TSTP Solution File: RNG039-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG039-1 : 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 : n028.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 0.53s 0.73s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 71
% Syntax : Number of formulae : 367 ( 262 unt; 10 typ; 0 def)
% Number of atoms : 1851 ( 518 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 3899 ( 415 ~; 552 |; 0 &;2932 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 1164 ( 0 ^1164 !; 0 ?;1164 :)
% 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_additive_inverse,type,
additive_inverse: $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
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,
( ( multiply @ b @ a )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(34,axiom,
( ( multiply @ a @ b )
= c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(35,axiom,
! [A: $i] :
( ( multiply @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(36,axiom,
! [A: $i] :
( ( add @ A @ A )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(37,axiom,
! [A: $i] :
( ( 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,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(42,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(43,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(44,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(45,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(46,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(47,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(48,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(49,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(50,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(51,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(52,axiom,
! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(53,axiom,
! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(54,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(55,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(56,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(57,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(58,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(59,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[58]) ).
thf(60,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
thf(61,negated_conjecture,
product @ b @ a @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a) ).
thf(62,negated_conjecture,
product @ a @ b @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
thf(63,plain,
$false = $false,
inference(unfold_def,[status(thm)],[59]) ).
thf(64,plain,
( ( ! [A: $i] : ( product @ A @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(65,plain,
( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(66,plain,
( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(67,plain,
( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(68,plain,
( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(69,plain,
( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(70,plain,
( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(71,plain,
( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(72,plain,
( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(73,plain,
( ( product @ c @ a @ ( multiply @ a @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(74,plain,
( ( product @ ( multiply @ d @ b ) @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(75,plain,
( ( product @ b @ a @ ( multiply @ b @ d ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(76,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(77,plain,
( ( product @ d @ b @ ( multiply @ b @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(78,plain,
( ( product @ ( multiply @ c @ a ) @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(79,plain,
( ( product @ a @ b @ ( multiply @ a @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(80,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(82,plain,
( ( product @ a @ d @ ( multiply @ c @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(83,plain,
( ( product @ b @ c @ ( multiply @ d @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(84,plain,
( ( product @ b @ ( multiply @ a @ d ) @ d )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(85,plain,
( ( product @ b @ a @ ( multiply @ d @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(86,plain,
( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(87,plain,
( ( product @ a @ ( multiply @ b @ c ) @ c )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(88,plain,
( ( product @ a @ b @ ( multiply @ c @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(91,plain,
( ( product @ d @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(92,plain,
( ( product @ c @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(93,plain,
( ( product @ b @ d @ d )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(94,plain,
( ( product @ a @ c @ c )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(96,plain,
( ( ( multiply @ b @ a )
= d )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(97,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( multiply @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( add @ A @ A )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( add @ A @ additive_identity )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(101,plain,
( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(105,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(106,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)],[43]) ).
thf(107,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)],[44]) ).
thf(108,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)],[45]) ).
thf(109,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)],[46]) ).
thf(110,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)],[47]) ).
thf(111,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)],[48]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(113,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)],[50]) ).
thf(114,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)],[51]) ).
thf(115,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(116,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(119,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(120,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(121,plain,
( ( ( c != d ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(122,plain,
( ( product @ b @ a @ d )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(123,plain,
( ( product @ a @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(124,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[63]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(126,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(127,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)],[106]) ).
thf(128,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)],[107]) ).
