TSTP Solution File: FLD025-5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : FLD025-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 : Sat Jul 16 02:16:59 EDT 2022
% Result : Unsatisfiable 0.45s 0.70s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 54
% Syntax : Number of formulae : 318 ( 163 unt; 16 typ; 0 def)
% Number of atoms : 1932 ( 496 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3537 ( 515 ~; 638 |; 0 &;2384 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 993 ( 0 ^ 993 !; 0 ?; 993 :)
% 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_defined,type,
defined: $i > $o ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiplicative_inverse,type,
multiplicative_inverse: $i > $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(tp_u,type,
u: $i ).
thf(tp_v,type,
v: $i ).
thf(1,axiom,
~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(2,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( less_or_equal @ additive_identity @ Z )
| ~ ( less_or_equal @ additive_identity @ X )
| ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( product @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(3,axiom,
! [U: $i,V: $i,X: $i,Y: $i,Z: $i] :
( ( less_or_equal @ U @ V )
| ~ ( less_or_equal @ X @ Y )
| ~ ( sum @ X @ Z @ U )
| ~ ( sum @ Y @ Z @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
| ( less_or_equal @ Y @ X )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(5,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ X @ Z )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( sum @ additive_identity @ X @ Y )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( sum @ X @ Y @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
thf(9,axiom,
! [X: $i] :
( ( defined @ ( multiplicative_inverse @ X ) )
| ~ ( defined @ X )
| ( sum @ additive_identity @ X @ additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(10,axiom,
defined @ multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( defined @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(12,axiom,
! [X: $i] :
( ( defined @ ( additive_inverse @ X ) )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(13,axiom,
defined @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(14,axiom,
! [X: $i,Y: $i] :
( ( defined @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(15,axiom,
! [A: $i,Z: $i,B: $i,X: $i,Y: $i,C: $i,D: $i] :
( ( product @ A @ Z @ B )
| ~ ( sum @ X @ Y @ A )
| ~ ( product @ X @ Z @ C )
| ~ ( product @ Y @ Z @ D )
| ~ ( sum @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
thf(16,axiom,
! [C: $i,D: $i,B: $i,X: $i,Y: $i,A: $i,Z: $i] :
( ( sum @ C @ D @ B )
| ~ ( sum @ X @ Y @ A )
| ~ ( product @ A @ Z @ B )
| ~ ( product @ X @ Z @ C )
| ~ ( product @ Y @ Z @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
thf(17,axiom,
! [Y: $i,X: $i,Z: $i] :
( ( product @ Y @ X @ Z )
| ~ ( product @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(18,axiom,
! [X: $i] :
( ( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity )
| ( sum @ additive_identity @ X @ additive_identity )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(19,axiom,
! [X: $i] :
( ( product @ multiplicative_identity @ X @ X )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(20,axiom,
! [U: $i,Z: $i,W: $i,X: $i,Y: $i,V: $i] :
( ( product @ U @ Z @ W )
| ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
thf(21,axiom,
! [X: $i,V: $i,W: $i,Y: $i,U: $i,Z: $i] :
( ( product @ X @ V @ W )
| ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
thf(22,axiom,
! [Y: $i,X: $i,Z: $i] :
( ( sum @ Y @ X @ Z )
| ~ ( sum @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
thf(23,axiom,
! [X: $i] :
( ( sum @ ( additive_inverse @ X ) @ X @ additive_identity )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(24,axiom,
! [X: $i] :
( ( sum @ additive_identity @ X @ X )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(25,axiom,
! [U: $i,Z: $i,W: $i,X: $i,Y: $i,V: $i] :
( ( sum @ U @ Z @ W )
| ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
thf(26,axiom,
! [X: $i,V: $i,W: $i,Y: $i,U: $i,Z: $i] :
( ( sum @ X @ V @ W )
| ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
thf(27,axiom,
defined @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).
thf(28,axiom,
defined @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
thf(29,axiom,
defined @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
thf(30,axiom,
defined @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
thf(31,axiom,
defined @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(32,axiom,
defined @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(33,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(34,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[33]) ).
thf(35,negated_conjecture,
~ ( product @ multiplicative_identity @ u @ v ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_11) ).
thf(36,negated_conjecture,
product @ d @ b @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
thf(37,negated_conjecture,
product @ a @ c @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_9) ).
thf(38,negated_conjecture,
product @ multiplicative_identity @ c @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_8) ).
thf(39,negated_conjecture,
product @ multiplicative_identity @ a @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
thf(40,plain,
$false = $false,
inference(unfold_def,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(42,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( less_or_equal @ additive_identity @ Z )
| ~ ( less_or_equal @ additive_identity @ X )
| ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( product @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(43,plain,
( ( ! [U: $i,V: $i,X: $i,Y: $i,Z: $i] :
( ( less_or_equal @ U @ V )
| ~ ( less_or_equal @ X @ Y )
| ~ ( sum @ X @ Z @ U )
| ~ ( sum @ Y @ Z @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
| ( less_or_equal @ Y @ X )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(45,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ X @ Z )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( sum @ additive_identity @ X @ Y )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( sum @ X @ Y @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(49,plain,
( ( ! [X: $i] :
( ( defined @ ( multiplicative_inverse @ X ) )
| ~ ( defined @ X )
| ( sum @ additive_identity @ X @ additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(50,plain,
( ( defined @ multiplicative_identity )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( defined @ ( additive_inverse @ X ) )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(53,plain,
( ( defined @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(55,plain,
( ( ! [A: $i,Z: $i,B: $i,X: $i,Y: $i,C: $i,D: $i] :
( ( product @ A @ Z @ B )
| ~ ( sum @ X @ Y @ A )
| ~ ( product @ X @ Z @ C )
| ~ ( product @ Y @ Z @ D )
| ~ ( sum @ C @ D @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(56,plain,
( ( ! [C: $i,D: $i,B: $i,X: $i,Y: $i,A: $i,Z: $i] :
( ( sum @ C @ D @ B )
| ~ ( sum @ X @ Y @ A )
| ~ ( product @ A @ Z @ B )
| ~ ( product @ X @ Z @ C )
| ~ ( product @ Y @ Z @ D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(57,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( product @ Y @ X @ Z )
| ~ ( product @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity )
| ( sum @ additive_identity @ X @ additive_identity )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(59,plain,
