TSTP Solution File: RNG040-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG040-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 20:34:03 EDT 2022
% Result : Unsatisfiable 2.39s 2.57s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 40
% Syntax : Number of formulae : 226 ( 132 unt; 14 typ; 0 def)
% Number of atoms : 1262 ( 351 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2535 ( 311 ~; 420 |; 0 &;1804 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 10 con; 0-3 aty)
% Number of variables : 850 ( 0 ^ 850 !; 0 ?; 850 :)
% 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_h,type,
h: $i > $i ).
thf(tp_l,type,
l: $i ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_n,type,
n: $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i > $i > $o ).
thf(1,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(2,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(3,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(4,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(5,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(6,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(7,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(8,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(9,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(10,axiom,
! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
thf(11,axiom,
! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(12,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(13,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(14,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(15,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_symmetry) ).
thf(17,axiom,
! [A: $i] :
( ( product @ ( h @ A ) @ A @ multiplicative_identity )
| ( A = additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(18,axiom,
! [A: $i] :
( ( product @ A @ ( h @ A ) @ multiplicative_identity )
| ( A = additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(19,axiom,
! [A: $i] : ( product @ multiplicative_identity @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_identity) ).
thf(20,axiom,
! [A: $i] : ( product @ A @ multiplicative_identity @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_identity) ).
thf(21,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(22,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,negated_conjecture,
~ ( sum @ l @ n @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(24,negated_conjecture,
product @ c @ a @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_a) ).
thf(25,negated_conjecture,
product @ b @ a @ l,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_a) ).
thf(26,negated_conjecture,
product @ d @ a @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_plus_a) ).
thf(27,negated_conjecture,
sum @ b @ c @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_c) ).
thf(28,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(29,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)],[1]) ).
thf(30,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)],[2]) ).
thf(31,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)],[3]) ).
thf(32,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)],[4]) ).
thf(33,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)],[5]) ).
thf(34,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)],[6]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(36,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)],[8]) ).
thf(37,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)],[9]) ).
thf(38,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(39,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(42,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(43,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ B @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( product @ ( h @ A ) @ A @ multiplicative_identity )
| ( A = additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( product @ A @ ( h @ A ) @ multiplicative_identity )
| ( A = additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [A: $i] : ( product @ multiplicative_identity @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [A: $i] : ( product @ A @ multiplicative_identity @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( ~ ( sum @ l @ n @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(50,plain,
( ( product @ c @ a @ n )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(51,plain,
( ( product @ b @ a @ l )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(52,plain,
( ( product @ d @ a @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(53,plain,
( ( sum @ b @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(55,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)],[29]) ).
thf(56,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)],[30]) ).
thf(57,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)],[31]) ).
thf(58,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)],[32]) ).
thf(59,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)],[33]) ).
thf(60,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)],[34]) ).
thf(61,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)],[36]) ).
thf(62,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)],[37]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( A = additive_identity )
| ( product @ ( h @ A ) @ A @ multiplicative_identity ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( A = additive_identity )
| ( product @ A @ ( h @ A ) @ multiplicative_identity ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(65,plain,
( ( sum @ b @ c @ d )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(66,plain,
( ( product @ d @ a @ additive_identity )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(67,plain,
( ( product @ b @ a @ l )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(68,plain,
( ( product @ c @ a @ n )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(69,plain,
( ( ~ ( sum @ l @ n @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(70,plain,
( ( ! [A: $i] : ( product @ A @ multiplicative_identity @ A ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(71,plain,
( ( ! [A: $i] : ( product @ multiplicative_identity @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( A = additive_identity )
| ( product @ A @ ( h @ A ) @ multiplicative_identity ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(73,plain,
( ( ! [A: $i] :
( ( A = additive_identity )
| ( product @ ( h @ A ) @ A @ multiplicative_identity ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(74,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ B @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(75,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(76,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(79,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(80,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(81,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)],[62]) ).
thf(82,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)],[61]) ).
thf(83,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(84,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)],[60]) ).
thf(85,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)],[59]) ).
thf(86,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)],[58]) ).
thf(87,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)],[57]) ).