thf(129,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)],[108]) ).
thf(130,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)],[109]) ).
thf(131,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)],[110]) ).
thf(132,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)],[111]) ).
thf(133,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)],[113]) ).
thf(134,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)],[114]) ).
thf(135,plain,
( ( ( c != d ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(136,plain,
( ( product @ a @ b @ c )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(137,plain,
( ( product @ b @ a @ d )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(138,plain,
( ( ( c != d ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(139,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(140,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(142,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(143,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(144,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(145,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)],[134]) ).
thf(146,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)],[133]) ).
thf(147,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(148,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)],[132]) ).
thf(149,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)],[131]) ).
thf(150,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)],[130]) ).
thf(151,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)],[129]) ).
thf(152,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)],[128]) ).
thf(153,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)],[127]) ).
thf(154,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(155,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ ( add @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] : ( sum @ ( add @ A @ B ) @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(158,plain,
( ( ! [A: $i] : ( sum @ A @ A @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(159,plain,
( ( ! [A: $i] :
( ( add @ A @ additive_identity )
= A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(160,plain,
( ( ! [A: $i] :
( ( add @ A @ A )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(161,plain,
( ( ! [A: $i] :
( ( multiply @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(162,plain,
( ( ( multiply @ a @ b )
= c )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(163,plain,
( ( ( multiply @ b @ a )
= d )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(164,plain,
( ( ! [A: $i,B: $i] : ( sum @ A @ B @ ( add @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(165,plain,
( ( product @ a @ c @ c )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(166,plain,
( ( product @ b @ d @ d )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(167,plain,
( ( product @ c @ b @ c )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(168,plain,
( ( product @ d @ a @ d )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(171,plain,
( ( product @ a @ b @ ( multiply @ c @ b ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(172,plain,
( ( product @ a @ ( multiply @ b @ c ) @ c )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(173,plain,
( ( ! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(174,plain,
( ( product @ b @ a @ ( multiply @ d @ a ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(175,plain,
( ( product @ b @ ( multiply @ a @ d ) @ d )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(176,plain,
( ( product @ b @ c @ ( multiply @ d @ b ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(177,plain,
( ( product @ a @ d @ ( multiply @ c @ a ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(179,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(180,plain,
( ( product @ a @ b @ ( multiply @ a @ c ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(181,plain,
( ( product @ ( multiply @ c @ a ) @ b @ c )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(182,plain,
( ( product @ d @ b @ ( multiply @ b @ c ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(183,plain,
( ( ! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(184,plain,
( ( product @ b @ a @ ( multiply @ b @ d ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(185,plain,
( ( product @ ( multiply @ d @ b ) @ a @ d )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(186,plain,
( ( product @ c @ a @ ( multiply @ a @ d ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(187,plain,
( ( product @ a @ ( add @ b @ a ) @ ( add @ c @ a ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(188,plain,
( ( product @ a @ ( add @ a @ b ) @ ( add @ a @ c ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(189,plain,
( ( product @ b @ ( add @ a @ b ) @ ( add @ d @ b ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(190,plain,
( ( product @ b @ ( add @ b @ a ) @ ( add @ b @ d ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(191,plain,
( ( product @ ( add @ a @ b ) @ b @ ( add @ c @ b ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(192,plain,
( ( product @ ( add @ b @ a ) @ b @ ( add @ b @ c ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(193,plain,
( ( product @ ( add @ b @ a ) @ a @ ( add @ d @ a ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(194,plain,
( ( product @ ( add @ a @ b ) @ a @ ( add @ a @ d ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(195,plain,
( ( ! [A: $i] : ( product @ A @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(196,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(197,plain,
( ( c = d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(198,plain,
! [SV1: $i] :
( ( sum @ additive_identity @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(199,plain,
! [SV2: $i] :
( ( sum @ SV2 @ additive_identity @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(200,plain,
! [SV3: $i] :
( ( ! [SY91: $i] : ( product @ SV3 @ SY91 @ ( multiply @ SV3 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(201,plain,
! [SV4: $i] :
( ( ! [SY92: $i] : ( sum @ SV4 @ SY92 @ ( add @ SV4 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(202,plain,
! [SV5: $i] :
( ( sum @ ( additive_inverse @ SV5 ) @ SV5 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(203,plain,
! [SV6: $i] :
( ( sum @ SV6 @ ( additive_inverse @ SV6 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(204,plain,
! [SV7: $i] :
( ( ! [SY93: $i,SY94: $i,SY95: $i] :
( ~ ( sum @ SV7 @ SY93 @ SY94 )
| ! [SY96: $i] :
( ~ ( sum @ SY93 @ SY95 @ SY96 )
| ! [SY97: $i] :
( ~ ( sum @ SY94 @ SY95 @ SY97 )
| ( sum @ SV7 @ SY96 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(205,plain,
! [SV8: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i] :
( ~ ( sum @ SV8 @ SY98 @ SY99 )
| ! [SY101: $i] :
( ~ ( sum @ SY98 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( sum @ SV8 @ SY101 @ SY102 )