( ( ! [X: $i] :
( ( product @ multiplicative_identity @ X @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(60,plain,
( ( ! [U: $i,Z: $i,W: $i,X: $i,Y: $i,V: $i] :
( ( product @ U @ Z @ W )
| ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(61,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,U: $i,Z: $i] :
( ( product @ X @ V @ W )
| ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(62,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( sum @ Y @ X @ Z )
| ~ ( sum @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( sum @ ( additive_inverse @ X ) @ X @ additive_identity )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(64,plain,
( ( ! [X: $i] :
( ( sum @ additive_identity @ X @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(65,plain,
( ( ! [U: $i,Z: $i,W: $i,X: $i,Y: $i,V: $i] :
( ( sum @ U @ Z @ W )
| ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(66,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,U: $i,Z: $i] :
( ( sum @ X @ V @ W )
| ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(67,plain,
( ( defined @ v )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(68,plain,
( ( defined @ u )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(69,plain,
( ( defined @ d )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(70,plain,
( ( defined @ c )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(71,plain,
( ( defined @ b )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(72,plain,
( ( defined @ a )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(73,plain,
( ( ~ ( product @ multiplicative_identity @ u @ v ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(74,plain,
( ( product @ d @ b @ v )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(75,plain,
( ( product @ a @ c @ u )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(76,plain,
( ( product @ multiplicative_identity @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(77,plain,
( ( product @ multiplicative_identity @ a @ b )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(78,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(79,plain,
( ( ! [Z: $i] :
( ( less_or_equal @ additive_identity @ Z )
| ! [X: $i] :
( ~ ( less_or_equal @ additive_identity @ X )
| ! [Y: $i] :
( ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( product @ X @ Y @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ( less_or_equal @ U @ V )
| ! [Y: $i] :
( ~ ( less_or_equal @ X @ Y )
| ! [Z: $i] :
( ~ ( sum @ X @ Z @ U )
| ~ ( sum @ Y @ Z @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(81,plain,
( ( ! [X: $i,Z: $i] :
( ( less_or_equal @ X @ Z )
| ! [Y: $i] :
( ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(82,plain,
( ( ! [A: $i,Z: $i,B: $i,X: $i,Y: $i] :
( ( product @ A @ Z @ B )
| ~ ( sum @ X @ Y @ A )
| ! [C: $i] :
( ~ ( product @ X @ Z @ C )
| ! [D: $i] :
( ~ ( product @ Y @ Z @ D )
| ~ ( sum @ C @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(83,plain,
( ( ! [C: $i,D: $i,B: $i,X: $i,Y: $i] :
( ( sum @ C @ D @ B )
| ! [A: $i] :
( ~ ( sum @ X @ Y @ A )
| ! [Z: $i] :
( ~ ( product @ A @ Z @ B )
| ~ ( product @ X @ Z @ C )
| ~ ( product @ Y @ Z @ D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(84,plain,
( ( ! [U: $i,Z: $i,W: $i,X: $i] :
( ( product @ U @ Z @ W )
| ! [Y: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(85,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i] :
( ( product @ X @ V @ W )
| ! [U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [Z: $i] :
( ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(86,plain,
( ( ! [U: $i,Z: $i,W: $i,X: $i] :
( ( sum @ U @ Z @ W )
| ! [Y: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(87,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i] :
( ( sum @ X @ V @ W )
| ! [U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [Z: $i] :
( ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(88,plain,
( ( product @ multiplicative_identity @ a @ b )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(89,plain,
( ( product @ multiplicative_identity @ c @ d )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(90,plain,
( ( product @ a @ c @ u )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(91,plain,
( ( product @ d @ b @ v )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(92,plain,
( ( ~ ( product @ multiplicative_identity @ u @ v ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(93,plain,
( ( defined @ a )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(94,plain,
( ( defined @ b )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(95,plain,
( ( defined @ c )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(96,plain,
( ( defined @ d )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(97,plain,
( ( defined @ u )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(98,plain,
( ( defined @ v )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(99,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i] :
( ( sum @ X @ V @ W )
| ! [U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [Z: $i] :
( ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(100,plain,
( ( ! [U: $i,Z: $i,W: $i,X: $i] :
( ( sum @ U @ Z @ W )
| ! [Y: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(101,plain,
( ( ! [X: $i] :
( ( sum @ additive_identity @ X @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(102,plain,
( ( ! [X: $i] :
( ( sum @ ( additive_inverse @ X ) @ X @ additive_identity )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(103,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( sum @ Y @ X @ Z )
| ~ ( sum @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(104,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i] :
( ( product @ X @ V @ W )
| ! [U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [Z: $i] :
( ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(105,plain,
( ( ! [U: $i,Z: $i,W: $i,X: $i] :
( ( product @ U @ Z @ W )
| ! [Y: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( product @ multiplicative_identity @ X @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(107,plain,
( ( ! [X: $i] :
( ( product @ ( multiplicative_inverse @ X ) @ X @ multiplicative_identity )
| ( sum @ additive_identity @ X @ additive_identity )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(108,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( product @ Y @ X @ Z )
| ~ ( product @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(109,plain,
( ( ! [C: $i,D: $i,B: $i,X: $i,Y: $i] :
( ( sum @ C @ D @ B )
| ! [A: $i] :
( ~ ( sum @ X @ Y @ A )
| ! [Z: $i] :
( ~ ( product @ A @ Z @ B )
| ~ ( product @ X @ Z @ C )
| ~ ( product @ Y @ Z @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(110,plain,
( ( ! [A: $i,Z: $i,B: $i,X: $i,Y: $i] :
( ( product @ A @ Z @ B )
| ~ ( sum @ X @ Y @ A )
| ! [C: $i] :
( ~ ( product @ X @ Z @ C )
| ! [D: $i] :
( ~ ( product @ Y @ Z @ D )
| ~ ( sum @ C @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(112,plain,
( ( defined @ additive_identity )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(113,plain,
( ( ! [X: $i] :
( ( defined @ ( additive_inverse @ X ) )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(115,plain,
( ( defined @ multiplicative_identity )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(116,plain,
( ( ! [X: $i] :
( ( defined @ ( multiplicative_inverse @ X ) )
| ~ ( defined @ X )