thf(88,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(90,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(91,plain,
( ( sum @ l @ n @ additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV1: $i] :
( ( product @ SV1 @ multiplicative_identity @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV2: $i] :
( ( product @ multiplicative_identity @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV3: $i] :
( ( ( SV3 = additive_identity )
| ( product @ SV3 @ ( h @ SV3 ) @ multiplicative_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(95,plain,
! [SV4: $i] :
( ( ( SV4 = additive_identity )
| ( product @ ( h @ SV4 ) @ SV4 @ multiplicative_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(96,plain,
! [SV5: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( product @ SV5 @ SY64 @ SY65 )
| ( product @ SY64 @ SV5 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(97,plain,
! [SV6: $i] :
( ( sum @ additive_identity @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV7: $i] :
( ( sum @ SV7 @ additive_identity @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV8: $i] :
( ( ! [SY66: $i] : ( product @ SV8 @ SY66 @ ( multiply @ SV8 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
! [SV9: $i] :
( ( ! [SY67: $i] : ( sum @ SV9 @ SY67 @ ( add @ SV9 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(101,plain,
! [SV10: $i] :
( ( sum @ ( additive_inverse @ SV10 ) @ SV10 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(102,plain,
! [SV11: $i] :
( ( sum @ SV11 @ ( additive_inverse @ SV11 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(103,plain,
! [SV12: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i] :
( ~ ( sum @ SV12 @ SY68 @ SY69 )
| ! [SY71: $i] :
( ~ ( sum @ SY68 @ SY70 @ SY71 )
| ! [SY72: $i] :
( ~ ( sum @ SY69 @ SY70 @ SY72 )
| ( sum @ SV12 @ SY71 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(104,plain,
! [SV13: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ( sum @ SV13 @ SY73 @ SY74 )
| ! [SY76: $i] :
( ~ ( sum @ SY73 @ SY75 @ SY76 )
| ! [SY77: $i] :
( ~ ( sum @ SV13 @ SY76 @ SY77 )
| ( sum @ SY74 @ SY75 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV14: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( sum @ SV14 @ SY78 @ SY79 )
| ( sum @ SY78 @ SV14 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV15: $i] :
( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ~ ( product @ SV15 @ SY80 @ SY81 )
| ! [SY83: $i] :
( ~ ( product @ SY80 @ SY82 @ SY83 )
| ! [SY84: $i] :
( ~ ( product @ SY81 @ SY82 @ SY84 )
| ( product @ SV15 @ SY83 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(107,plain,
! [SV16: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ( product @ SV16 @ SY85 @ SY86 )
| ! [SY88: $i] :
( ~ ( product @ SY85 @ SY87 @ SY88 )
| ! [SY89: $i] :
( ~ ( product @ SV16 @ SY88 @ SY89 )
| ( product @ SY86 @ SY87 @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV17: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i,SY93: $i] :
( ~ ( product @ SV17 @ SY90 @ SY91 )
| ~ ( product @ SV17 @ SY92 @ SY93 )
| ! [SY94: $i] :
( ~ ( sum @ SY90 @ SY92 @ SY94 )
| ! [SY95: $i] :
( ~ ( product @ SV17 @ SY94 @ SY95 )
| ( sum @ SY91 @ SY93 @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV18: $i] :
( ( ! [SY96: $i,SY97: $i,SY98: $i,SY99: $i] :
( ~ ( product @ SV18 @ SY96 @ SY97 )
| ~ ( product @ SV18 @ SY98 @ SY99 )
| ! [SY100: $i] :
( ~ ( sum @ SY96 @ SY98 @ SY100 )
| ! [SY101: $i] :
( ~ ( sum @ SY97 @ SY99 @ SY101 )
| ( product @ SV18 @ SY100 @ SY101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(110,plain,
! [SV19: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( sum @ SV19 @ SY102 @ SY103 )
| ! [SY104: $i] :
( ~ ( sum @ SV19 @ SY102 @ SY104 )
| ( SY103 = SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(111,plain,
! [SV20: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( product @ SV20 @ SY105 @ SY106 )
| ! [SY107: $i] :
( ~ ( product @ SV20 @ SY105 @ SY107 )
| ( SY106 = SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(112,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(113,plain,
! [SV3: $i] :
( ( ( SV3 = additive_identity )
= $true )
| ( ( product @ SV3 @ ( h @ SV3 ) @ multiplicative_identity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV4: $i] :