| ( sum @ SY99 @ SY100 @ SY102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(206,plain,
! [SV9: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( sum @ SV9 @ SY103 @ SY104 )
| ( sum @ SY103 @ SV9 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(207,plain,
! [SV10: $i] :
( ( ! [SY105: $i,SY106: $i,SY107: $i] :
( ~ ( product @ SV10 @ SY105 @ SY106 )
| ! [SY108: $i] :
( ~ ( product @ SY105 @ SY107 @ SY108 )
| ! [SY109: $i] :
( ~ ( product @ SY106 @ SY107 @ SY109 )
| ( product @ SV10 @ SY108 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(208,plain,
! [SV11: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i] :
( ~ ( product @ SV11 @ SY110 @ SY111 )
| ! [SY113: $i] :
( ~ ( product @ SY110 @ SY112 @ SY113 )
| ! [SY114: $i] :
( ~ ( product @ SV11 @ SY113 @ SY114 )
| ( product @ SY111 @ SY112 @ SY114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(209,plain,
! [SV12: $i] :
( ( ! [SY115: $i,SY116: $i,SY117: $i,SY118: $i] :
( ~ ( product @ SV12 @ SY115 @ SY116 )
| ~ ( product @ SV12 @ SY117 @ SY118 )
| ! [SY119: $i] :
( ~ ( sum @ SY115 @ SY117 @ SY119 )
| ! [SY120: $i] :
( ~ ( product @ SV12 @ SY119 @ SY120 )
| ( sum @ SY116 @ SY118 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(210,plain,
! [SV13: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i,SY124: $i] :
( ~ ( product @ SV13 @ SY121 @ SY122 )
| ~ ( product @ SV13 @ SY123 @ SY124 )
| ! [SY125: $i] :
( ~ ( sum @ SY121 @ SY123 @ SY125 )
| ! [SY126: $i] :
( ~ ( sum @ SY122 @ SY124 @ SY126 )
| ( product @ SV13 @ SY125 @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(211,plain,
! [SV14: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i,SY130: $i] :
( ~ ( product @ SV14 @ SY127 @ SY128 )
| ~ ( product @ SY129 @ SY127 @ SY130 )
| ! [SY131: $i] :
( ~ ( sum @ SV14 @ SY129 @ SY131 )
| ! [V4: $i] :
( ~ ( product @ SY131 @ SY127 @ V4 )
| ( sum @ SY128 @ SY130 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(212,plain,
! [SV15: $i] :
( ( ! [SY133: $i,SY134: $i,SY135: $i,SY136: $i] :
( ~ ( product @ SV15 @ SY133 @ SY134 )
| ~ ( product @ SY135 @ SY133 @ SY136 )
| ! [SY137: $i] :
( ~ ( sum @ SV15 @ SY135 @ SY137 )
| ! [V4: $i] :
( ~ ( sum @ SY134 @ SY136 @ V4 )
| ( product @ SY137 @ SY133 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(213,plain,
! [SV16: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ~ ( sum @ SV16 @ SY139 @ SY140 )
| ! [SY141: $i] :
( ~ ( sum @ SV16 @ SY139 @ SY141 )
| ( SY140 = SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(214,plain,
! [SV17: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( product @ SV17 @ SY142 @ SY143 )
| ! [SY144: $i] :
( ~ ( product @ SV17 @ SY142 @ SY144 )
| ( SY143 = SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(215,plain,
! [SV18: $i] :
( ( ! [SY145: $i] : ( sum @ SV18 @ ( add @ SV18 @ SY145 ) @ SY145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(216,plain,
! [SV19: $i] :
( ( ! [SY146: $i] : ( sum @ ( add @ SV19 @ SY146 ) @ SY146 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(217,plain,
! [SV20: $i] :
( ( sum @ SV20 @ SV20 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(218,plain,
! [SV21: $i] :
( ( ( add @ SV21 @ additive_identity )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(219,plain,
! [SV22: $i] :
( ( ( add @ SV22 @ SV22 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(220,plain,
! [SV23: $i] :
( ( ( multiply @ SV23 @ SV23 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(221,plain,
! [SV24: $i] :
( ( ! [SY147: $i] : ( sum @ SV24 @ SY147 @ ( add @ SY147 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(222,plain,
! [SV25: $i] :
( ( ! [SY148: $i] : ( product @ SV25 @ ( multiply @ SV25 @ SY148 ) @ ( multiply @ SV25 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(223,plain,
! [SV26: $i] :
( ( ! [SY149: $i] : ( product @ a @ ( multiply @ b @ SV26 ) @ ( multiply @ SY149 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(224,plain,
! [SV27: $i] :
( ( product @ b @ ( multiply @ a @ SV27 ) @ ( multiply @ d @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(225,plain,
! [SV28: $i] :
( ( ! [SY150: $i] : ( product @ ( multiply @ SV28 @ SY150 ) @ SY150 @ ( multiply @ SV28 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(226,plain,
! [SV29: $i] :
( ( product @ ( multiply @ SV29 @ a ) @ b @ ( multiply @ SV29 @ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(227,plain,
! [SV30: $i] :
( ( product @ ( multiply @ SV30 @ b ) @ a @ ( multiply @ SV30 @ d ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(228,plain,
! [SV31: $i] :
( ( product @ SV31 @ SV31 @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(229,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(230,plain,
! [SV32: $i,SV3: $i] :
( ( product @ SV3 @ SV32 @ ( multiply @ SV3 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(231,plain,
! [SV33: $i,SV4: $i] :
( ( sum @ SV4 @ SV33 @ ( add @ SV4 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(232,plain,
! [SV34: $i,SV7: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ( sum @ SV7 @ SV34 @ SY151 )
| ! [SY153: $i] :
( ~ ( sum @ SV34 @ SY152 @ SY153 )
| ! [SY97: $i] :
( ~ ( sum @ SY151 @ SY152 @ SY97 )
| ( sum @ SV7 @ SY153 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(233,plain,
! [SV35: $i,SV8: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ~ ( sum @ SV8 @ SV35 @ SY155 )
| ! [SY157: $i] :
( ~ ( sum @ SV35 @ SY156 @ SY157 )
| ! [SY102: $i] :
( ~ ( sum @ SV8 @ SY157 @ SY102 )
| ( sum @ SY155 @ SY156 @ SY102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(234,plain,
! [SV36: $i,SV9: $i] :
( ( ! [SY159: $i] :
( ~ ( sum @ SV9 @ SV36 @ SY159 )
| ( sum @ SV36 @ SV9 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(235,plain,
! [SV37: $i,SV10: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ~ ( product @ SV10 @ SV37 @ SY160 )
| ! [SY162: $i] :
( ~ ( product @ SV37 @ SY161 @ SY162 )
| ! [SY109: $i] :
( ~ ( product @ SY160 @ SY161 @ SY109 )
| ( product @ SV10 @ SY162 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(236,plain,
! [SV38: $i,SV11: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ( product @ SV11 @ SV38 @ SY164 )
| ! [SY166: $i] :
( ~ ( product @ SV38 @ SY165 @ SY166 )
| ! [SY114: $i] :
( ~ ( product @ SV11 @ SY166 @ SY114 )
| ( product @ SY164 @ SY165 @ SY114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(237,plain,
! [SV39: $i,SV12: $i] :
( ( ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( product @ SV12 @ SV39 @ SY168 )
| ~ ( product @ SV12 @ SY169 @ SY170 )
| ! [SY171: $i] :
( ~ ( sum @ SV39 @ SY169 @ SY171 )
| ! [SY120: $i] :
( ~ ( product @ SV12 @ SY171 @ SY120 )
| ( sum @ SY168 @ SY170 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(238,plain,
! [SV40: $i,SV13: $i] :
( ( ! [SY173: $i,SY174: $i,SY175: $i] :
( ~ ( product @ SV13 @ SV40 @ SY173 )
| ~ ( product @ SV13 @ SY174 @ SY175 )
| ! [SY176: $i] :
( ~ ( sum @ SV40 @ SY174 @ SY176 )
| ! [SY126: $i] :
( ~ ( sum @ SY173 @ SY175 @ SY126 )