| ( sum @ additive_identity @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ( sum @ X @ Y @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ( product @ X @ Y @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ( sum @ additive_identity @ X @ Y )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(120,plain,
( ( ! [X: $i,Z: $i] :
( ( less_or_equal @ X @ Z )
| ! [Y: $i] :
( ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
| ( less_or_equal @ Y @ X )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(122,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ( less_or_equal @ U @ V )
| ! [Y: $i] :
( ~ ( less_or_equal @ X @ Y )
| ! [Z: $i] :
( ~ ( sum @ X @ Z @ U )
| ~ ( sum @ Y @ Z @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(123,plain,
( ( ! [Z: $i] :
( ( less_or_equal @ additive_identity @ Z )
| ! [X: $i] :
( ~ ( less_or_equal @ additive_identity @ X )
| ! [Y: $i] :
( ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( product @ X @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(124,plain,
( ( ~ ( sum @ additive_identity @ additive_identity @ multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(125,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(126,plain,
( ( product @ multiplicative_identity @ u @ v )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(127,plain,
! [SV1: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ( sum @ SV1 @ SY73 @ SY74 )
| ! [SY76: $i] :
( ~ ( sum @ SV1 @ SY75 @ SY76 )
| ! [Z: $i] :
( ~ ( sum @ SY75 @ Z @ SY73 )
| ~ ( sum @ SY76 @ Z @ SY74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(128,plain,
! [SV2: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i] :
( ( sum @ SV2 @ SY78 @ SY79 )
| ! [SY81: $i] :
( ~ ( sum @ SY80 @ SY81 @ SV2 )
| ! [V: $i] :
( ~ ( sum @ SY81 @ SY78 @ V )
| ~ ( sum @ SY80 @ V @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(129,plain,
! [SV3: $i] :
( ( ( sum @ additive_identity @ SV3 @ SV3 )
| ~ ( defined @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(130,plain,
! [SV4: $i] :
( ( ( sum @ ( additive_inverse @ SV4 ) @ SV4 @ additive_identity )
| ~ ( defined @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(131,plain,
! [SV5: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ( sum @ SV5 @ SY83 @ SY84 )
| ~ ( sum @ SY83 @ SV5 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(132,plain,
! [SV6: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ( product @ SV6 @ SY85 @ SY86 )
| ! [SY88: $i] :
( ~ ( product @ SV6 @ SY87 @ SY88 )
| ! [Z: $i] :
( ~ ( product @ SY87 @ Z @ SY85 )
| ~ ( product @ SY88 @ Z @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(133,plain,
! [SV7: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( product @ SV7 @ SY90 @ SY91 )
| ! [SY93: $i] :
( ~ ( product @ SY92 @ SY93 @ SV7 )
| ! [V: $i] :
( ~ ( product @ SY93 @ SY90 @ V )
| ~ ( product @ SY92 @ V @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(134,plain,
! [SV8: $i] :
( ( ( product @ multiplicative_identity @ SV8 @ SV8 )
| ~ ( defined @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(135,plain,
! [SV9: $i] :
( ( ( product @ ( multiplicative_inverse @ SV9 ) @ SV9 @ multiplicative_identity )
| ( sum @ additive_identity @ SV9 @ additive_identity )
| ~ ( defined @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(136,plain,
! [SV10: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ( product @ SV10 @ SY95 @ SY96 )
| ~ ( product @ SY95 @ SV10 @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(137,plain,
! [SV11: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i,SY100: $i] :
( ( sum @ SV11 @ SY97 @ SY98 )
| ! [SY101: $i] :
( ~ ( sum @ SY99 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( product @ SY101 @ SY102 @ SY98 )
| ~ ( product @ SY99 @ SY102 @ SV11 )
| ~ ( product @ SY100 @ SY102 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(138,plain,
! [SV12: $i] :
( ( ! [SY103: $i,SY104: $i,SY105: $i,SY106: $i] :
( ( product @ SV12 @ SY103 @ SY104 )
| ~ ( sum @ SY105 @ SY106 @ SV12 )
| ! [C: $i] :
( ~ ( product @ SY105 @ SY103 @ C )
| ! [D: $i] :
( ~ ( product @ SY106 @ SY103 @ D )
| ~ ( sum @ C @ D @ SY104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(139,plain,
! [SV13: $i] :
( ( ! [SY109: $i] :
( ( defined @ ( add @ SV13 @ SY109 ) )
| ~ ( defined @ SV13 )
| ~ ( defined @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(140,plain,
! [SV14: $i] :
( ( ( defined @ ( additive_inverse @ SV14 ) )
| ~ ( defined @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(141,plain,
! [SV15: $i] :
( ( ! [SY110: $i] :
( ( defined @ ( multiply @ SV15 @ SY110 ) )
| ~ ( defined @ SV15 )
| ~ ( defined @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(142,plain,
! [SV16: $i] :
( ( ( defined @ ( multiplicative_inverse @ SV16 ) )
| ~ ( defined @ SV16 )
| ( sum @ additive_identity @ SV16 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV17: $i] :
( ( ! [SY111: $i] :
( ( sum @ SV17 @ SY111 @ ( add @ SV17 @ SY111 ) )
| ~ ( defined @ SV17 )
| ~ ( defined @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
! [SV18: $i] :
( ( ! [SY112: $i] :
( ( product @ SV18 @ SY112 @ ( multiply @ SV18 @ SY112 ) )
| ~ ( defined @ SV18 )
| ~ ( defined @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(145,plain,
! [SV19: $i] :
( ( ! [SY113: $i] :
( ( sum @ additive_identity @ SV19 @ SY113 )
| ~ ( less_or_equal @ SV19 @ SY113 )
| ~ ( less_or_equal @ SY113 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(146,plain,
! [SV20: $i] :
( ( ! [SY114: $i] :
( ( less_or_equal @ SV20 @ SY114 )
| ! [SY115: $i] :
( ~ ( less_or_equal @ SV20 @ SY115 )
| ~ ( less_or_equal @ SY115 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(147,plain,
! [SV21: $i] :
( ( ! [SY116: $i] :
( ( less_or_equal @ SV21 @ SY116 )
| ( less_or_equal @ SY116 @ SV21 )
| ~ ( defined @ SV21 )
| ~ ( defined @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(148,plain,
! [SV22: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ( less_or_equal @ SV22 @ SY117 )
| ! [SY119: $i] :
( ~ ( less_or_equal @ SY118 @ SY119 )
| ! [SY120: $i] :
( ~ ( sum @ SY118 @ SY120 @ SV22 )
| ~ ( sum @ SY119 @ SY120 @ SY117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(149,plain,
! [SV23: $i] :
( ( ( less_or_equal @ additive_identity @ SV23 )
| ! [SY121: $i] :
( ~ ( less_or_equal @ additive_identity @ SY121 )
| ! [SY122: $i] :
( ~ ( less_or_equal @ additive_identity @ SY122 )
| ~ ( product @ SY121 @ SY122 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(150,plain,
( ( sum @ additive_identity @ additive_identity @ multiplicative_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(151,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV24: $i,SV1: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ( sum @ SV1 @ SV24 @ SY123 )
| ! [SY125: $i] :
( ~ ( sum @ SV1 @ SY124 @ SY125 )
| ! [SY126: $i] :
( ~ ( sum @ SY124 @ SY126 @ SV24 )
| ~ ( sum @ SY125 @ SY126 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(153,plain,
! [SV25: $i,SV2: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ( sum @ SV2 @ SV25 @ SY127 )
| ! [SY129: $i] :
( ~ ( sum @ SY128 @ SY129 @ SV2 )
| ! [SY130: $i] :
( ~ ( sum @ SY129 @ SV25 @ SY130 )
| ~ ( sum @ SY128 @ SY130 @ SY127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(154,plain,
! [SV3: $i] :
( ( ( sum @ additive_identity @ SV3 @ SV3 )
= $true )
| ( ( ~ ( defined @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(155,plain,
! [SV4: $i] :
( ( ( sum @ ( additive_inverse @ SV4 ) @ SV4 @ additive_identity )