( ( ( SV4 = additive_identity )
= $true )
| ( ( product @ ( h @ SV4 ) @ SV4 @ multiplicative_identity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY108: $i] :
( ~ ( product @ SV5 @ SV21 @ SY108 )
| ( product @ SV21 @ SV5 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV22: $i,SV8: $i] :
( ( product @ SV8 @ SV22 @ ( multiply @ SV8 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV23: $i,SV9: $i] :
( ( sum @ SV9 @ SV23 @ ( add @ SV9 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV24: $i,SV12: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ( sum @ SV12 @ SV24 @ SY109 )
| ! [SY111: $i] :
( ~ ( sum @ SV24 @ SY110 @ SY111 )
| ! [SY72: $i] :
( ~ ( sum @ SY109 @ SY110 @ SY72 )
| ( sum @ SV12 @ SY111 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( sum @ SV13 @ SV25 @ SY113 )
| ! [SY115: $i] :
( ~ ( sum @ SV25 @ SY114 @ SY115 )
| ! [SY77: $i] :
( ~ ( sum @ SV13 @ SY115 @ SY77 )
| ( sum @ SY113 @ SY114 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY117: $i] :
( ~ ( sum @ SV14 @ SV26 @ SY117 )
| ( sum @ SV26 @ SV14 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( product @ SV15 @ SV27 @ SY118 )
| ! [SY120: $i] :
( ~ ( product @ SV27 @ SY119 @ SY120 )
| ! [SY84: $i] :
( ~ ( product @ SY118 @ SY119 @ SY84 )
| ( product @ SV15 @ SY120 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV28: $i,SV16: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( product @ SV16 @ SV28 @ SY122 )
| ! [SY124: $i] :
( ~ ( product @ SV28 @ SY123 @ SY124 )
| ! [SY89: $i] :
( ~ ( product @ SV16 @ SY124 @ SY89 )
| ( product @ SY122 @ SY123 @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV29: $i,SV17: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ( product @ SV17 @ SV29 @ SY126 )
| ~ ( product @ SV17 @ SY127 @ SY128 )
| ! [SY129: $i] :
( ~ ( sum @ SV29 @ SY127 @ SY129 )
| ! [SY95: $i] :
( ~ ( product @ SV17 @ SY129 @ SY95 )
| ( sum @ SY126 @ SY128 @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV30: $i,SV18: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i] :
( ~ ( product @ SV18 @ SV30 @ SY131 )
| ~ ( product @ SV18 @ SY132 @ SY133 )
| ! [SY134: $i] :
( ~ ( sum @ SV30 @ SY132 @ SY134 )
| ! [SY101: $i] :
( ~ ( sum @ SY131 @ SY133 @ SY101 )
| ( product @ SV18 @ SY134 @ SY101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV31: $i,SV19: $i] :
( ( ! [SY136: $i] :
( ~ ( sum @ SV19 @ SV31 @ SY136 )
| ! [SY137: $i] :
( ~ ( sum @ SV19 @ SV31 @ SY137 )
| ( SY136 = SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV32: $i,SV20: $i] :
( ( ! [SY138: $i] :
( ~ ( product @ SV20 @ SV32 @ SY138 )
| ! [SY139: $i] :
( ~ ( product @ SV20 @ SV32 @ SY139 )
| ( SY138 = SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV33: $i,SV21: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV21 @ SV33 )
| ( product @ SV21 @ SV5 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV34: $i,SV24: $i,SV12: $i] :
( ( ! [SY140: $i] :
( ~ ( sum @ SV12 @ SV24 @ SV34 )
| ! [SY141: $i] :
( ~ ( sum @ SV24 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( sum @ SV34 @ SY140 @ SY142 )
| ( sum @ SV12 @ SY141 @ SY142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV35: $i,SV25: $i,SV13: $i] :
( ( ! [SY143: $i] :
( ~ ( sum @ SV13 @ SV25 @ SV35 )
| ! [SY144: $i] :
( ~ ( sum @ SV25 @ SY143 @ SY144 )
| ! [SY145: $i] :
( ~ ( sum @ SV13 @ SY144 @ SY145 )
| ( sum @ SV35 @ SY143 @ SY145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV36: $i,SV26: $i,SV14: $i] :
( ( ~ ( sum @ SV14 @ SV26 @ SV36 )
| ( sum @ SV26 @ SV14 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV37: $i,SV27: $i,SV15: $i] :
( ( ! [SY146: $i] :
( ~ ( product @ SV15 @ SV27 @ SV37 )
| ! [SY147: $i] :
( ~ ( product @ SV27 @ SY146 @ SY147 )
| ! [SY148: $i] :
( ~ ( product @ SV37 @ SY146 @ SY148 )
| ( product @ SV15 @ SY147 @ SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV38: $i,SV28: $i,SV16: $i] :
( ( ! [SY149: $i] :
( ~ ( product @ SV16 @ SV28 @ SV38 )
| ! [SY150: $i] :
( ~ ( product @ SV28 @ SY149 @ SY150 )
| ! [SY151: $i] :
( ~ ( product @ SV16 @ SY150 @ SY151 )
| ( product @ SV38 @ SY149 @ SY151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV39: $i,SV29: $i,SV17: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ~ ( product @ SV17 @ SV29 @ SV39 )
| ~ ( product @ SV17 @ SY152 @ SY153 )