| ( product @ SV13 @ SY176 @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(239,plain,
! [SV41: $i,SV14: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ( product @ SV14 @ SV41 @ SY178 )
| ~ ( product @ SY179 @ SV41 @ SY180 )
| ! [SY181: $i] :
( ~ ( sum @ SV14 @ SY179 @ SY181 )
| ! [SY182: $i] :
( ~ ( product @ SY181 @ SV41 @ SY182 )
| ( sum @ SY178 @ SY180 @ SY182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(240,plain,
! [SV42: $i,SV15: $i] :
( ( ! [SY183: $i,SY184: $i,SY185: $i] :
( ~ ( product @ SV15 @ SV42 @ SY183 )
| ~ ( product @ SY184 @ SV42 @ SY185 )
| ! [SY186: $i] :
( ~ ( sum @ SV15 @ SY184 @ SY186 )
| ! [SY187: $i] :
( ~ ( sum @ SY183 @ SY185 @ SY187 )
| ( product @ SY186 @ SV42 @ SY187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(241,plain,
! [SV43: $i,SV16: $i] :
( ( ! [SY188: $i] :
( ~ ( sum @ SV16 @ SV43 @ SY188 )
| ! [SY189: $i] :
( ~ ( sum @ SV16 @ SV43 @ SY189 )
| ( SY188 = SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(242,plain,
! [SV44: $i,SV17: $i] :
( ( ! [SY190: $i] :
( ~ ( product @ SV17 @ SV44 @ SY190 )
| ! [SY191: $i] :
( ~ ( product @ SV17 @ SV44 @ SY191 )
| ( SY190 = SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(243,plain,
! [SV45: $i,SV18: $i] :
( ( sum @ SV18 @ ( add @ SV18 @ SV45 ) @ SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(244,plain,
! [SV46: $i,SV19: $i] :
( ( sum @ ( add @ SV19 @ SV46 ) @ SV46 @ SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(245,plain,
! [SV47: $i,SV24: $i] :
( ( sum @ SV24 @ SV47 @ ( add @ SV47 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(246,plain,
! [SV48: $i,SV25: $i] :
( ( product @ SV25 @ ( multiply @ SV25 @ SV48 ) @ ( multiply @ SV25 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(247,plain,
! [SV49: $i,SV26: $i] :
( ( product @ a @ ( multiply @ b @ SV26 ) @ ( multiply @ SV49 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(248,plain,
! [SV50: $i,SV28: $i] :
( ( product @ ( multiply @ SV28 @ SV50 ) @ SV50 @ ( multiply @ SV28 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(249,plain,
! [SV51: $i,SV34: $i,SV7: $i] :
( ( ! [SY192: $i] :
( ~ ( sum @ SV7 @ SV34 @ SV51 )
| ! [SY193: $i] :
( ~ ( sum @ SV34 @ SY192 @ SY193 )
| ! [SY194: $i] :
( ~ ( sum @ SV51 @ SY192 @ SY194 )
| ( sum @ SV7 @ SY193 @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(250,plain,
! [SV52: $i,SV35: $i,SV8: $i] :
( ( ! [SY195: $i] :
( ~ ( sum @ SV8 @ SV35 @ SV52 )
| ! [SY196: $i] :
( ~ ( sum @ SV35 @ SY195 @ SY196 )
| ! [SY197: $i] :
( ~ ( sum @ SV8 @ SY196 @ SY197 )
| ( sum @ SV52 @ SY195 @ SY197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(251,plain,
! [SV53: $i,SV36: $i,SV9: $i] :
( ( ~ ( sum @ SV9 @ SV36 @ SV53 )
| ( sum @ SV36 @ SV9 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(252,plain,
! [SV54: $i,SV37: $i,SV10: $i] :
( ( ! [SY198: $i] :
( ~ ( product @ SV10 @ SV37 @ SV54 )
| ! [SY199: $i] :
( ~ ( product @ SV37 @ SY198 @ SY199 )
| ! [SY200: $i] :
( ~ ( product @ SV54 @ SY198 @ SY200 )
| ( product @ SV10 @ SY199 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(253,plain,
! [SV55: $i,SV38: $i,SV11: $i] :
( ( ! [SY201: $i] :
( ~ ( product @ SV11 @ SV38 @ SV55 )
| ! [SY202: $i] :
( ~ ( product @ SV38 @ SY201 @ SY202 )
| ! [SY203: $i] :
( ~ ( product @ SV11 @ SY202 @ SY203 )
| ( product @ SV55 @ SY201 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(254,plain,
! [SV56: $i,SV39: $i,SV12: $i] :
( ( ! [SY204: $i,SY205: $i] :
( ~ ( product @ SV12 @ SV39 @ SV56 )
| ~ ( product @ SV12 @ SY204 @ SY205 )
| ! [SY206: $i] :
( ~ ( sum @ SV39 @ SY204 @ SY206 )
| ! [SY207: $i] :
( ~ ( product @ SV12 @ SY206 @ SY207 )
| ( sum @ SV56 @ SY205 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(255,plain,
! [SV57: $i,SV40: $i,SV13: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ~ ( product @ SV13 @ SV40 @ SV57 )
| ~ ( product @ SV13 @ SY208 @ SY209 )
| ! [SY210: $i] :
( ~ ( sum @ SV40 @ SY208 @ SY210 )
| ! [SY211: $i] :
( ~ ( sum @ SV57 @ SY209 @ SY211 )
| ( product @ SV13 @ SY210 @ SY211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(256,plain,
! [SV58: $i,SV41: $i,SV14: $i] :
( ( ! [SY212: $i,SY213: $i] :
( ~ ( product @ SV14 @ SV41 @ SV58 )
| ~ ( product @ SY212 @ SV41 @ SY213 )
| ! [SY214: $i] :
( ~ ( sum @ SV14 @ SY212 @ SY214 )
| ! [SY215: $i] :
( ~ ( product @ SY214 @ SV41 @ SY215 )
| ( sum @ SV58 @ SY213 @ SY215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(257,plain,
! [SV59: $i,SV42: $i,SV15: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ~ ( product @ SV15 @ SV42 @ SV59 )
| ~ ( product @ SY216 @ SV42 @ SY217 )
| ! [SY218: $i] :
( ~ ( sum @ SV15 @ SY216 @ SY218 )
| ! [SY219: $i] :
( ~ ( sum @ SV59 @ SY217 @ SY219 )
| ( product @ SY218 @ SV42 @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(258,plain,
! [SV60: $i,SV43: $i,SV16: $i] :
( ( ~ ( sum @ SV16 @ SV43 @ SV60 )
| ! [SY220: $i] :
( ~ ( sum @ SV16 @ SV43 @ SY220 )
| ( SV60 = SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(259,plain,
! [SV61: $i,SV44: $i,SV17: $i] :
( ( ~ ( product @ SV17 @ SV44 @ SV61 )
| ! [SY221: $i] :
( ~ ( product @ SV17 @ SV44 @ SY221 )
| ( SV61 = SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(260,plain,
! [SV62: $i,SV51: $i,SV34: $i,SV7: $i] :
( ( ~ ( sum @ SV7 @ SV34 @ SV51 )
| ! [SY222: $i] :
( ~ ( sum @ SV34 @ SV62 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV51 @ SV62 @ SY223 )
| ( sum @ SV7 @ SY222 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(261,plain,
! [SV63: $i,SV52: $i,SV35: $i,SV8: $i] :
( ( ~ ( sum @ SV8 @ SV35 @ SV52 )
| ! [SY224: $i] :
( ~ ( sum @ SV35 @ SV63 @ SY224 )
| ! [SY225: $i] :
( ~ ( sum @ SV8 @ SY224 @ SY225 )
| ( sum @ SV52 @ SV63 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV53: $i,SV36: $i,SV9: $i] :
( ( ( ~ ( sum @ SV9 @ SV36 @ SV53 ) )
= $true )
| ( ( sum @ SV36 @ SV9 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV64: $i,SV54: $i,SV37: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV37 @ SV54 )
| ! [SY226: $i] :
( ~ ( product @ SV37 @ SV64 @ SY226 )
| ! [SY227: $i] :
( ~ ( product @ SV54 @ SV64 @ SY227 )
| ( product @ SV10 @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV65: $i,SV55: $i,SV38: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV38 @ SV55 )
| ! [SY228: $i] :
( ~ ( product @ SV38 @ SV65 @ SY228 )
| ! [SY229: $i] :
( ~ ( product @ SV11 @ SY228 @ SY229 )
| ( product @ SV55 @ SV65 @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
( ( ! [SY230: $i] :
( ~ ( product @ SV12 @ SV39 @ SV56 )
| ~ ( product @ SV12 @ SV66 @ SY230 )
| ! [SY231: $i] :
( ~ ( sum @ SV39 @ SV66 @ SY231 )
| ! [SY207: $i] :
( ~ ( product @ SV12 @ SY231 @ SY207 )
| ( sum @ SV56 @ SY230 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
( ( ! [SY233: $i] :
( ~ ( product @ SV13 @ SV40 @ SV57 )
| ~ ( product @ SV13 @ SV67 @ SY233 )
| ! [SY234: $i] :
( ~ ( sum @ SV40 @ SV67 @ SY234 )
| ! [SY211: $i] :
( ~ ( sum @ SV57 @ SY233 @ SY211 )