= $true )
| ( ( ~ ( defined @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(156,plain,
! [SV26: $i,SV5: $i] :
( ( ! [SY131: $i] :
( ( sum @ SV5 @ SV26 @ SY131 )
| ~ ( sum @ SV26 @ SV5 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(157,plain,
! [SV27: $i,SV6: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( product @ SV6 @ SV27 @ SY132 )
| ! [SY134: $i] :
( ~ ( product @ SV6 @ SY133 @ SY134 )
| ! [SY135: $i] :
( ~ ( product @ SY133 @ SY135 @ SV27 )
| ~ ( product @ SY134 @ SY135 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(158,plain,
! [SV28: $i,SV7: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ( product @ SV7 @ SV28 @ SY136 )
| ! [SY138: $i] :
( ~ ( product @ SY137 @ SY138 @ SV7 )
| ! [SY139: $i] :
( ~ ( product @ SY138 @ SV28 @ SY139 )
| ~ ( product @ SY137 @ SY139 @ SY136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(159,plain,
! [SV8: $i] :
( ( ( product @ multiplicative_identity @ SV8 @ SV8 )
= $true )
| ( ( ~ ( defined @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(160,plain,
! [SV9: $i] :
( ( ( product @ ( multiplicative_inverse @ SV9 ) @ SV9 @ multiplicative_identity )
= $true )
| ( ( ( sum @ additive_identity @ SV9 @ additive_identity )
| ~ ( defined @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(161,plain,
! [SV29: $i,SV10: $i] :
( ( ! [SY140: $i] :
( ( product @ SV10 @ SV29 @ SY140 )
| ~ ( product @ SV29 @ SV10 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(162,plain,
! [SV30: $i,SV11: $i] :
( ( ! [SY141: $i,SY142: $i,SY143: $i] :
( ( sum @ SV11 @ SV30 @ SY141 )
| ! [SY144: $i] :
( ~ ( sum @ SY142 @ SY143 @ SY144 )
| ! [SY145: $i] :
( ~ ( product @ SY144 @ SY145 @ SY141 )
| ~ ( product @ SY142 @ SY145 @ SV11 )
| ~ ( product @ SY143 @ SY145 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(163,plain,
! [SV31: $i,SV12: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i] :
( ( product @ SV12 @ SV31 @ SY146 )
| ~ ( sum @ SY147 @ SY148 @ SV12 )
| ! [SY149: $i] :
( ~ ( product @ SY147 @ SV31 @ SY149 )
| ! [SY150: $i] :
( ~ ( product @ SY148 @ SV31 @ SY150 )
| ~ ( sum @ SY149 @ SY150 @ SY146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(164,plain,
! [SV32: $i,SV13: $i] :
( ( ( defined @ ( add @ SV13 @ SV32 ) )
| ~ ( defined @ SV13 )
| ~ ( defined @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(165,plain,
! [SV14: $i] :
( ( ( defined @ ( additive_inverse @ SV14 ) )
= $true )
| ( ( ~ ( defined @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(166,plain,
! [SV33: $i,SV15: $i] :
( ( ( defined @ ( multiply @ SV15 @ SV33 ) )
| ~ ( defined @ SV15 )
| ~ ( defined @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(167,plain,
! [SV16: $i] :
( ( ( defined @ ( multiplicative_inverse @ SV16 ) )
= $true )
| ( ( ~ ( defined @ SV16 )
| ( sum @ additive_identity @ SV16 @ additive_identity ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(168,plain,
! [SV34: $i,SV17: $i] :
( ( ( sum @ SV17 @ SV34 @ ( add @ SV17 @ SV34 ) )
| ~ ( defined @ SV17 )
| ~ ( defined @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(169,plain,
! [SV35: $i,SV18: $i] :
( ( ( product @ SV18 @ SV35 @ ( multiply @ SV18 @ SV35 ) )
| ~ ( defined @ SV18 )
| ~ ( defined @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(170,plain,
! [SV36: $i,SV19: $i] :
( ( ( sum @ additive_identity @ SV19 @ SV36 )
| ~ ( less_or_equal @ SV19 @ SV36 )
| ~ ( less_or_equal @ SV36 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(171,plain,
! [SV37: $i,SV20: $i] :
( ( ( less_or_equal @ SV20 @ SV37 )
| ! [SY151: $i] :
( ~ ( less_or_equal @ SV20 @ SY151 )
| ~ ( less_or_equal @ SY151 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(172,plain,
! [SV38: $i,SV21: $i] :
( ( ( less_or_equal @ SV21 @ SV38 )
| ( less_or_equal @ SV38 @ SV21 )
| ~ ( defined @ SV21 )
| ~ ( defined @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(173,plain,
! [SV39: $i,SV22: $i] :
( ( ! [SY152: $i] :
( ( less_or_equal @ SV22 @ SV39 )
| ! [SY153: $i] :
( ~ ( less_or_equal @ SY152 @ SY153 )
| ! [SY154: $i] :
( ~ ( sum @ SY152 @ SY154 @ SV22 )
| ~ ( sum @ SY153 @ SY154 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(174,plain,
! [SV23: $i] :
( ( ( less_or_equal @ additive_identity @ SV23 )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( less_or_equal @ additive_identity @ SY121 )
| ! [SY122: $i] :
( ~ ( less_or_equal @ additive_identity @ SY122 )
| ~ ( product @ SY121 @ SY122 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(175,plain,
! [SV40: $i,SV24: $i,SV1: $i] :
( ( ! [SY155: $i] :
( ( sum @ SV1 @ SV24 @ SV40 )
| ! [SY156: $i] :
( ~ ( sum @ SV1 @ SY155 @ SY156 )
| ! [SY157: $i] :
( ~ ( sum @ SY155 @ SY157 @ SV24 )
| ~ ( sum @ SY156 @ SY157 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(176,plain,
! [SV41: $i,SV25: $i,SV2: $i] :
( ( ! [SY158: $i] :
( ( sum @ SV2 @ SV25 @ SV41 )
| ! [SY159: $i] :
( ~ ( sum @ SY158 @ SY159 @ SV2 )
| ! [SY160: $i] :
( ~ ( sum @ SY159 @ SV25 @ SY160 )
| ~ ( sum @ SY158 @ SY160 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(177,plain,
! [SV3: $i] :
( ( ( defined @ SV3 )
= $false )
| ( ( sum @ additive_identity @ SV3 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(178,plain,
! [SV4: $i] :
( ( ( defined @ SV4 )
= $false )
| ( ( sum @ ( additive_inverse @ SV4 ) @ SV4 @ additive_identity )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV42: $i,SV26: $i,SV5: $i] :
( ( ( sum @ SV5 @ SV26 @ SV42 )
| ~ ( sum @ SV26 @ SV5 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV43: $i,SV27: $i,SV6: $i] :
( ( ! [SY161: $i] :
( ( product @ SV6 @ SV27 @ SV43 )
| ! [SY162: $i] :
( ~ ( product @ SV6 @ SY161 @ SY162 )
| ! [SY163: $i] :
( ~ ( product @ SY161 @ SY163 @ SV27 )
| ~ ( product @ SY162 @ SY163 @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV44: $i,SV28: $i,SV7: $i] :
( ( ! [SY164: $i] :
( ( product @ SV7 @ SV28 @ SV44 )
| ! [SY165: $i] :
( ~ ( product @ SY164 @ SY165 @ SV7 )
| ! [SY166: $i] :
( ~ ( product @ SY165 @ SV28 @ SY166 )
| ~ ( product @ SY164 @ SY166 @ SV44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV8: $i] :
( ( ( defined @ SV8 )
= $false )
| ( ( product @ multiplicative_identity @ SV8 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(183,plain,
! [SV9: $i] :
( ( ( sum @ additive_identity @ SV9 @ additive_identity )
= $true )
| ( ( ~ ( defined @ SV9 ) )
= $true )
| ( ( product @ ( multiplicative_inverse @ SV9 ) @ SV9 @ multiplicative_identity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(184,plain,
! [SV45: $i,SV29: $i,SV10: $i] :
( ( ( product @ SV10 @ SV29 @ SV45 )
| ~ ( product @ SV29 @ SV10 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV46: $i,SV30: $i,SV11: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ( sum @ SV11 @ SV30 @ SV46 )
| ! [SY169: $i] :
( ~ ( sum @ SY167 @ SY168 @ SY169 )
| ! [SY170: $i] :
( ~ ( product @ SY169 @ SY170 @ SV46 )
| ~ ( product @ SY167 @ SY170 @ SV11 )
| ~ ( product @ SY168 @ SY170 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV47: $i,SV31: $i,SV12: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( product @ SV12 @ SV31 @ SV47 )
| ~ ( sum @ SY171 @ SY172 @ SV12 )
| ! [SY173: $i] :
( ~ ( product @ SY171 @ SV31 @ SY173 )
| ! [SY174: $i] :
( ~ ( product @ SY172 @ SV31 @ SY174 )
| ~ ( sum @ SY173 @ SY174 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV32: $i,SV13: $i] :
( ( ( defined @ ( add @ SV13 @ SV32 ) )
= $true )
| ( ( ~ ( defined @ SV13 )
| ~ ( defined @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV14: $i] :