| ! [SY154: $i] :
( ~ ( sum @ SV29 @ SY152 @ SY154 )
| ! [SY155: $i] :
( ~ ( product @ SV17 @ SY154 @ SY155 )
| ( sum @ SV39 @ SY153 @ SY155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV40: $i,SV30: $i,SV18: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ~ ( product @ SV18 @ SV30 @ SV40 )
| ~ ( product @ SV18 @ SY156 @ SY157 )
| ! [SY158: $i] :
( ~ ( sum @ SV30 @ SY156 @ SY158 )
| ! [SY159: $i] :
( ~ ( sum @ SV40 @ SY157 @ SY159 )
| ( product @ SV18 @ SY158 @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV41: $i,SV31: $i,SV19: $i] :
( ( ~ ( sum @ SV19 @ SV31 @ SV41 )
| ! [SY160: $i] :
( ~ ( sum @ SV19 @ SV31 @ SY160 )
| ( SV41 = SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV42: $i,SV32: $i,SV20: $i] :
( ( ~ ( product @ SV20 @ SV32 @ SV42 )
| ! [SY161: $i] :
( ~ ( product @ SV20 @ SV32 @ SY161 )
| ( SV42 = SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV33: $i,SV21: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV21 @ SV33 ) )
= $true )
| ( ( product @ SV21 @ SV5 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV43: $i,SV34: $i,SV24: $i,SV12: $i] :
( ( ~ ( sum @ SV12 @ SV24 @ SV34 )
| ! [SY162: $i] :
( ~ ( sum @ SV24 @ SV43 @ SY162 )
| ! [SY163: $i] :
( ~ ( sum @ SV34 @ SV43 @ SY163 )
| ( sum @ SV12 @ SY162 @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV44: $i,SV35: $i,SV25: $i,SV13: $i] :
( ( ~ ( sum @ SV13 @ SV25 @ SV35 )
| ! [SY164: $i] :
( ~ ( sum @ SV25 @ SV44 @ SY164 )
| ! [SY165: $i] :
( ~ ( sum @ SV13 @ SY164 @ SY165 )
| ( sum @ SV35 @ SV44 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV36: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV26 @ SV36 ) )
= $true )
| ( ( sum @ SV26 @ SV14 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV45: $i,SV37: $i,SV27: $i,SV15: $i] :
( ( ~ ( product @ SV15 @ SV27 @ SV37 )
| ! [SY166: $i] :
( ~ ( product @ SV27 @ SV45 @ SY166 )
| ! [SY167: $i] :
( ~ ( product @ SV37 @ SV45 @ SY167 )
| ( product @ SV15 @ SY166 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV46: $i,SV38: $i,SV28: $i,SV16: $i] :
( ( ~ ( product @ SV16 @ SV28 @ SV38 )
| ! [SY168: $i] :
( ~ ( product @ SV28 @ SV46 @ SY168 )
| ! [SY169: $i] :
( ~ ( product @ SV16 @ SY168 @ SY169 )
| ( product @ SV38 @ SV46 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV47: $i,SV39: $i,SV29: $i,SV17: $i] :
( ( ! [SY170: $i] :
( ~ ( product @ SV17 @ SV29 @ SV39 )
| ~ ( product @ SV17 @ SV47 @ SY170 )
| ! [SY171: $i] :
( ~ ( sum @ SV29 @ SV47 @ SY171 )
| ! [SY155: $i] :
( ~ ( product @ SV17 @ SY171 @ SY155 )
| ( sum @ SV39 @ SY170 @ SY155 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV48: $i,SV40: $i,SV30: $i,SV18: $i] :
( ( ! [SY173: $i] :
( ~ ( product @ SV18 @ SV30 @ SV40 )
| ~ ( product @ SV18 @ SV48 @ SY173 )
| ! [SY174: $i] :
( ~ ( sum @ SV30 @ SV48 @ SY174 )
| ! [SY159: $i] :
( ~ ( sum @ SV40 @ SY173 @ SY159 )
| ( product @ SV18 @ SY174 @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV41: $i,SV31: $i,SV19: $i] :
( ( ( ~ ( sum @ SV19 @ SV31 @ SV41 ) )
= $true )
| ( ( ! [SY160: $i] :
( ~ ( sum @ SV19 @ SV31 @ SY160 )
| ( SV41 = SY160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV42: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV32 @ SV42 ) )
= $true )
| ( ( ! [SY161: $i] :
( ~ ( product @ SV20 @ SV32 @ SY161 )
| ( SV42 = SY161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV33: $i,SV21: $i,SV5: $i] :
( ( ( product @ SV5 @ SV21 @ SV33 )
= $false )
| ( ( product @ SV21 @ SV5 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV43: $i,SV34: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( sum @ SV12 @ SV24 @ SV34 ) )
= $true )
| ( ( ! [SY162: $i] :
( ~ ( sum @ SV24 @ SV43 @ SY162 )
| ! [SY163: $i] :
( ~ ( sum @ SV34 @ SV43 @ SY163 )
| ( sum @ SV12 @ SY162 @ SY163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV44: $i,SV35: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV25 @ SV35 ) )
= $true )
| ( ( ! [SY164: $i] :
( ~ ( sum @ SV25 @ SV44 @ SY164 )
| ! [SY165: $i] :
( ~ ( sum @ SV13 @ SY164 @ SY165 )
| ( sum @ SV35 @ SV44 @ SY165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV36: $i,SV26: $i,SV14: $i] :
( ( ( sum @ SV14 @ SV26 @ SV36 )
= $false )
| ( ( sum @ SV26 @ SV14 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV45: $i,SV37: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV27 @ SV37 ) )