| ( product @ SV13 @ SY234 @ SY211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
( ( ! [SY236: $i] :
( ~ ( product @ SV14 @ SV41 @ SV58 )
| ~ ( product @ SV68 @ SV41 @ SY236 )
| ! [SY237: $i] :
( ~ ( sum @ SV14 @ SV68 @ SY237 )
| ! [SY215: $i] :
( ~ ( product @ SY237 @ SV41 @ SY215 )
| ( sum @ SV58 @ SY236 @ SY215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(268,plain,
! [SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
( ( ! [SY239: $i] :
( ~ ( product @ SV15 @ SV42 @ SV59 )
| ~ ( product @ SV69 @ SV42 @ SY239 )
| ! [SY240: $i] :
( ~ ( sum @ SV15 @ SV69 @ SY240 )
| ! [SY219: $i] :
( ~ ( sum @ SV59 @ SY239 @ SY219 )
| ( product @ SY240 @ SV42 @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(269,plain,
! [SV60: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV43 @ SV60 ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( sum @ SV16 @ SV43 @ SY220 )
| ( SV60 = SY220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV61: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV44 @ SV61 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( product @ SV17 @ SV44 @ SY221 )
| ( SV61 = SY221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV62: $i,SV51: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( sum @ SV7 @ SV34 @ SV51 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( sum @ SV34 @ SV62 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV51 @ SV62 @ SY223 )
| ( sum @ SV7 @ SY222 @ SY223 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV63: $i,SV52: $i,SV35: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV35 @ SV52 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( sum @ SV35 @ SV63 @ SY224 )
| ! [SY225: $i] :
( ~ ( sum @ SV8 @ SY224 @ SY225 )
| ( sum @ SV52 @ SV63 @ SY225 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV53: $i,SV36: $i,SV9: $i] :
( ( ( sum @ SV9 @ SV36 @ SV53 )
= $false )
| ( ( sum @ SV36 @ SV9 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(274,plain,
! [SV64: $i,SV54: $i,SV37: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV37 @ SV54 ) )
= $true )
| ( ( ! [SY226: $i] :
( ~ ( product @ SV37 @ SV64 @ SY226 )
| ! [SY227: $i] :
( ~ ( product @ SV54 @ SV64 @ SY227 )
| ( product @ SV10 @ SY226 @ SY227 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(275,plain,
! [SV65: $i,SV55: $i,SV38: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV38 @ SV55 ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( product @ SV38 @ SV65 @ SY228 )
| ! [SY229: $i] :
( ~ ( product @ SV11 @ SY228 @ SY229 )
| ( product @ SV55 @ SV65 @ SY229 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV70: $i,SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV39 @ SV56 )
| ~ ( product @ SV12 @ SV66 @ SV70 )
| ! [SY242: $i] :
( ~ ( sum @ SV39 @ SV66 @ SY242 )
| ! [SY243: $i] :
( ~ ( product @ SV12 @ SY242 @ SY243 )
| ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV71: $i,SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
( ( ~ ( product @ SV13 @ SV40 @ SV57 )
| ~ ( product @ SV13 @ SV67 @ SV71 )
| ! [SY244: $i] :
( ~ ( sum @ SV40 @ SV67 @ SY244 )
| ! [SY245: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY245 )
| ( product @ SV13 @ SY244 @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(278,plain,
! [SV72: $i,SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
( ( ~ ( product @ SV14 @ SV41 @ SV58 )
| ~ ( product @ SV68 @ SV41 @ SV72 )
| ! [SY246: $i] :
( ~ ( sum @ SV14 @ SV68 @ SY246 )
| ! [SY247: $i] :
( ~ ( product @ SY246 @ SV41 @ SY247 )
| ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV73: $i,SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
( ( ~ ( product @ SV15 @ SV42 @ SV59 )
| ~ ( product @ SV69 @ SV42 @ SV73 )
| ! [SY248: $i] :
( ~ ( sum @ SV15 @ SV69 @ SY248 )
| ! [SY249: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY249 )
| ( product @ SY248 @ SV42 @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV60: $i,SV43: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV43 @ SV60 )
= $false )
| ( ( ! [SY220: $i] :
( ~ ( sum @ SV16 @ SV43 @ SY220 )
| ( SV60 = SY220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV61: $i,SV44: $i,SV17: $i] :
( ( ( product @ SV17 @ SV44 @ SV61 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( product @ SV17 @ SV44 @ SY221 )
| ( SV61 = SY221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(282,plain,
! [SV62: $i,SV51: $i,SV34: $i,SV7: $i] :
( ( ( sum @ SV7 @ SV34 @ SV51 )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( sum @ SV34 @ SV62 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV51 @ SV62 @ SY223 )
| ( sum @ SV7 @ SY222 @ SY223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(283,plain,
! [SV63: $i,SV52: $i,SV35: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV35 @ SV52 )
= $false )
| ( ( ! [SY224: $i] :
( ~ ( sum @ SV35 @ SV63 @ SY224 )
| ! [SY225: $i] :
( ~ ( sum @ SV8 @ SY224 @ SY225 )
| ( sum @ SV52 @ SV63 @ SY225 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(284,plain,
! [SV64: $i,SV54: $i,SV37: $i,SV10: $i] :
( ( ( product @ SV10 @ SV37 @ SV54 )
= $false )
| ( ( ! [SY226: $i] :
( ~ ( product @ SV37 @ SV64 @ SY226 )
| ! [SY227: $i] :
( ~ ( product @ SV54 @ SV64 @ SY227 )
| ( product @ SV10 @ SY226 @ SY227 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(285,plain,
! [SV65: $i,SV55: $i,SV38: $i,SV11: $i] :
( ( ( product @ SV11 @ SV38 @ SV55 )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( product @ SV38 @ SV65 @ SY228 )
| ! [SY229: $i] :
( ~ ( product @ SV11 @ SY228 @ SY229 )
| ( product @ SV55 @ SV65 @ SY229 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(286,plain,
! [SV70: $i,SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV39 @ SV56 ) )
= $true )
| ( ( ~ ( product @ SV12 @ SV66 @ SV70 )
| ! [SY242: $i] :
( ~ ( sum @ SV39 @ SV66 @ SY242 )
| ! [SY243: $i] :
( ~ ( product @ SV12 @ SY242 @ SY243 )
| ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(287,plain,
! [SV71: $i,SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV40 @ SV57 ) )
= $true )
| ( ( ~ ( product @ SV13 @ SV67 @ SV71 )
| ! [SY244: $i] :
( ~ ( sum @ SV40 @ SV67 @ SY244 )
| ! [SY245: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY245 )
| ( product @ SV13 @ SY244 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(288,plain,
! [SV72: $i,SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV41 @ SV58 ) )
= $true )
| ( ( ~ ( product @ SV68 @ SV41 @ SV72 )
| ! [SY246: $i] :
( ~ ( sum @ SV14 @ SV68 @ SY246 )
| ! [SY247: $i] :
( ~ ( product @ SY246 @ SV41 @ SY247 )
| ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(289,plain,
! [SV73: $i,SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV42 @ SV59 ) )
= $true )
| ( ( ~ ( product @ SV69 @ SV42 @ SV73 )
| ! [SY248: $i] :
( ~ ( sum @ SV15 @ SV69 @ SY248 )
| ! [SY249: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY249 )
| ( product @ SY248 @ SV42 @ SY249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(290,plain,
