67 @ SY368 ) ) )
= $true )
| ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(490,plain,
! [SV95: $i,SV64: $i,SV110: $i,SV83: $i,SV136: $i,SV132: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV132 @ SV136 )
| ( sum @ SV83 @ SV110 @ SV136 ) )
= $true )
| ( ( sum @ SV64 @ SV95 @ SV132 )
= $false )
| ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(491,plain,
! [SV96: $i,SV65: $i,SV133: $i,SV23: $i,SV137: $i,SV111: $i,SV84: $i] :
( ( ( ~ ( sum @ SV84 @ SV111 @ SV137 )
| ( product @ SV23 @ SV133 @ SV137 ) )
= $true )
| ( ( sum @ SV65 @ SV96 @ SV133 )
= $false )
| ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(492,plain,
! [SV97: $i,SV24: $i,SV112: $i,SV85: $i,SV138: $i,SV66: $i,SV134: $i] :
( ( ( ~ ( product @ SV134 @ SV66 @ SV138 )
| ( sum @ SV85 @ SV112 @ SV138 ) )
= $true )
| ( ( sum @ SV24 @ SV97 @ SV134 )
= $false )
| ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(493,plain,
! [SV98: $i,SV25: $i,SV67: $i,SV135: $i,SV139: $i,SV113: $i,SV86: $i] :
( ( ( ~ ( sum @ SV86 @ SV113 @ SV139 )
| ( product @ SV135 @ SV67 @ SV139 ) )
= $true )
| ( ( sum @ SV25 @ SV98 @ SV135 )
= $false )
| ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(494,plain,
! [SV95: $i,SV64: $i,SV110: $i,SV83: $i,SV136: $i,SV132: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV132 @ SV136 ) )
= $true )
| ( ( sum @ SV83 @ SV110 @ SV136 )
= $true )
| ( ( sum @ SV64 @ SV95 @ SV132 )
= $false )
| ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(495,plain,
! [SV96: $i,SV65: $i,SV133: $i,SV23: $i,SV137: $i,SV111: $i,SV84: $i] :
( ( ( ~ ( sum @ SV84 @ SV111 @ SV137 ) )
= $true )
| ( ( product @ SV23 @ SV133 @ SV137 )
= $true )
| ( ( sum @ SV65 @ SV96 @ SV133 )
= $false )
| ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(496,plain,
! [SV97: $i,SV24: $i,SV112: $i,SV85: $i,SV138: $i,SV66: $i,SV134: $i] :
( ( ( ~ ( product @ SV134 @ SV66 @ SV138 ) )
= $true )
| ( ( sum @ SV85 @ SV112 @ SV138 )
= $true )
| ( ( sum @ SV24 @ SV97 @ SV134 )
= $false )
| ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(497,plain,
! [SV98: $i,SV25: $i,SV67: $i,SV135: $i,SV139: $i,SV113: $i,SV86: $i] :
( ( ( ~ ( sum @ SV86 @ SV113 @ SV139 ) )
= $true )
| ( ( product @ SV135 @ SV67 @ SV139 )
= $true )
| ( ( sum @ SV25 @ SV98 @ SV135 )
= $false )
| ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(498,plain,
! [SV95: $i,SV64: $i,SV110: $i,SV83: $i,SV136: $i,SV132: $i,SV22: $i] :
( ( ( product @ SV22 @ SV132 @ SV136 )
= $false )
| ( ( sum @ SV83 @ SV110 @ SV136 )
= $true )
| ( ( sum @ SV64 @ SV95 @ SV132 )
= $false )
| ( ( product @ SV22 @ SV95 @ SV110 )
= $false )
| ( ( product @ SV22 @ SV64 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(499,plain,
! [SV96: $i,SV65: $i,SV133: $i,SV23: $i,SV137: $i,SV111: $i,SV84: $i] :
( ( ( sum @ SV84 @ SV111 @ SV137 )
= $false )
| ( ( product @ SV23 @ SV133 @ SV137 )
= $true )
| ( ( sum @ SV65 @ SV96 @ SV133 )
= $false )
| ( ( product @ SV23 @ SV96 @ SV111 )
= $false )
| ( ( product @ SV23 @ SV65 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(500,plain,
! [SV97: $i,SV24: $i,SV112: $i,SV85: $i,SV138: $i,SV66: $i,SV134: $i] :
( ( ( product @ SV134 @ SV66 @ SV138 )
= $false )
| ( ( sum @ SV85 @ SV112 @ SV138 )
= $true )
| ( ( sum @ SV24 @ SV97 @ SV134 )
= $false )
| ( ( product @ SV97 @ SV66 @ SV112 )
= $false )
| ( ( product @ SV24 @ SV66 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(501,plain,
! [SV98: $i,SV25: $i,SV67: $i,SV135: $i,SV139: $i,SV113: $i,SV86: $i] :
( ( ( sum @ SV86 @ SV113 @ SV139 )
= $false )
| ( ( product @ SV135 @ SV67 @ SV139 )
= $true )
| ( ( sum @ SV25 @ SV98 @ SV135 )
= $false )
| ( ( product @ SV98 @ SV67 @ SV113 )
= $false )
| ( ( product @ SV25 @ SV67 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(502,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[176,501,500,499,498,485,484,483,482,457,456,455,454,445,444,443,442,441,440,427,391,384,383,379,378,329,328,327,326,325,324,310,309,297,296,295,294,292,288,287,286,285,278,277,265,264,262,251,248,247,246,245,244,243,242,241,240,239,238,236,235,234,231,230,229,228,226,225,222,221,220,219,217,216,177]) ).
thf(503,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG039-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 17:10:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.40 .
% 0.13/0.40
% 0.13/0.40 No.of.Axioms: 74
% 0.13/0.40
% 0.13/0.40 Length.of.Defs: 0
% 0.13/0.40
% 0.13/0.40 Contains.Choice.Funs: false
% 0.19/0.43 .
% 0.19/0.46 (rf:0,axioms:74,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:76,loop_count:0,foatp_calls:0,translation:fof_full)..............................
% 0.44/0.78
% 0.44/0.78 ********************************
% 0.44/0.78 * All subproblems solved! *
% 0.44/0.78 ********************************
% 0.44/0.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:74,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:502,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.68/0.87
% 0.68/0.87 %**** Beginning of derivation protocol ****
% 0.68/0.87 % SZS output start CNFRefutation
% See solution above
% 0.68/0.88
% 0.68/0.88 %**** End of derivation protocol ****
% 0.68/0.88 %**** no. of clauses in derivation: 503 ****
% 0.68/0.88 %**** clause counter: 502 ****
% 0.68/0.88
% 0.68/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:74,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:502,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------