= $true )
| ( ( ! [SY166: $i] :
( ~ ( product @ SV27 @ SV45 @ SY166 )
| ! [SY167: $i] :
( ~ ( product @ SV37 @ SV45 @ SY167 )
| ( product @ SV15 @ SY166 @ SY167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV46: $i,SV38: $i,SV28: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV28 @ SV38 ) )
= $true )
| ( ( ! [SY168: $i] :
( ~ ( product @ SV28 @ SV46 @ SY168 )
| ! [SY169: $i] :
( ~ ( product @ SV16 @ SY168 @ SY169 )
| ( product @ SV38 @ SV46 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV49: $i,SV47: $i,SV39: $i,SV29: $i,SV17: $i] :
( ( ~ ( product @ SV17 @ SV29 @ SV39 )
| ~ ( product @ SV17 @ SV47 @ SV49 )
| ! [SY176: $i] :
( ~ ( sum @ SV29 @ SV47 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV17 @ SY176 @ SY177 )
| ( sum @ SV39 @ SV49 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV50: $i,SV48: $i,SV40: $i,SV30: $i,SV18: $i] :
( ( ~ ( product @ SV18 @ SV30 @ SV40 )
| ~ ( product @ SV18 @ SV48 @ SV50 )
| ! [SY178: $i] :
( ~ ( sum @ SV30 @ SV48 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY179 )
| ( product @ SV18 @ SY178 @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV41: $i,SV31: $i,SV19: $i] :
( ( ( sum @ SV19 @ SV31 @ SV41 )
= $false )
| ( ( ! [SY160: $i] :
( ~ ( sum @ SV19 @ SV31 @ SY160 )
| ( SV41 = SY160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV42: $i,SV32: $i,SV20: $i] :
( ( ( product @ SV20 @ SV32 @ SV42 )
= $false )
| ( ( ! [SY161: $i] :
( ~ ( product @ SV20 @ SV32 @ SY161 )
| ( SV42 = SY161 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV43: $i,SV34: $i,SV24: $i,SV12: $i] :
( ( ( sum @ SV12 @ SV24 @ SV34 )
= $false )
| ( ( ! [SY162: $i] :
( ~ ( sum @ SV24 @ SV43 @ SY162 )
| ! [SY163: $i] :
( ~ ( sum @ SV34 @ SV43 @ SY163 )
| ( sum @ SV12 @ SY162 @ SY163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV44: $i,SV35: $i,SV25: $i,SV13: $i] :
( ( ( sum @ SV13 @ SV25 @ SV35 )
= $false )
| ( ( ! [SY164: $i] :
( ~ ( sum @ SV25 @ SV44 @ SY164 )
| ! [SY165: $i] :
( ~ ( sum @ SV13 @ SY164 @ SY165 )
| ( sum @ SV35 @ SV44 @ SY165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(159,plain,
! [SV45: $i,SV37: $i,SV27: $i,SV15: $i] :
( ( ( product @ SV15 @ SV27 @ SV37 )
= $false )
| ( ( ! [SY166: $i] :
( ~ ( product @ SV27 @ SV45 @ SY166 )
| ! [SY167: $i] :
( ~ ( product @ SV37 @ SV45 @ SY167 )
| ( product @ SV15 @ SY166 @ SY167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV46: $i,SV38: $i,SV28: $i,SV16: $i] :
( ( ( product @ SV16 @ SV28 @ SV38 )
= $false )
| ( ( ! [SY168: $i] :
( ~ ( product @ SV28 @ SV46 @ SY168 )
| ! [SY169: $i] :
( ~ ( product @ SV16 @ SY168 @ SY169 )
| ( product @ SV38 @ SV46 @ SY169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV49: $i,SV47: $i,SV39: $i,SV29: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV29 @ SV39 ) )
= $true )
| ( ( ~ ( product @ SV17 @ SV47 @ SV49 )
| ! [SY176: $i] :
( ~ ( sum @ SV29 @ SV47 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV17 @ SY176 @ SY177 )
| ( sum @ SV39 @ SV49 @ SY177 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV50: $i,SV48: $i,SV40: $i,SV30: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV30 @ SV40 ) )
= $true )
| ( ( ~ ( product @ SV18 @ SV48 @ SV50 )
| ! [SY178: $i] :
( ~ ( sum @ SV30 @ SV48 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY179 )
| ( product @ SV18 @ SY178 @ SY179 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV41: $i,SV51: $i,SV31: $i,SV19: $i] :
( ( ( ~ ( sum @ SV19 @ SV31 @ SV51 )
| ( SV41 = SV51 ) )
= $true )
| ( ( sum @ SV19 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV42: $i,SV52: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV32 @ SV52 )
| ( SV42 = SV52 ) )
= $true )
| ( ( product @ SV20 @ SV32 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(165,plain,
! [SV12: $i,SV34: $i,SV53: $i,SV43: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV43 @ SV53 )
| ! [SY180: $i] :
( ~ ( sum @ SV34 @ SV43 @ SY180 )
| ( sum @ SV12 @ SV53 @ SY180 ) ) )
= $true )
| ( ( sum @ SV12 @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(166,plain,
! [SV35: $i,SV13: $i,SV54: $i,SV44: $i,SV25: $i] :
( ( ( ~ ( sum @ SV25 @ SV44 @ SV54 )
| ! [SY181: $i] :
( ~ ( sum @ SV13 @ SV54 @ SY181 )
| ( sum @ SV35 @ SV44 @ SY181 ) ) )