! [SV60: $i,SV74: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV43 @ SV74 )
| ( SV60 = SV74 ) )
= $true )
| ( ( sum @ SV16 @ SV43 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(291,plain,
! [SV61: $i,SV75: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV44 @ SV75 )
| ( SV61 = SV75 ) )
= $true )
| ( ( product @ SV17 @ SV44 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(292,plain,
! [SV7: $i,SV51: $i,SV76: $i,SV62: $i,SV34: $i] :
( ( ( ~ ( sum @ SV34 @ SV62 @ SV76 )
| ! [SY250: $i] :
( ~ ( sum @ SV51 @ SV62 @ SY250 )
| ( sum @ SV7 @ SV76 @ SY250 ) ) )
= $true )
| ( ( sum @ SV7 @ SV34 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(293,plain,
! [SV52: $i,SV8: $i,SV77: $i,SV63: $i,SV35: $i] :
( ( ( ~ ( sum @ SV35 @ SV63 @ SV77 )
| ! [SY251: $i] :
( ~ ( sum @ SV8 @ SV77 @ SY251 )
| ( sum @ SV52 @ SV63 @ SY251 ) ) )
= $true )
| ( ( sum @ SV8 @ SV35 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(294,plain,
! [SV10: $i,SV54: $i,SV78: $i,SV64: $i,SV37: $i] :
( ( ( ~ ( product @ SV37 @ SV64 @ SV78 )
| ! [SY252: $i] :
( ~ ( product @ SV54 @ SV64 @ SY252 )
| ( product @ SV10 @ SV78 @ SY252 ) ) )
= $true )
| ( ( product @ SV10 @ SV37 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(295,plain,
! [SV55: $i,SV11: $i,SV79: $i,SV65: $i,SV38: $i] :
( ( ( ~ ( product @ SV38 @ SV65 @ SV79 )
| ! [SY253: $i] :
( ~ ( product @ SV11 @ SV79 @ SY253 )
| ( product @ SV55 @ SV65 @ SY253 ) ) )
= $true )
| ( ( product @ SV11 @ SV38 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(296,plain,
! [SV70: $i,SV66: $i,SV56: $i,SV39: $i,SV12: $i] :
( ( ( product @ SV12 @ SV39 @ SV56 )
= $false )
| ( ( ~ ( product @ SV12 @ SV66 @ SV70 )
| ! [SY242: $i] :
( ~ ( sum @ SV39 @ SV66 @ SY242 )
| ! [SY243: $i] :
( ~ ( product @ SV12 @ SY242 @ SY243 )
| ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(297,plain,
! [SV71: $i,SV67: $i,SV57: $i,SV40: $i,SV13: $i] :
( ( ( product @ SV13 @ SV40 @ SV57 )
= $false )
| ( ( ~ ( product @ SV13 @ SV67 @ SV71 )
| ! [SY244: $i] :
( ~ ( sum @ SV40 @ SV67 @ SY244 )
| ! [SY245: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY245 )
| ( product @ SV13 @ SY244 @ SY245 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(298,plain,
! [SV72: $i,SV68: $i,SV58: $i,SV41: $i,SV14: $i] :
( ( ( product @ SV14 @ SV41 @ SV58 )
= $false )
| ( ( ~ ( product @ SV68 @ SV41 @ SV72 )
| ! [SY246: $i] :
( ~ ( sum @ SV14 @ SV68 @ SY246 )
| ! [SY247: $i] :
( ~ ( product @ SY246 @ SV41 @ SY247 )
| ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(299,plain,
! [SV73: $i,SV69: $i,SV59: $i,SV42: $i,SV15: $i] :
( ( ( product @ SV15 @ SV42 @ SV59 )
= $false )
| ( ( ~ ( product @ SV69 @ SV42 @ SV73 )
| ! [SY248: $i] :
( ~ ( sum @ SV15 @ SV69 @ SY248 )
| ! [SY249: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY249 )
| ( product @ SY248 @ SV42 @ SY249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(300,plain,
! [SV60: $i,SV74: $i,SV43: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV43 @ SV74 ) )
= $true )
| ( ( SV60 = SV74 )
= $true )
| ( ( sum @ SV16 @ SV43 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(301,plain,
! [SV61: $i,SV75: $i,SV44: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV44 @ SV75 ) )
= $true )
| ( ( SV61 = SV75 )
= $true )
| ( ( product @ SV17 @ SV44 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(302,plain,
! [SV7: $i,SV51: $i,SV76: $i,SV62: $i,SV34: $i] :
( ( ( ~ ( sum @ SV34 @ SV62 @ SV76 ) )
= $true )
| ( ( ! [SY250: $i] :
( ~ ( sum @ SV51 @ SV62 @ SY250 )
| ( sum @ SV7 @ SV76 @ SY250 ) ) )
= $true )
| ( ( sum @ SV7 @ SV34 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(303,plain,
! [SV52: $i,SV8: $i,SV77: $i,SV63: $i,SV35: $i] :
( ( ( ~ ( sum @ SV35 @ SV63 @ SV77 ) )
= $true )
| ( ( ! [SY251: $i] :
( ~ ( sum @ SV8 @ SV77 @ SY251 )
| ( sum @ SV52 @ SV63 @ SY251 ) ) )
= $true )
| ( ( sum @ SV8 @ SV35 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(304,plain,
! [SV10: $i,SV54: $i,SV78: $i,SV64: $i,SV37: $i] :
( ( ( ~ ( product @ SV37 @ SV64 @ SV78 ) )
= $true )
| ( ( ! [SY252: $i] :
( ~ ( product @ SV54 @ SV64 @ SY252 )
| ( product @ SV10 @ SV78 @ SY252 ) ) )
= $true )
| ( ( product @ SV10 @ SV37 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(305,plain,
! [SV55: $i,SV11: $i,SV79: $i,SV65: $i,SV38: $i] :
( ( ( ~ ( product @ SV38 @ SV65 @ SV79 ) )
= $true )
| ( ( ! [SY253: $i] :
( ~ ( product @ SV11 @ SV79 @ SY253 )
| ( product @ SV55 @ SV65 @ SY253 ) ) )
= $true )
| ( ( product @ SV11 @ SV38 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(306,plain,
! [SV56: $i,SV39: $i,SV70: $i,SV66: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV66 @ SV70 ) )
= $true )
| ( ( ! [SY242: $i] :
( ~ ( sum @ SV39 @ SV66 @ SY242 )
| ! [SY243: $i] :
( ~ ( product @ SV12 @ SY242 @ SY243 )
| ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(307,plain,
! [SV57: $i,SV40: $i,SV71: $i,SV67: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV67 @ SV71 ) )
= $true )
| ( ( ! [SY244: $i] :
( ~ ( sum @ SV40 @ SV67 @ SY244 )
| ! [SY245: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY245 )
| ( product @ SV13 @ SY244 @ SY245 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(308,plain,
! [SV58: $i,SV14: $i,SV72: $i,SV41: $i,SV68: $i] :
( ( ( ~ ( product @ SV68 @ SV41 @ SV72 ) )
= $true )
| ( ( ! [SY246: $i] :
( ~ ( sum @ SV14 @ SV68 @ SY246 )
| ! [SY247: $i] :
( ~ ( product @ SY246 @ SV41 @ SY247 )
| ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(309,plain,
! [SV59: $i,SV15: $i,SV73: $i,SV42: $i,SV69: $i] :
( ( ( ~ ( product @ SV69 @ SV42 @ SV73 ) )
= $true )
| ( ( ! [SY248: $i] :
( ~ ( sum @ SV15 @ SV69 @ SY248 )
| ! [SY249: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY249 )
| ( product @ SY248 @ SV42 @ SY249 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(310,plain,
! [SV60: $i,SV74: $i,SV43: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV43 @ SV74 )
= $false )
| ( ( SV60 = SV74 )
= $true )
| ( ( sum @ SV16 @ SV43 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(311,plain,
! [SV61: $i,SV75: $i,SV44: $i,SV17: $i] :
( ( ( product @ SV17 @ SV44 @ SV75 )
= $false )
| ( ( SV61 = SV75 )
= $true )
| ( ( product @ SV17 @ SV44 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(312,plain,
! [SV7: $i,SV51: $i,SV76: $i,SV62: $i,SV34: $i] :
( ( ( sum @ SV34 @ SV62 @ SV76 )
= $false )
| ( ( ! [SY250: $i] :
( ~ ( sum @ SV51 @ SV62 @ SY250 )
| ( sum @ SV7 @ SV76 @ SY250 ) ) )
= $true )
| ( ( sum @ SV7 @ SV34 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(313,plain,
! [SV52: $i,SV8: $i,SV77: $i,SV63: $i,SV35: $i] :
( ( ( sum @ SV35 @ SV63 @ SV77 )
= $false )
| ( ( ! [SY251: $i] :
( ~ ( sum @ SV8 @ SV77 @ SY251 )
| ( sum @ SV52 @ SV63 @ SY251 ) ) )
= $true )
| ( ( sum @ SV8 @ SV35 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(314,plain,
! [SV10: $i,SV54: $i,SV78: $i,SV64: $i,SV37: $i] :
( ( ( product @ SV37 @ SV64 @ SV78 )
= $false )
| ( ( ! [SY252: $i] :