( ( ( defined @ SV14 )
= $false )
| ( ( defined @ ( additive_inverse @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV33: $i,SV15: $i] :
( ( ( defined @ ( multiply @ SV15 @ SV33 ) )
= $true )
| ( ( ~ ( defined @ SV15 )
| ~ ( defined @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV16: $i] :
( ( ( ~ ( defined @ SV16 ) )
= $true )
| ( ( sum @ additive_identity @ SV16 @ additive_identity )
= $true )
| ( ( defined @ ( multiplicative_inverse @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV34: $i,SV17: $i] :
( ( ( sum @ SV17 @ SV34 @ ( add @ SV17 @ SV34 ) )
= $true )
| ( ( ~ ( defined @ SV17 )
| ~ ( defined @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV35: $i,SV18: $i] :
( ( ( product @ SV18 @ SV35 @ ( multiply @ SV18 @ SV35 ) )
= $true )
| ( ( ~ ( defined @ SV18 )
| ~ ( defined @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV36: $i,SV19: $i] :
( ( ( sum @ additive_identity @ SV19 @ SV36 )
= $true )
| ( ( ~ ( less_or_equal @ SV19 @ SV36 )
| ~ ( less_or_equal @ SV36 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV37: $i,SV20: $i] :
( ( ( less_or_equal @ SV20 @ SV37 )
= $true )
| ( ( ! [SY151: $i] :
( ~ ( less_or_equal @ SV20 @ SY151 )
| ~ ( less_or_equal @ SY151 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV38: $i,SV21: $i] :
( ( ( less_or_equal @ SV21 @ SV38 )
= $true )
| ( ( ( less_or_equal @ SV38 @ SV21 )
| ~ ( defined @ SV21 )
| ~ ( defined @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV48: $i,SV39: $i,SV22: $i] :
( ( ( less_or_equal @ SV22 @ SV39 )
| ! [SY175: $i] :
( ~ ( less_or_equal @ SV48 @ SY175 )
| ! [SY176: $i] :
( ~ ( sum @ SV48 @ SY176 @ SV22 )
| ~ ( sum @ SY175 @ SY176 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV23: $i,SV49: $i] :
( ( ( ~ ( less_or_equal @ additive_identity @ SV49 )
| ! [SY177: $i] :
( ~ ( less_or_equal @ additive_identity @ SY177 )
| ~ ( product @ SV49 @ SY177 @ SV23 ) ) )
= $true )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV50: $i,SV40: $i,SV24: $i,SV1: $i] :
( ( ( sum @ SV1 @ SV24 @ SV40 )
| ! [SY178: $i] :
( ~ ( sum @ SV1 @ SV50 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV50 @ SY179 @ SV24 )
| ~ ( sum @ SY178 @ SY179 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV51: $i,SV41: $i,SV25: $i,SV2: $i] :
( ( ( sum @ SV2 @ SV25 @ SV41 )
| ! [SY180: $i] :
( ~ ( sum @ SV51 @ SY180 @ SV2 )
| ! [SY181: $i] :
( ~ ( sum @ SY180 @ SV25 @ SY181 )
| ~ ( sum @ SV51 @ SY181 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV42: $i,SV26: $i,SV5: $i] :
( ( ( sum @ SV5 @ SV26 @ SV42 )
= $true )
| ( ( ~ ( sum @ SV26 @ SV5 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(201,plain,
! [SV52: $i,SV43: $i,SV27: $i,SV6: $i] :
( ( ( product @ SV6 @ SV27 @ SV43 )
| ! [SY182: $i] :
( ~ ( product @ SV6 @ SV52 @ SY182 )
| ! [SY183: $i] :
( ~ ( product @ SV52 @ SY183 @ SV27 )
| ~ ( product @ SY182 @ SY183 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(202,plain,
! [SV53: $i,SV44: $i,SV28: $i,SV7: $i] :
( ( ( product @ SV7 @ SV28 @ SV44 )
| ! [SY184: $i] :
( ~ ( product @ SV53 @ SY184 @ SV7 )
| ! [SY185: $i] :
( ~ ( product @ SY184 @ SV28 @ SY185 )
| ~ ( product @ SV53 @ SY185 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(203,plain,
! [SV9: $i] :
( ( ( defined @ SV9 )
= $false )
| ( ( sum @ additive_identity @ SV9 @ additive_identity )
= $true )
| ( ( product @ ( multiplicative_inverse @ SV9 ) @ SV9 @ multiplicative_identity )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(204,plain,
! [SV45: $i,SV29: $i,SV10: $i] :
( ( ( product @ SV10 @ SV29 @ SV45 )
= $true )
| ( ( ~ ( product @ SV29 @ SV10 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(205,plain,
! [SV54: $i,SV46: $i,SV30: $i,SV11: $i] :
( ( ! [SY186: $i] :
( ( sum @ SV11 @ SV30 @ SV46 )
| ! [SY187: $i] :
( ~ ( sum @ SV54 @ SY186 @ SY187 )
| ! [SY188: $i] :
( ~ ( product @ SY187 @ SY188 @ SV46 )
| ~ ( product @ SV54 @ SY188 @ SV11 )
| ~ ( product @ SY186 @ SY188 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(206,plain,
! [SV55: $i,SV47: $i,SV31: $i,SV12: $i] :
( ( ! [SY189: $i] :
( ( product @ SV12 @ SV31 @ SV47 )
| ~ ( sum @ SV55 @ SY189 @ SV12 )
| ! [SY190: $i] :
( ~ ( product @ SV55 @ SV31 @ SY190 )
| ! [SY174: $i] :
( ~ ( product @ SY189 @ SV31 @ SY174 )
| ~ ( sum @ SY190 @ SY174 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(207,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( defined @ SV13 ) )
= $true )
| ( ( ~ ( defined @ SV32 ) )
= $true )
| ( ( defined @ ( add @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(208,plain,
! [SV33: $i,SV15: $i] :
( ( ( ~ ( defined @ SV15 ) )
= $true )
| ( ( ~ ( defined @ SV33 ) )
= $true )
| ( ( defined @ ( multiply @ SV15 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(209,plain,
! [SV16: $i] :
( ( ( defined @ SV16 )
= $false )
| ( ( sum @ additive_identity @ SV16 @ additive_identity )
= $true )
| ( ( defined @ ( multiplicative_inverse @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(210,plain,
! [SV34: $i,SV17: $i] :
( ( ( ~ ( defined @ SV17 ) )
= $true )
| ( ( ~ ( defined @ SV34 ) )
= $true )
| ( ( sum @ SV17 @ SV34 @ ( add @ SV17 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(211,plain,
! [SV35: $i,SV18: $i] :
( ( ( ~ ( defined @ SV18 ) )
= $true )
| ( ( ~ ( defined @ SV35 ) )
= $true )
| ( ( product @ SV18 @ SV35 @ ( multiply @ SV18 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(212,plain,
! [SV36: $i,SV19: $i] :
( ( ( ~ ( less_or_equal @ SV19 @ SV36 ) )
= $true )
| ( ( ~ ( less_or_equal @ SV36 @ SV19 ) )
= $true )
| ( ( sum @ additive_identity @ SV19 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(213,plain,
! [SV37: $i,SV56: $i,SV20: $i] :
( ( ( ~ ( less_or_equal @ SV20 @ SV56 )
| ~ ( less_or_equal @ SV56 @ SV37 ) )
= $true )
| ( ( less_or_equal @ SV20 @ SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(214,plain,
! [SV21: $i,SV38: $i] :
( ( ( less_or_equal @ SV38 @ SV21 )
= $true )
| ( ( ~ ( defined @ SV21 )
| ~ ( defined @ SV38 ) )
= $true )
| ( ( less_or_equal @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(215,plain,
! [SV48: $i,SV39: $i,SV22: $i] :
( ( ( less_or_equal @ SV22 @ SV39 )
= $true )
| ( ( ! [SY175: $i] :
( ~ ( less_or_equal @ SV48 @ SY175 )
| ! [SY176: $i] :
( ~ ( sum @ SV48 @ SY176 @ SV22 )
| ~ ( sum @ SY175 @ SY176 @ SV39 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(216,plain,
! [SV23: $i,SV49: $i] :
( ( ( ~ ( less_or_equal @ additive_identity @ SV49 ) )
= $true )
| ( ( ! [SY177: $i] :
( ~ ( less_or_equal @ additive_identity @ SY177 )
| ~ ( product @ SV49 @ SY177 @ SV23 ) ) )
= $true )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV50: $i,SV40: $i,SV24: $i,SV1: $i] :
( ( ( sum @ SV1 @ SV24 @ SV40 )
= $true )
| ( ( ! [SY178: $i] :
( ~ ( sum @ SV1 @ SV50 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV50 @ SY179 @ SV24 )
| ~ ( sum @ SY178 @ SY179 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(218,plain,
! [SV51: $i,SV41: $i,SV25: $i,SV2: $i] :
( ( ( sum @ SV2 @ SV25 @ SV41 )
= $true )
| ( ( ! [SY180: $i] :
( ~ ( sum @ SV51 @ SY180 @ SV2 )
| ! [SY181: $i] :
( ~ ( sum @ SY180 @ SV25 @ SY181 )
| ~ ( sum @ SV51 @ SY181 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(219,plain,
! [SV42: $i,SV5: $i,SV26: $i] :
( ( ( sum @ SV26 @ SV5 @ SV42 )
= $false )
| ( ( sum @ SV5 @ SV26 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(220,plain,
! [SV52: $i,SV43: $i,SV27: $i,SV6: $i] :
( ( ( product @ SV6 @ SV27 @ SV43 )