= $true )
| ( ( sum @ SV13 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(167,plain,
! [SV15: $i,SV37: $i,SV55: $i,SV45: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV45 @ SV55 )
| ! [SY182: $i] :
( ~ ( product @ SV37 @ SV45 @ SY182 )
| ( product @ SV15 @ SV55 @ SY182 ) ) )
= $true )
| ( ( product @ SV15 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV38: $i,SV16: $i,SV56: $i,SV46: $i,SV28: $i] :
( ( ( ~ ( product @ SV28 @ SV46 @ SV56 )
| ! [SY183: $i] :
( ~ ( product @ SV16 @ SV56 @ SY183 )
| ( product @ SV38 @ SV46 @ SY183 ) ) )
= $true )
| ( ( product @ SV16 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV49: $i,SV47: $i,SV39: $i,SV29: $i,SV17: $i] :
( ( ( product @ SV17 @ SV29 @ SV39 )
= $false )
| ( ( ~ ( product @ SV17 @ SV47 @ SV49 )
| ! [SY176: $i] :
( ~ ( sum @ SV29 @ SV47 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV17 @ SY176 @ SY177 )
| ( sum @ SV39 @ SV49 @ SY177 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV50: $i,SV48: $i,SV40: $i,SV30: $i,SV18: $i] :
( ( ( product @ SV18 @ SV30 @ SV40 )
= $false )
| ( ( ~ ( product @ SV18 @ SV48 @ SV50 )
| ! [SY178: $i] :
( ~ ( sum @ SV30 @ SV48 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY179 )
| ( product @ SV18 @ SY178 @ SY179 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV41: $i,SV51: $i,SV31: $i,SV19: $i] :
( ( ( ~ ( sum @ SV19 @ SV31 @ SV51 ) )
= $true )
| ( ( SV41 = SV51 )
= $true )
| ( ( sum @ SV19 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV42: $i,SV52: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV32 @ SV52 ) )
= $true )
| ( ( SV42 = SV52 )
= $true )
| ( ( product @ SV20 @ SV32 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV12: $i,SV34: $i,SV53: $i,SV43: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV43 @ SV53 ) )
= $true )
| ( ( ! [SY180: $i] :
( ~ ( sum @ SV34 @ SV43 @ SY180 )
| ( sum @ SV12 @ SV53 @ SY180 ) ) )
= $true )
| ( ( sum @ SV12 @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV35: $i,SV13: $i,SV54: $i,SV44: $i,SV25: $i] :
( ( ( ~ ( sum @ SV25 @ SV44 @ SV54 ) )
= $true )
| ( ( ! [SY181: $i] :
( ~ ( sum @ SV13 @ SV54 @ SY181 )
| ( sum @ SV35 @ SV44 @ SY181 ) ) )
= $true )
| ( ( sum @ SV13 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV15: $i,SV37: $i,SV55: $i,SV45: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV45 @ SV55 ) )
= $true )
| ( ( ! [SY182: $i] :
( ~ ( product @ SV37 @ SV45 @ SY182 )
| ( product @ SV15 @ SV55 @ SY182 ) ) )
= $true )
| ( ( product @ SV15 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV38: $i,SV16: $i,SV56: $i,SV46: $i,SV28: $i] :
( ( ( ~ ( product @ SV28 @ SV46 @ SV56 ) )
= $true )
| ( ( ! [SY183: $i] :
( ~ ( product @ SV16 @ SV56 @ SY183 )
| ( product @ SV38 @ SV46 @ SY183 ) ) )
= $true )
| ( ( product @ SV16 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV39: $i,SV29: $i,SV49: $i,SV47: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV47 @ SV49 ) )
= $true )
| ( ( ! [SY176: $i] :
( ~ ( sum @ SV29 @ SV47 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV17 @ SY176 @ SY177 )
| ( sum @ SV39 @ SV49 @ SY177 ) ) ) )
= $true )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV40: $i,SV30: $i,SV50: $i,SV48: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV48 @ SV50 ) )
= $true )
| ( ( ! [SY178: $i] :
( ~ ( sum @ SV30 @ SV48 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY179 )
| ( product @ SV18 @ SY178 @ SY179 ) ) ) )
= $true )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV41: $i,SV51: $i,SV31: $i,SV19: $i] :
( ( ( sum @ SV19 @ SV31 @ SV51 )
= $false )
| ( ( SV41 = SV51 )
= $true )
| ( ( sum @ SV19 @ SV31 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(180,plain,
! [SV42: $i,SV52: $i,SV32: $i,SV20: $i] :
( ( ( product @ SV20 @ SV32 @ SV52 )
= $false )
| ( ( SV42 = SV52 )
= $true )
| ( ( product @ SV20 @ SV32 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV12: $i,SV34: $i,SV53: $i,SV43: $i,SV24: $i] :
( ( ( sum @ SV24 @ SV43 @ SV53 )
= $false )
| ( ( ! [SY180: $i] :
( ~ ( sum @ SV34 @ SV43 @ SY180 )
| ( sum @ SV12 @ SV53 @ SY180 ) ) )
= $true )
| ( ( sum @ SV12 @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV35: $i,SV13: $i,SV54: $i,SV44: $i,SV25: $i] :
( ( ( sum @ SV25 @ SV44 @ SV54 )
= $false )
| ( ( ! [SY181: $i] :