( ~ ( product @ SV54 @ SV64 @ SY252 )
| ( product @ SV10 @ SV78 @ SY252 ) ) )
= $true )
| ( ( product @ SV10 @ SV37 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(315,plain,
! [SV55: $i,SV11: $i,SV79: $i,SV65: $i,SV38: $i] :
( ( ( product @ SV38 @ SV65 @ SV79 )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( product @ SV11 @ SV79 @ SY253 )
| ( product @ SV55 @ SV65 @ SY253 ) ) )
= $true )
| ( ( product @ SV11 @ SV38 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(316,plain,
! [SV56: $i,SV39: $i,SV70: $i,SV66: $i,SV12: $i] :
( ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( ! [SY242: $i] :
( ~ ( sum @ SV39 @ SV66 @ SY242 )
| ! [SY243: $i] :
( ~ ( product @ SV12 @ SY242 @ SY243 )
| ( sum @ SV56 @ SV70 @ SY243 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(317,plain,
! [SV57: $i,SV40: $i,SV71: $i,SV67: $i,SV13: $i] :
( ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( ! [SY244: $i] :
( ~ ( sum @ SV40 @ SV67 @ SY244 )
| ! [SY245: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY245 )
| ( product @ SV13 @ SY244 @ SY245 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(318,plain,
! [SV58: $i,SV14: $i,SV72: $i,SV41: $i,SV68: $i] :
( ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( ! [SY246: $i] :
( ~ ( sum @ SV14 @ SV68 @ SY246 )
| ! [SY247: $i] :
( ~ ( product @ SY246 @ SV41 @ SY247 )
| ( sum @ SV58 @ SV72 @ SY247 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(319,plain,
! [SV59: $i,SV15: $i,SV73: $i,SV42: $i,SV69: $i] :
( ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( ! [SY248: $i] :
( ~ ( sum @ SV15 @ SV69 @ SY248 )
| ! [SY249: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY249 )
| ( product @ SY248 @ SV42 @ SY249 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(320,plain,
! [SV34: $i,SV76: $i,SV7: $i,SV80: $i,SV62: $i,SV51: $i] :
( ( ( ~ ( sum @ SV51 @ SV62 @ SV80 )
| ( sum @ SV7 @ SV76 @ SV80 ) )
= $true )
| ( ( sum @ SV34 @ SV62 @ SV76 )
= $false )
| ( ( sum @ SV7 @ SV34 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(321,plain,
! [SV35: $i,SV63: $i,SV52: $i,SV81: $i,SV77: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV77 @ SV81 )
| ( sum @ SV52 @ SV63 @ SV81 ) )
= $true )
| ( ( sum @ SV35 @ SV63 @ SV77 )
= $false )
| ( ( sum @ SV8 @ SV35 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(322,plain,
! [SV37: $i,SV78: $i,SV10: $i,SV82: $i,SV64: $i,SV54: $i] :
( ( ( ~ ( product @ SV54 @ SV64 @ SV82 )
| ( product @ SV10 @ SV78 @ SV82 ) )
= $true )
| ( ( product @ SV37 @ SV64 @ SV78 )
= $false )
| ( ( product @ SV10 @ SV37 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(323,plain,
! [SV38: $i,SV65: $i,SV55: $i,SV83: $i,SV79: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV79 @ SV83 )
| ( product @ SV55 @ SV65 @ SV83 ) )
= $true )
| ( ( product @ SV38 @ SV65 @ SV79 )
= $false )
| ( ( product @ SV11 @ SV38 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(324,plain,
! [SV70: $i,SV56: $i,SV12: $i,SV84: $i,SV66: $i,SV39: $i] :
( ( ( ~ ( sum @ SV39 @ SV66 @ SV84 )
| ! [SY254: $i] :
( ~ ( product @ SV12 @ SV84 @ SY254 )
| ( sum @ SV56 @ SV70 @ SY254 ) ) )
= $true )
| ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(325,plain,
! [SV13: $i,SV71: $i,SV57: $i,SV85: $i,SV67: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV67 @ SV85 )
| ! [SY255: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY255 )
| ( product @ SV13 @ SV85 @ SY255 ) ) )
= $true )
| ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(326,plain,
! [SV72: $i,SV58: $i,SV41: $i,SV86: $i,SV68: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV68 @ SV86 )
| ! [SY256: $i] :
( ~ ( product @ SV86 @ SV41 @ SY256 )
| ( sum @ SV58 @ SV72 @ SY256 ) ) )
= $true )
| ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(327,plain,
! [SV42: $i,SV73: $i,SV59: $i,SV87: $i,SV69: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV69 @ SV87 )
| ! [SY257: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY257 )
| ( product @ SV87 @ SV42 @ SY257 ) ) )
= $true )
| ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(328,plain,
! [SV34: $i,SV76: $i,SV7: $i,SV80: $i,SV62: $i,SV51: $i] :
( ( ( ~ ( sum @ SV51 @ SV62 @ SV80 ) )
= $true )
| ( ( sum @ SV7 @ SV76 @ SV80 )
= $true )
| ( ( sum @ SV34 @ SV62 @ SV76 )
= $false )
| ( ( sum @ SV7 @ SV34 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(329,plain,
! [SV35: $i,SV63: $i,SV52: $i,SV81: $i,SV77: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV77 @ SV81 ) )
= $true )
| ( ( sum @ SV52 @ SV63 @ SV81 )
= $true )
| ( ( sum @ SV35 @ SV63 @ SV77 )
= $false )
| ( ( sum @ SV8 @ SV35 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(330,plain,
! [SV37: $i,SV78: $i,SV10: $i,SV82: $i,SV64: $i,SV54: $i] :
( ( ( ~ ( product @ SV54 @ SV64 @ SV82 ) )
= $true )
| ( ( product @ SV10 @ SV78 @ SV82 )
= $true )
| ( ( product @ SV37 @ SV64 @ SV78 )
= $false )
| ( ( product @ SV10 @ SV37 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(331,plain,
! [SV38: $i,SV65: $i,SV55: $i,SV83: $i,SV79: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV79 @ SV83 ) )
= $true )
| ( ( product @ SV55 @ SV65 @ SV83 )
= $true )
| ( ( product @ SV38 @ SV65 @ SV79 )
= $false )
| ( ( product @ SV11 @ SV38 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(332,plain,
! [SV70: $i,SV56: $i,SV12: $i,SV84: $i,SV66: $i,SV39: $i] :
( ( ( ~ ( sum @ SV39 @ SV66 @ SV84 ) )
= $true )
| ( ( ! [SY254: $i] :
( ~ ( product @ SV12 @ SV84 @ SY254 )
| ( sum @ SV56 @ SV70 @ SY254 ) ) )
= $true )
| ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(333,plain,
! [SV13: $i,SV71: $i,SV57: $i,SV85: $i,SV67: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV67 @ SV85 ) )
= $true )
| ( ( ! [SY255: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY255 )
| ( product @ SV13 @ SV85 @ SY255 ) ) )
= $true )
| ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(334,plain,
! [SV72: $i,SV58: $i,SV41: $i,SV86: $i,SV68: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV68 @ SV86 ) )
= $true )
| ( ( ! [SY256: $i] :
( ~ ( product @ SV86 @ SV41 @ SY256 )
| ( sum @ SV58 @ SV72 @ SY256 ) ) )
= $true )
| ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(335,plain,
! [SV42: $i,SV73: $i,SV59: $i,SV87: $i,SV69: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV69 @ SV87 ) )
= $true )
| ( ( ! [SY257: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY257 )
| ( product @ SV87 @ SV42 @ SY257 ) ) )
= $true )
| ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(336,plain,
! [SV34: $i,SV76: $i,SV7: $i,SV80: $i,SV62: $i,SV51: $i] :
( ( ( sum @ SV51 @ SV62 @ SV80 )
= $false )
| ( ( sum @ SV7 @ SV76 @ SV80 )
= $true )
| ( ( sum @ SV34 @ SV62 @ SV76 )
= $false )
| ( ( sum @ SV7 @ SV34 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(337,plain,
! [SV35: $i,SV63: $i,SV52: $i,SV81: $i,SV77: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV77 @ SV81 )
= $false )
| ( ( sum @ SV52 @ SV63 @ SV81 )
= $true )
| ( ( sum @ SV35 @ SV63 @ SV77 )