= $true )
| ( ( ! [SY182: $i] :
( ~ ( product @ SV6 @ SV52 @ SY182 )
| ! [SY183: $i] :
( ~ ( product @ SV52 @ SY183 @ SV27 )
| ~ ( product @ SY182 @ SY183 @ SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(221,plain,
! [SV53: $i,SV44: $i,SV28: $i,SV7: $i] :
( ( ( product @ SV7 @ SV28 @ SV44 )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( product @ SV53 @ SY184 @ SV7 )
| ! [SY185: $i] :
( ~ ( product @ SY184 @ SV28 @ SY185 )
| ~ ( product @ SV53 @ SY185 @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(222,plain,
! [SV45: $i,SV10: $i,SV29: $i] :
( ( ( product @ SV29 @ SV10 @ SV45 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(223,plain,
! [SV57: $i,SV54: $i,SV46: $i,SV30: $i,SV11: $i] :
( ( ( sum @ SV11 @ SV30 @ SV46 )
| ! [SY192: $i] :
( ~ ( sum @ SV54 @ SV57 @ SY192 )
| ! [SY193: $i] :
( ~ ( product @ SY192 @ SY193 @ SV46 )
| ~ ( product @ SV54 @ SY193 @ SV11 )
| ~ ( product @ SV57 @ SY193 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(224,plain,
! [SV58: $i,SV55: $i,SV47: $i,SV31: $i,SV12: $i] :
( ( ( product @ SV12 @ SV31 @ SV47 )
| ~ ( sum @ SV55 @ SV58 @ SV12 )
| ! [SY194: $i] :
( ~ ( product @ SV55 @ SV31 @ SY194 )
| ! [SY195: $i] :
( ~ ( product @ SV58 @ SV31 @ SY195 )
| ~ ( sum @ SY194 @ SY195 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(225,plain,
! [SV32: $i,SV13: $i] :
( ( ( defined @ SV13 )
= $false )
| ( ( ~ ( defined @ SV32 ) )
= $true )
| ( ( defined @ ( add @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(226,plain,
! [SV33: $i,SV15: $i] :
( ( ( defined @ SV15 )
= $false )
| ( ( ~ ( defined @ SV33 ) )
= $true )
| ( ( defined @ ( multiply @ SV15 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV34: $i,SV17: $i] :
( ( ( defined @ SV17 )
= $false )
| ( ( ~ ( defined @ SV34 ) )
= $true )
| ( ( sum @ SV17 @ SV34 @ ( add @ SV17 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(228,plain,
! [SV35: $i,SV18: $i] :
( ( ( defined @ SV18 )
= $false )
| ( ( ~ ( defined @ SV35 ) )
= $true )
| ( ( product @ SV18 @ SV35 @ ( multiply @ SV18 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV36: $i,SV19: $i] :
( ( ( less_or_equal @ SV19 @ SV36 )
= $false )
| ( ( ~ ( less_or_equal @ SV36 @ SV19 ) )
= $true )
| ( ( sum @ additive_identity @ SV19 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV37: $i,SV56: $i,SV20: $i] :
( ( ( ~ ( less_or_equal @ SV20 @ SV56 ) )
= $true )
| ( ( ~ ( less_or_equal @ SV56 @ SV37 ) )
= $true )
| ( ( less_or_equal @ SV20 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(231,plain,
! [SV38: $i,SV21: $i] :
( ( ( ~ ( defined @ SV21 ) )
= $true )
| ( ( ~ ( defined @ SV38 ) )
= $true )
| ( ( less_or_equal @ SV38 @ SV21 )
= $true )
| ( ( less_or_equal @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(232,plain,
! [SV39: $i,SV22: $i,SV59: $i,SV48: $i] :
( ( ( ~ ( less_or_equal @ SV48 @ SV59 )
| ! [SY196: $i] :
( ~ ( sum @ SV48 @ SY196 @ SV22 )
| ~ ( sum @ SV59 @ SY196 @ SV39 ) ) )
= $true )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV23: $i,SV49: $i] :
( ( ( less_or_equal @ additive_identity @ SV49 )
= $false )
| ( ( ! [SY177: $i] :
( ~ ( less_or_equal @ additive_identity @ SY177 )
| ~ ( product @ SV49 @ SY177 @ SV23 ) ) )
= $true )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV40: $i,SV24: $i,SV60: $i,SV50: $i,SV1: $i] :
( ( ( ~ ( sum @ SV1 @ SV50 @ SV60 )
| ! [SY197: $i] :
( ~ ( sum @ SV50 @ SY197 @ SV24 )
| ~ ( sum @ SV60 @ SY197 @ SV40 ) ) )
= $true )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV41: $i,SV25: $i,SV2: $i,SV61: $i,SV51: $i] :
( ( ( ~ ( sum @ SV51 @ SV61 @ SV2 )
| ! [SY198: $i] :
( ~ ( sum @ SV61 @ SV25 @ SY198 )
| ~ ( sum @ SV51 @ SY198 @ SV41 ) ) )
= $true )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV43: $i,SV27: $i,SV62: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV52 @ SV62 )
| ! [SY199: $i] :
( ~ ( product @ SV52 @ SY199 @ SV27 )
| ~ ( product @ SV62 @ SY199 @ SV43 ) ) )
= $true )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(237,plain,
! [SV44: $i,SV28: $i,SV7: $i,SV63: $i,SV53: $i] :
( ( ( ~ ( product @ SV53 @ SV63 @ SV7 )
| ! [SY200: $i] :
( ~ ( product @ SV63 @ SV28 @ SY200 )
| ~ ( product @ SV53 @ SY200 @ SV44 ) ) )
= $true )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(238,plain,
! [SV57: $i,SV54: $i,SV46: $i,SV30: $i,SV11: $i] :
( ( ( sum @ SV11 @ SV30 @ SV46 )
= $true )
| ( ( ! [SY192: $i] :
( ~ ( sum @ SV54 @ SV57 @ SY192 )
| ! [SY193: $i] :
( ~ ( product @ SY192 @ SY193 @ SV46 )
| ~ ( product @ SV54 @ SY193 @ SV11 )
| ~ ( product @ SV57 @ SY193 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV58: $i,SV55: $i,SV47: $i,SV31: $i,SV12: $i] :
( ( ( product @ SV12 @ SV31 @ SV47 )
= $true )
| ( ( ~ ( sum @ SV55 @ SV58 @ SV12 )
| ! [SY194: $i] :
( ~ ( product @ SV55 @ SV31 @ SY194 )
| ! [SY195: $i] :
( ~ ( product @ SV58 @ SV31 @ SY195 )
| ~ ( sum @ SY194 @ SY195 @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(240,plain,
! [SV13: $i,SV32: $i] :
( ( ( defined @ SV32 )
= $false )
| ( ( defined @ SV13 )
= $false )
| ( ( defined @ ( add @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(241,plain,
! [SV15: $i,SV33: $i] :
( ( ( defined @ SV33 )
= $false )
| ( ( defined @ SV15 )
= $false )
| ( ( defined @ ( multiply @ SV15 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(242,plain,
! [SV17: $i,SV34: $i] :
( ( ( defined @ SV34 )
= $false )
| ( ( defined @ SV17 )
= $false )
| ( ( sum @ SV17 @ SV34 @ ( add @ SV17 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV18: $i,SV35: $i] :
( ( ( defined @ SV35 )
= $false )
| ( ( defined @ SV18 )
= $false )
| ( ( product @ SV18 @ SV35 @ ( multiply @ SV18 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV19: $i,SV36: $i] :
( ( ( less_or_equal @ SV36 @ SV19 )
= $false )
| ( ( less_or_equal @ SV19 @ SV36 )
= $false )
| ( ( sum @ additive_identity @ SV19 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV37: $i,SV56: $i,SV20: $i] :
( ( ( less_or_equal @ SV20 @ SV56 )
= $false )
| ( ( ~ ( less_or_equal @ SV56 @ SV37 ) )
= $true )
| ( ( less_or_equal @ SV20 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV38: $i,SV21: $i] :
( ( ( defined @ SV21 )
= $false )
| ( ( ~ ( defined @ SV38 ) )
= $true )
| ( ( less_or_equal @ SV38 @ SV21 )
= $true )
| ( ( less_or_equal @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(247,plain,
! [SV39: $i,SV22: $i,SV59: $i,SV48: $i] :
( ( ( ~ ( less_or_equal @ SV48 @ SV59 ) )
= $true )
| ( ( ! [SY196: $i] :
( ~ ( sum @ SV48 @ SY196 @ SV22 )
| ~ ( sum @ SV59 @ SY196 @ SV39 ) ) )
= $true )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV23: $i,SV49: $i,SV64: $i] :
( ( ( ~ ( less_or_equal @ additive_identity @ SV64 )
| ~ ( product @ SV49 @ SV64 @ SV23 ) )
= $true )
| ( ( less_or_equal @ additive_identity @ SV49 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV40: $i,SV24: $i,SV60: $i,SV50: $i,SV1: $i] :
( ( ( ~ ( sum @ SV1 @ SV50 @ SV60 ) )
= $true )
| ( ( ! [SY197: $i] :
( ~ ( sum @ SV50 @ SY197 @ SV24 )
| ~ ( sum @ SV60 @ SY197 @ SV40 ) ) )
= $true )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(250,plain,
! [SV41: $i,SV25: $i,SV2: $i,SV61: $i,SV51: $i] :
( ( ( ~ ( sum @ SV51 @ SV61 @ SV2 ) )
= $true )
| ( ( ! [SY198: $i] :
( ~ ( sum @ SV61 @ SV25 @ SY198 )
| ~ ( sum @ SV51 @ SY198 @ SV41 ) ) )
= $true )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(251,plain,
! [SV43: $i,SV27: $i,SV62: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV52 @ SV62 ) )
= $true )
| ( ( ! [SY199: $i] :