( ~ ( sum @ SV13 @ SV54 @ SY181 )
| ( sum @ SV35 @ SV44 @ SY181 ) ) )
= $true )
| ( ( sum @ SV13 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV15: $i,SV37: $i,SV55: $i,SV45: $i,SV27: $i] :
( ( ( product @ SV27 @ SV45 @ SV55 )
= $false )
| ( ( ! [SY182: $i] :
( ~ ( product @ SV37 @ SV45 @ SY182 )
| ( product @ SV15 @ SV55 @ SY182 ) ) )
= $true )
| ( ( product @ SV15 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV38: $i,SV16: $i,SV56: $i,SV46: $i,SV28: $i] :
( ( ( product @ SV28 @ SV46 @ SV56 )
= $false )
| ( ( ! [SY183: $i] :
( ~ ( product @ SV16 @ SV56 @ SY183 )
| ( product @ SV38 @ SV46 @ SY183 ) ) )
= $true )
| ( ( product @ SV16 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV39: $i,SV29: $i,SV49: $i,SV47: $i,SV17: $i] :
( ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( ! [SY176: $i] :
( ~ ( sum @ SV29 @ SV47 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV17 @ SY176 @ SY177 )
| ( sum @ SV39 @ SV49 @ SY177 ) ) ) )
= $true )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV40: $i,SV30: $i,SV50: $i,SV48: $i,SV18: $i] :
( ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( ! [SY178: $i] :
( ~ ( sum @ SV30 @ SV48 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY179 )
| ( product @ SV18 @ SY178 @ SY179 ) ) ) )
= $true )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV24: $i,SV53: $i,SV12: $i,SV57: $i,SV43: $i,SV34: $i] :
( ( ( ~ ( sum @ SV34 @ SV43 @ SV57 )
| ( sum @ SV12 @ SV53 @ SV57 ) )
= $true )
| ( ( sum @ SV24 @ SV43 @ SV53 )
= $false )
| ( ( sum @ SV12 @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(188,plain,
! [SV25: $i,SV44: $i,SV35: $i,SV58: $i,SV54: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV54 @ SV58 )
| ( sum @ SV35 @ SV44 @ SV58 ) )
= $true )
| ( ( sum @ SV25 @ SV44 @ SV54 )
= $false )
| ( ( sum @ SV13 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(189,plain,
! [SV27: $i,SV55: $i,SV15: $i,SV59: $i,SV45: $i,SV37: $i] :
( ( ( ~ ( product @ SV37 @ SV45 @ SV59 )
| ( product @ SV15 @ SV55 @ SV59 ) )
= $true )
| ( ( product @ SV27 @ SV45 @ SV55 )
= $false )
| ( ( product @ SV15 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(190,plain,
! [SV28: $i,SV46: $i,SV38: $i,SV60: $i,SV56: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV56 @ SV60 )
| ( product @ SV38 @ SV46 @ SV60 ) )
= $true )
| ( ( product @ SV28 @ SV46 @ SV56 )
= $false )
| ( ( product @ SV16 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(191,plain,
! [SV49: $i,SV39: $i,SV17: $i,SV61: $i,SV47: $i,SV29: $i] :
( ( ( ~ ( sum @ SV29 @ SV47 @ SV61 )
| ! [SY184: $i] :
( ~ ( product @ SV17 @ SV61 @ SY184 )
| ( sum @ SV39 @ SV49 @ SY184 ) ) )
= $true )
| ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(192,plain,
! [SV18: $i,SV50: $i,SV40: $i,SV62: $i,SV48: $i,SV30: $i] :
( ( ( ~ ( sum @ SV30 @ SV48 @ SV62 )
| ! [SY185: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY185 )
| ( product @ SV18 @ SV62 @ SY185 ) ) )
= $true )
| ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(193,plain,
! [SV24: $i,SV53: $i,SV12: $i,SV57: $i,SV43: $i,SV34: $i] :
( ( ( ~ ( sum @ SV34 @ SV43 @ SV57 ) )
= $true )
| ( ( sum @ SV12 @ SV53 @ SV57 )
= $true )
| ( ( sum @ SV24 @ SV43 @ SV53 )
= $false )
| ( ( sum @ SV12 @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(194,plain,
! [SV25: $i,SV44: $i,SV35: $i,SV58: $i,SV54: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV54 @ SV58 ) )
= $true )
| ( ( sum @ SV35 @ SV44 @ SV58 )
= $true )
| ( ( sum @ SV25 @ SV44 @ SV54 )
= $false )
| ( ( sum @ SV13 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(195,plain,
! [SV27: $i,SV55: $i,SV15: $i,SV59: $i,SV45: $i,SV37: $i] :
( ( ( ~ ( product @ SV37 @ SV45 @ SV59 ) )
= $true )
| ( ( product @ SV15 @ SV55 @ SV59 )
= $true )
| ( ( product @ SV27 @ SV45 @ SV55 )
= $false )
| ( ( product @ SV15 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(196,plain,
! [SV28: $i,SV46: $i,SV38: $i,SV60: $i,SV56: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV56 @ SV60 ) )
= $true )
| ( ( product @ SV38 @ SV46 @ SV60 )
= $true )
| ( ( product @ SV28 @ SV46 @ SV56 )
= $false )
| ( ( product @ SV16 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(197,plain,
! [SV49: $i,SV39: $i,SV17: $i,SV61: $i,SV47: $i,SV29: $i] :
( ( ( ~ ( sum @ SV29 @ SV47 @ SV61 ) )