= $false )
| ( ( sum @ SV8 @ SV35 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(338,plain,
! [SV37: $i,SV78: $i,SV10: $i,SV82: $i,SV64: $i,SV54: $i] :
( ( ( product @ SV54 @ SV64 @ SV82 )
= $false )
| ( ( product @ SV10 @ SV78 @ SV82 )
= $true )
| ( ( product @ SV37 @ SV64 @ SV78 )
= $false )
| ( ( product @ SV10 @ SV37 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(339,plain,
! [SV38: $i,SV65: $i,SV55: $i,SV83: $i,SV79: $i,SV11: $i] :
( ( ( product @ SV11 @ SV79 @ SV83 )
= $false )
| ( ( product @ SV55 @ SV65 @ SV83 )
= $true )
| ( ( product @ SV38 @ SV65 @ SV79 )
= $false )
| ( ( product @ SV11 @ SV38 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(340,plain,
! [SV70: $i,SV56: $i,SV12: $i,SV84: $i,SV66: $i,SV39: $i] :
( ( ( sum @ SV39 @ SV66 @ SV84 )
= $false )
| ( ( ! [SY254: $i] :
( ~ ( product @ SV12 @ SV84 @ SY254 )
| ( sum @ SV56 @ SV70 @ SY254 ) ) )
= $true )
| ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(341,plain,
! [SV13: $i,SV71: $i,SV57: $i,SV85: $i,SV67: $i,SV40: $i] :
( ( ( sum @ SV40 @ SV67 @ SV85 )
= $false )
| ( ( ! [SY255: $i] :
( ~ ( sum @ SV57 @ SV71 @ SY255 )
| ( product @ SV13 @ SV85 @ SY255 ) ) )
= $true )
| ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(342,plain,
! [SV72: $i,SV58: $i,SV41: $i,SV86: $i,SV68: $i,SV14: $i] :
( ( ( sum @ SV14 @ SV68 @ SV86 )
= $false )
| ( ( ! [SY256: $i] :
( ~ ( product @ SV86 @ SV41 @ SY256 )
| ( sum @ SV58 @ SV72 @ SY256 ) ) )
= $true )
| ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(343,plain,
! [SV42: $i,SV73: $i,SV59: $i,SV87: $i,SV69: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV69 @ SV87 )
= $false )
| ( ( ! [SY257: $i] :
( ~ ( sum @ SV59 @ SV73 @ SY257 )
| ( product @ SV87 @ SV42 @ SY257 ) ) )
= $true )
| ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(344,plain,
! [SV66: $i,SV39: $i,SV70: $i,SV56: $i,SV88: $i,SV84: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV84 @ SV88 )
| ( sum @ SV56 @ SV70 @ SV88 ) )
= $true )
| ( ( sum @ SV39 @ SV66 @ SV84 )
= $false )
| ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(345,plain,
! [SV67: $i,SV40: $i,SV85: $i,SV13: $i,SV89: $i,SV71: $i,SV57: $i] :
( ( ( ~ ( sum @ SV57 @ SV71 @ SV89 )
| ( product @ SV13 @ SV85 @ SV89 ) )
= $true )
| ( ( sum @ SV40 @ SV67 @ SV85 )
= $false )
| ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(346,plain,
! [SV68: $i,SV14: $i,SV72: $i,SV58: $i,SV90: $i,SV41: $i,SV86: $i] :
( ( ( ~ ( product @ SV86 @ SV41 @ SV90 )
| ( sum @ SV58 @ SV72 @ SV90 ) )
= $true )
| ( ( sum @ SV14 @ SV68 @ SV86 )
= $false )
| ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(347,plain,
! [SV69: $i,SV15: $i,SV42: $i,SV87: $i,SV91: $i,SV73: $i,SV59: $i] :
( ( ( ~ ( sum @ SV59 @ SV73 @ SV91 )
| ( product @ SV87 @ SV42 @ SV91 ) )
= $true )
| ( ( sum @ SV15 @ SV69 @ SV87 )
= $false )
| ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(348,plain,
! [SV66: $i,SV39: $i,SV70: $i,SV56: $i,SV88: $i,SV84: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV84 @ SV88 ) )
= $true )
| ( ( sum @ SV56 @ SV70 @ SV88 )
= $true )
| ( ( sum @ SV39 @ SV66 @ SV84 )
= $false )
| ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(349,plain,
! [SV67: $i,SV40: $i,SV85: $i,SV13: $i,SV89: $i,SV71: $i,SV57: $i] :
( ( ( ~ ( sum @ SV57 @ SV71 @ SV89 ) )
= $true )
| ( ( product @ SV13 @ SV85 @ SV89 )
= $true )
| ( ( sum @ SV40 @ SV67 @ SV85 )
= $false )
| ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(350,plain,
! [SV68: $i,SV14: $i,SV72: $i,SV58: $i,SV90: $i,SV41: $i,SV86: $i] :
( ( ( ~ ( product @ SV86 @ SV41 @ SV90 ) )
= $true )
| ( ( sum @ SV58 @ SV72 @ SV90 )
= $true )
| ( ( sum @ SV14 @ SV68 @ SV86 )
= $false )
| ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(351,plain,
! [SV69: $i,SV15: $i,SV42: $i,SV87: $i,SV91: $i,SV73: $i,SV59: $i] :
( ( ( ~ ( sum @ SV59 @ SV73 @ SV91 ) )
= $true )
| ( ( product @ SV87 @ SV42 @ SV91 )
= $true )
| ( ( sum @ SV15 @ SV69 @ SV87 )
= $false )
| ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(352,plain,
! [SV66: $i,SV39: $i,SV70: $i,SV56: $i,SV88: $i,SV84: $i,SV12: $i] :
( ( ( product @ SV12 @ SV84 @ SV88 )
= $false )
| ( ( sum @ SV56 @ SV70 @ SV88 )
= $true )
| ( ( sum @ SV39 @ SV66 @ SV84 )
= $false )
| ( ( product @ SV12 @ SV66 @ SV70 )
= $false )
| ( ( product @ SV12 @ SV39 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(353,plain,
! [SV67: $i,SV40: $i,SV85: $i,SV13: $i,SV89: $i,SV71: $i,SV57: $i] :
( ( ( sum @ SV57 @ SV71 @ SV89 )
= $false )
| ( ( product @ SV13 @ SV85 @ SV89 )
= $true )
| ( ( sum @ SV40 @ SV67 @ SV85 )
= $false )
| ( ( product @ SV13 @ SV67 @ SV71 )
= $false )
| ( ( product @ SV13 @ SV40 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(354,plain,
! [SV68: $i,SV14: $i,SV72: $i,SV58: $i,SV90: $i,SV41: $i,SV86: $i] :
( ( ( product @ SV86 @ SV41 @ SV90 )
= $false )
| ( ( sum @ SV58 @ SV72 @ SV90 )
= $true )
| ( ( sum @ SV14 @ SV68 @ SV86 )
= $false )
| ( ( product @ SV68 @ SV41 @ SV72 )
= $false )
| ( ( product @ SV14 @ SV41 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(355,plain,
! [SV69: $i,SV15: $i,SV42: $i,SV87: $i,SV91: $i,SV73: $i,SV59: $i] :
( ( ( sum @ SV59 @ SV73 @ SV91 )
= $false )
| ( ( product @ SV87 @ SV42 @ SV91 )
= $true )
| ( ( sum @ SV15 @ SV69 @ SV87 )
= $false )
| ( ( product @ SV69 @ SV42 @ SV73 )
= $false )
| ( ( product @ SV15 @ SV42 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(356,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[136,355,354,353,352,339,338,337,336,311,310,273,248,247,246,245,244,243,231,230,229,228,227,226,224,220,219,218,217,203,202,199,198,197,194,193,192,191,190,189,188,187,186,185,184,182,181,180,177,176,175,174,172,171,168,167,166,165,163,162,137]) ).
thf(357,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : RNG039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 11:21:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.38
% 0.13/0.38 No.of.Axioms: 60
% 0.13/0.38
% 0.13/0.38 Length.of.Defs: 0
% 0.13/0.38
% 0.13/0.38 Contains.Choice.Funs: false
% 0.13/0.39 .
% 0.18/0.42 (rf:0,axioms:60,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:62,loop_count:0,foatp_calls:0,translation:fof_full)......................
% 0.53/0.73
% 0.53/0.73 ********************************
% 0.53/0.73 * All subproblems solved! *
% 0.53/0.73 ********************************
% 0.53/0.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:60,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.53/0.77
% 0.53/0.77 %**** Beginning of derivation protocol ****
% 0.53/0.77 % SZS output start CNFRefutation
% See solution above
% 0.53/0.77
% 0.53/0.77 %**** End of derivation protocol ****
% 0.53/0.77 %**** no. of clauses in derivation: 357 ****
% 0.53/0.77 %**** clause counter: 356 ****
% 0.53/0.77
% 0.53/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:60,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:356,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------