( ~ ( product @ SV52 @ SY199 @ SV27 )
| ~ ( product @ SV62 @ SY199 @ SV43 ) ) )
= $true )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(252,plain,
! [SV44: $i,SV28: $i,SV7: $i,SV63: $i,SV53: $i] :
( ( ( ~ ( product @ SV53 @ SV63 @ SV7 ) )
= $true )
| ( ( ! [SY200: $i] :
( ~ ( product @ SV63 @ SV28 @ SY200 )
| ~ ( product @ SV53 @ SY200 @ SV44 ) ) )
= $true )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV30: $i,SV11: $i,SV46: $i,SV65: $i,SV57: $i,SV54: $i] :
( ( ( ~ ( sum @ SV54 @ SV57 @ SV65 )
| ! [SY201: $i] :
( ~ ( product @ SV65 @ SY201 @ SV46 )
| ~ ( product @ SV54 @ SY201 @ SV11 )
| ~ ( product @ SV57 @ SY201 @ SV30 ) ) )
= $true )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV47: $i,SV31: $i,SV12: $i,SV58: $i,SV55: $i] :
( ( ( ~ ( sum @ SV55 @ SV58 @ SV12 ) )
= $true )
| ( ( ! [SY194: $i] :
( ~ ( product @ SV55 @ SV31 @ SY194 )
| ! [SY195: $i] :
( ~ ( product @ SV58 @ SV31 @ SY195 )
| ~ ( sum @ SY194 @ SY195 @ SV47 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV20: $i,SV37: $i,SV56: $i] :
( ( ( less_or_equal @ SV56 @ SV37 )
= $false )
| ( ( less_or_equal @ SV20 @ SV56 )
= $false )
| ( ( less_or_equal @ SV20 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(256,plain,
! [SV21: $i,SV38: $i] :
( ( ( defined @ SV38 )
= $false )
| ( ( defined @ SV21 )
= $false )
| ( ( less_or_equal @ SV38 @ SV21 )
= $true )
| ( ( less_or_equal @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(257,plain,
! [SV39: $i,SV22: $i,SV59: $i,SV48: $i] :
( ( ( less_or_equal @ SV48 @ SV59 )
= $false )
| ( ( ! [SY196: $i] :
( ~ ( sum @ SV48 @ SY196 @ SV22 )
| ~ ( sum @ SV59 @ SY196 @ SV39 ) ) )
= $true )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(258,plain,
! [SV23: $i,SV49: $i,SV64: $i] :
( ( ( ~ ( less_or_equal @ additive_identity @ SV64 ) )
= $true )
| ( ( ~ ( product @ SV49 @ SV64 @ SV23 ) )
= $true )
| ( ( less_or_equal @ additive_identity @ SV49 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(259,plain,
! [SV40: $i,SV24: $i,SV60: $i,SV50: $i,SV1: $i] :
( ( ( sum @ SV1 @ SV50 @ SV60 )
= $false )
| ( ( ! [SY197: $i] :
( ~ ( sum @ SV50 @ SY197 @ SV24 )
| ~ ( sum @ SV60 @ SY197 @ SV40 ) ) )
= $true )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(260,plain,
! [SV41: $i,SV25: $i,SV2: $i,SV61: $i,SV51: $i] :
( ( ( sum @ SV51 @ SV61 @ SV2 )
= $false )
| ( ( ! [SY198: $i] :
( ~ ( sum @ SV61 @ SV25 @ SY198 )
| ~ ( sum @ SV51 @ SY198 @ SV41 ) ) )
= $true )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(261,plain,
! [SV43: $i,SV27: $i,SV62: $i,SV52: $i,SV6: $i] :
( ( ( product @ SV6 @ SV52 @ SV62 )
= $false )
| ( ( ! [SY199: $i] :
( ~ ( product @ SV52 @ SY199 @ SV27 )
| ~ ( product @ SV62 @ SY199 @ SV43 ) ) )
= $true )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(262,plain,
! [SV44: $i,SV28: $i,SV7: $i,SV63: $i,SV53: $i] :
( ( ( product @ SV53 @ SV63 @ SV7 )
= $false )
| ( ( ! [SY200: $i] :
( ~ ( product @ SV63 @ SV28 @ SY200 )
| ~ ( product @ SV53 @ SY200 @ SV44 ) ) )
= $true )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV30: $i,SV11: $i,SV46: $i,SV65: $i,SV57: $i,SV54: $i] :
( ( ( ~ ( sum @ SV54 @ SV57 @ SV65 ) )
= $true )
| ( ( ! [SY201: $i] :
( ~ ( product @ SV65 @ SY201 @ SV46 )
| ~ ( product @ SV54 @ SY201 @ SV11 )
| ~ ( product @ SV57 @ SY201 @ SV30 ) ) )
= $true )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(264,plain,
! [SV47: $i,SV31: $i,SV12: $i,SV58: $i,SV55: $i] :
( ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( ! [SY194: $i] :
( ~ ( product @ SV55 @ SV31 @ SY194 )
| ! [SY195: $i] :
( ~ ( product @ SV58 @ SV31 @ SY195 )
| ~ ( sum @ SY194 @ SY195 @ SV47 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(265,plain,
! [SV39: $i,SV59: $i,SV22: $i,SV66: $i,SV48: $i] :
( ( ( ~ ( sum @ SV48 @ SV66 @ SV22 )
| ~ ( sum @ SV59 @ SV66 @ SV39 ) )
= $true )
| ( ( less_or_equal @ SV48 @ SV59 )
= $false )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV23: $i,SV49: $i,SV64: $i] :
( ( ( less_or_equal @ additive_identity @ SV64 )
= $false )
| ( ( ~ ( product @ SV49 @ SV64 @ SV23 ) )
= $true )
| ( ( less_or_equal @ additive_identity @ SV49 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV1: $i,SV40: $i,SV60: $i,SV24: $i,SV67: $i,SV50: $i] :
( ( ( ~ ( sum @ SV50 @ SV67 @ SV24 )
| ~ ( sum @ SV60 @ SV67 @ SV40 ) )
= $true )
| ( ( sum @ SV1 @ SV50 @ SV60 )
= $false )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV2: $i,SV41: $i,SV51: $i,SV68: $i,SV25: $i,SV61: $i] :
( ( ( ~ ( sum @ SV61 @ SV25 @ SV68 )
| ~ ( sum @ SV51 @ SV68 @ SV41 ) )
= $true )
| ( ( sum @ SV51 @ SV61 @ SV2 )
= $false )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(269,plain,
! [SV6: $i,SV43: $i,SV62: $i,SV27: $i,SV69: $i,SV52: $i] :
( ( ( ~ ( product @ SV52 @ SV69 @ SV27 )
| ~ ( product @ SV62 @ SV69 @ SV43 ) )
= $true )
| ( ( product @ SV6 @ SV52 @ SV62 )
= $false )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(270,plain,
! [SV7: $i,SV44: $i,SV53: $i,SV70: $i,SV28: $i,SV63: $i] :
( ( ( ~ ( product @ SV63 @ SV28 @ SV70 )
| ~ ( product @ SV53 @ SV70 @ SV44 ) )
= $true )
| ( ( product @ SV53 @ SV63 @ SV7 )
= $false )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(271,plain,
! [SV30: $i,SV11: $i,SV46: $i,SV65: $i,SV57: $i,SV54: $i] :
( ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( ! [SY201: $i] :
( ~ ( product @ SV65 @ SY201 @ SV46 )
| ~ ( product @ SV54 @ SY201 @ SV11 )
| ~ ( product @ SV57 @ SY201 @ SV30 ) ) )
= $true )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV12: $i,SV47: $i,SV58: $i,SV71: $i,SV31: $i,SV55: $i] :
( ( ( ~ ( product @ SV55 @ SV31 @ SV71 )
| ! [SY202: $i] :
( ~ ( product @ SV58 @ SV31 @ SY202 )
| ~ ( sum @ SV71 @ SY202 @ SV47 ) ) )
= $true )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV39: $i,SV59: $i,SV22: $i,SV66: $i,SV48: $i] :
( ( ( ~ ( sum @ SV48 @ SV66 @ SV22 ) )
= $true )
| ( ( ~ ( sum @ SV59 @ SV66 @ SV39 ) )
= $true )
| ( ( less_or_equal @ SV48 @ SV59 )
= $false )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV23: $i,SV64: $i,SV49: $i] :
( ( ( product @ SV49 @ SV64 @ SV23 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV64 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV49 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(275,plain,
! [SV1: $i,SV40: $i,SV60: $i,SV24: $i,SV67: $i,SV50: $i] :
( ( ( ~ ( sum @ SV50 @ SV67 @ SV24 ) )
= $true )
| ( ( ~ ( sum @ SV60 @ SV67 @ SV40 ) )
= $true )
| ( ( sum @ SV1 @ SV50 @ SV60 )
= $false )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV2: $i,SV41: $i,SV51: $i,SV68: $i,SV25: $i,SV61: $i] :
( ( ( ~ ( sum @ SV61 @ SV25 @ SV68 ) )
= $true )
| ( ( ~ ( sum @ SV51 @ SV68 @ SV41 ) )
= $true )
| ( ( sum @ SV51 @ SV61 @ SV2 )
= $false )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV6: $i,SV43: $i,SV62: $i,SV27: $i,SV69: $i,SV52: $i] :
( ( ( ~ ( product @ SV52 @ SV69 @ SV27 ) )
= $true )
| ( ( ~ ( product @ SV62 @ SV69 @ SV43 ) )
= $true )
| ( ( product @ SV6 @ SV52 @ SV62 )
= $false )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(278,plain,
! [SV7: $i,SV44: $i,SV53: $i,SV70: $i,SV28: $i,SV63: $i] :
( ( ( ~ ( product @ SV63 @ SV28 @ SV70 ) )
= $true )
| ( ( ~ ( product @ SV53 @ SV70 @ SV44 ) )
= $true )
| ( ( product @ SV53 @ SV63 @ SV7 )
= $false )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(279,plain,
! [SV30: $i,SV57: $i,SV11: $i,SV54: $i,SV46: $i,SV72: $i,SV65: $i] :
( ( ( ~ ( product @ SV65 @ SV72 @ SV46 )
| ~ ( product @ SV54 @ SV72 @ SV11 )
| ~ ( product @ SV57 @ SV72 @ SV30 ) )
= $true )
| ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(280,plain,
! [SV12: $i,SV47: $i,SV58: $i,SV71: $i,SV31: $i,SV55: $i] :
( ( ( ~ ( product @ SV55 @ SV31 @ SV71 ) )
= $true )
| ( ( ! [SY202: $i] :
( ~ ( product @ SV58 @ SV31 @ SY202 )
| ~ ( sum @ SV71 @ SY202 @ SV47 ) ) )
= $true )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(281,plain,
! [SV39: $i,SV59: $i,SV22: $i,SV66: $i,SV48: $i] :
( ( ( sum @ SV48 @ SV66 @ SV22 )
= $false )
| ( ( ~ ( sum @ SV59 @ SV66 @ SV39 ) )
= $true )
| ( ( less_or_equal @ SV48 @ SV59 )
= $false )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(282,plain,
! [SV1: $i,SV40: $i,SV60: $i,SV24: $i,SV67: $i,SV50: $i] :
( ( ( sum @ SV50 @ SV67 @ SV24 )
= $false )
| ( ( ~ ( sum @ SV60 @ SV67 @ SV40 ) )
= $true )
| ( ( sum @ SV1 @ SV50 @ SV60 )
= $false )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(283,plain,
! [SV2: $i,SV41: $i,SV51: $i,SV68: $i,SV25: $i,SV61: $i] :
( ( ( sum @ SV61 @ SV25 @ SV68 )
= $false )
| ( ( ~ ( sum @ SV51 @ SV68 @ SV41 ) )
= $true )
| ( ( sum @ SV51 @ SV61 @ SV2 )
= $false )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(284,plain,
! [SV6: $i,SV43: $i,SV62: $i,SV27: $i,SV69: $i,SV52: $i] :
( ( ( product @ SV52 @ SV69 @ SV27 )
= $false )
| ( ( ~ ( product @ SV62 @ SV69 @ SV43 ) )
= $true )
| ( ( product @ SV6 @ SV52 @ SV62 )
= $false )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(285,plain,
! [SV7: $i,SV44: $i,SV53: $i,SV70: $i,SV28: $i,SV63: $i] :
( ( ( product @ SV63 @ SV28 @ SV70 )
= $false )
| ( ( ~ ( product @ SV53 @ SV70 @ SV44 ) )
= $true )
| ( ( product @ SV53 @ SV63 @ SV7 )
= $false )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(286,plain,
! [SV30: $i,SV57: $i,SV11: $i,SV54: $i,SV46: $i,SV72: $i,SV65: $i] :
( ( ( ~ ( product @ SV65 @ SV72 @ SV46 ) )
= $true )
| ( ( ~ ( product @ SV54 @ SV72 @ SV11 )
| ~ ( product @ SV57 @ SV72 @ SV30 ) )
= $true )
| ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(287,plain,
! [SV12: $i,SV47: $i,SV58: $i,SV71: $i,SV31: $i,SV55: $i] :
( ( ( product @ SV55 @ SV31 @ SV71 )
= $false )
| ( ( ! [SY202: $i] :
( ~ ( product @ SV58 @ SV31 @ SY202 )
| ~ ( sum @ SV71 @ SY202 @ SV47 ) ) )
= $true )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(288,plain,
! [SV22: $i,SV48: $i,SV39: $i,SV66: $i,SV59: $i] :
( ( ( sum @ SV59 @ SV66 @ SV39 )
= $false )
| ( ( sum @ SV48 @ SV66 @ SV22 )
= $false )
| ( ( less_or_equal @ SV48 @ SV59 )
= $false )
| ( ( less_or_equal @ SV22 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(289,plain,
! [SV1: $i,SV24: $i,SV50: $i,SV40: $i,SV67: $i,SV60: $i] :
( ( ( sum @ SV60 @ SV67 @ SV40 )
= $false )
| ( ( sum @ SV50 @ SV67 @ SV24 )
= $false )
| ( ( sum @ SV1 @ SV50 @ SV60 )
= $false )
| ( ( sum @ SV1 @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(290,plain,
! [SV2: $i,SV25: $i,SV61: $i,SV41: $i,SV68: $i,SV51: $i] :
( ( ( sum @ SV51 @ SV68 @ SV41 )
= $false )
| ( ( sum @ SV61 @ SV25 @ SV68 )
= $false )
| ( ( sum @ SV51 @ SV61 @ SV2 )
= $false )
| ( ( sum @ SV2 @ SV25 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(291,plain,
! [SV6: $i,SV27: $i,SV52: $i,SV43: $i,SV69: $i,SV62: $i] :
( ( ( product @ SV62 @ SV69 @ SV43 )
= $false )
| ( ( product @ SV52 @ SV69 @ SV27 )
= $false )
| ( ( product @ SV6 @ SV52 @ SV62 )
= $false )
| ( ( product @ SV6 @ SV27 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(292,plain,
! [SV7: $i,SV28: $i,SV63: $i,SV44: $i,SV70: $i,SV53: $i] :
( ( ( product @ SV53 @ SV70 @ SV44 )
= $false )
| ( ( product @ SV63 @ SV28 @ SV70 )
= $false )
| ( ( product @ SV53 @ SV63 @ SV7 )
= $false )
| ( ( product @ SV7 @ SV28 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(293,plain,
! [SV30: $i,SV57: $i,SV11: $i,SV54: $i,SV46: $i,SV72: $i,SV65: $i] :
( ( ( product @ SV65 @ SV72 @ SV46 )
= $false )
| ( ( ~ ( product @ SV54 @ SV72 @ SV11 )
| ~ ( product @ SV57 @ SV72 @ SV30 ) )
= $true )
| ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(294,plain,
! [SV12: $i,SV55: $i,SV47: $i,SV71: $i,SV73: $i,SV31: $i,SV58: $i] :
( ( ( ~ ( product @ SV58 @ SV31 @ SV73 )
| ~ ( sum @ SV71 @ SV73 @ SV47 ) )
= $true )
| ( ( product @ SV55 @ SV31 @ SV71 )
= $false )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(295,plain,
! [SV46: $i,SV65: $i,SV30: $i,SV57: $i,SV11: $i,SV72: $i,SV54: $i] :
( ( ( ~ ( product @ SV54 @ SV72 @ SV11 ) )
= $true )
| ( ( ~ ( product @ SV57 @ SV72 @ SV30 ) )
= $true )
| ( ( product @ SV65 @ SV72 @ SV46 )
= $false )
| ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(296,plain,
! [SV12: $i,SV55: $i,SV47: $i,SV71: $i,SV73: $i,SV31: $i,SV58: $i] :
( ( ( ~ ( product @ SV58 @ SV31 @ SV73 ) )
= $true )
| ( ( ~ ( sum @ SV71 @ SV73 @ SV47 ) )
= $true )
| ( ( product @ SV55 @ SV31 @ SV71 )
= $false )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(297,plain,
! [SV46: $i,SV65: $i,SV30: $i,SV57: $i,SV11: $i,SV72: $i,SV54: $i] :
( ( ( product @ SV54 @ SV72 @ SV11 )
= $false )
| ( ( ~ ( product @ SV57 @ SV72 @ SV30 ) )
= $true )
| ( ( product @ SV65 @ SV72 @ SV46 )
= $false )
| ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(298,plain,
! [SV12: $i,SV55: $i,SV47: $i,SV71: $i,SV73: $i,SV31: $i,SV58: $i] :
( ( ( product @ SV58 @ SV31 @ SV73 )
= $false )
| ( ( ~ ( sum @ SV71 @ SV73 @ SV47 ) )
= $true )
| ( ( product @ SV55 @ SV31 @ SV71 )
= $false )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(299,plain,
! [SV46: $i,SV65: $i,SV11: $i,SV54: $i,SV30: $i,SV72: $i,SV57: $i] :
( ( ( product @ SV57 @ SV72 @ SV30 )
= $false )
| ( ( product @ SV54 @ SV72 @ SV11 )
= $false )
| ( ( product @ SV65 @ SV72 @ SV46 )
= $false )
| ( ( sum @ SV54 @ SV57 @ SV65 )
= $false )
| ( ( sum @ SV11 @ SV30 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(300,plain,
! [SV12: $i,SV55: $i,SV31: $i,SV58: $i,SV47: $i,SV73: $i,SV71: $i] :
( ( ( sum @ SV71 @ SV73 @ SV47 )
= $false )
| ( ( product @ SV58 @ SV31 @ SV73 )
= $false )
| ( ( product @ SV55 @ SV31 @ SV71 )
= $false )
| ( ( sum @ SV55 @ SV58 @ SV12 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(301,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[88,300,299,292,291,290,289,288,274,256,255,244,243,242,241,240,222,219,209,203,188,182,178,177,151,150,126,115,112,98,97,96,95,94,93,91,90,89]) ).
thf(302,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD025-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n021.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 Jun 6 12:28:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 37
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.39 .
% 0.19/0.41 (rf:0,axioms:37,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:39,loop_count:0,foatp_calls:0,translation:fof_full)................
% 0.45/0.70
% 0.45/0.70 ********************************
% 0.45/0.70 * All subproblems solved! *
% 0.45/0.70 ********************************
% 0.45/0.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:37,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:301,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.75
% 0.55/0.75 %**** Beginning of derivation protocol ****
% 0.55/0.75 % SZS output start CNFRefutation
% See solution above
% 0.55/0.75
% 0.55/0.75 %**** End of derivation protocol ****
% 0.55/0.75 %**** no. of clauses in derivation: 302 ****
% 0.55/0.75 %**** clause counter: 301 ****
% 0.55/0.75
% 0.55/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:37,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:301,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------