= $true )
| ( ( ! [SY184: $i] :
( ~ ( product @ SV17 @ SV61 @ SY184 )
| ( sum @ SV39 @ SV49 @ SY184 ) ) )
= $true )
| ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(198,plain,
! [SV18: $i,SV50: $i,SV40: $i,SV62: $i,SV48: $i,SV30: $i] :
( ( ( ~ ( sum @ SV30 @ SV48 @ SV62 ) )
= $true )
| ( ( ! [SY185: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY185 )
| ( product @ SV18 @ SV62 @ SY185 ) ) )
= $true )
| ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(199,plain,
! [SV24: $i,SV53: $i,SV12: $i,SV57: $i,SV43: $i,SV34: $i] :
( ( ( sum @ SV34 @ SV43 @ SV57 )
= $false )
| ( ( sum @ SV12 @ SV53 @ SV57 )
= $true )
| ( ( sum @ SV24 @ SV43 @ SV53 )
= $false )
| ( ( sum @ SV12 @ SV24 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV25: $i,SV44: $i,SV35: $i,SV58: $i,SV54: $i,SV13: $i] :
( ( ( sum @ SV13 @ SV54 @ SV58 )
= $false )
| ( ( sum @ SV35 @ SV44 @ SV58 )
= $true )
| ( ( sum @ SV25 @ SV44 @ SV54 )
= $false )
| ( ( sum @ SV13 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV27: $i,SV55: $i,SV15: $i,SV59: $i,SV45: $i,SV37: $i] :
( ( ( product @ SV37 @ SV45 @ SV59 )
= $false )
| ( ( product @ SV15 @ SV55 @ SV59 )
= $true )
| ( ( product @ SV27 @ SV45 @ SV55 )
= $false )
| ( ( product @ SV15 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV28: $i,SV46: $i,SV38: $i,SV60: $i,SV56: $i,SV16: $i] :
( ( ( product @ SV16 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV38 @ SV46 @ SV60 )
= $true )
| ( ( product @ SV28 @ SV46 @ SV56 )
= $false )
| ( ( product @ SV16 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV49: $i,SV39: $i,SV17: $i,SV61: $i,SV47: $i,SV29: $i] :
( ( ( sum @ SV29 @ SV47 @ SV61 )
= $false )
| ( ( ! [SY184: $i] :
( ~ ( product @ SV17 @ SV61 @ SY184 )
| ( sum @ SV39 @ SV49 @ SY184 ) ) )
= $true )
| ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(204,plain,
! [SV18: $i,SV50: $i,SV40: $i,SV62: $i,SV48: $i,SV30: $i] :
( ( ( sum @ SV30 @ SV48 @ SV62 )
= $false )
| ( ( ! [SY185: $i] :
( ~ ( sum @ SV40 @ SV50 @ SY185 )
| ( product @ SV18 @ SV62 @ SY185 ) ) )
= $true )
| ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV47: $i,SV29: $i,SV49: $i,SV39: $i,SV63: $i,SV61: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV61 @ SV63 )
| ( sum @ SV39 @ SV49 @ SV63 ) )
= $true )
| ( ( sum @ SV29 @ SV47 @ SV61 )
= $false )
| ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(206,plain,
! [SV48: $i,SV30: $i,SV62: $i,SV18: $i,SV64: $i,SV50: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV50 @ SV64 )
| ( product @ SV18 @ SV62 @ SV64 ) )
= $true )
| ( ( sum @ SV30 @ SV48 @ SV62 )
= $false )
| ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(207,plain,
! [SV47: $i,SV29: $i,SV49: $i,SV39: $i,SV63: $i,SV61: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV61 @ SV63 ) )
= $true )
| ( ( sum @ SV39 @ SV49 @ SV63 )
= $true )
| ( ( sum @ SV29 @ SV47 @ SV61 )
= $false )
| ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(208,plain,
! [SV48: $i,SV30: $i,SV62: $i,SV18: $i,SV64: $i,SV50: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV50 @ SV64 ) )
= $true )
| ( ( product @ SV18 @ SV62 @ SV64 )
= $true )
| ( ( sum @ SV30 @ SV48 @ SV62 )
= $false )
| ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(209,plain,
! [SV47: $i,SV29: $i,SV49: $i,SV39: $i,SV63: $i,SV61: $i,SV17: $i] :
( ( ( product @ SV17 @ SV61 @ SV63 )
= $false )
| ( ( sum @ SV39 @ SV49 @ SV63 )
= $true )
| ( ( sum @ SV29 @ SV47 @ SV61 )
= $false )
| ( ( product @ SV17 @ SV47 @ SV49 )
= $false )
| ( ( product @ SV17 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(210,plain,
! [SV48: $i,SV30: $i,SV62: $i,SV18: $i,SV64: $i,SV50: $i,SV40: $i] :
( ( ( sum @ SV40 @ SV50 @ SV64 )
= $false )
| ( ( product @ SV18 @ SV62 @ SV64 )
= $true )
| ( ( sum @ SV30 @ SV48 @ SV62 )
= $false )
| ( ( product @ SV18 @ SV48 @ SV50 )
= $false )
| ( ( product @ SV18 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(211,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,210,209,202,201,200,199,180,179,150,147,117,116,114,113,112,102,101,98,97,93,92,91,68,67,66]) ).
thf(212,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG040-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 07:07:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.37
% 0.12/0.37 No.of.Axioms: 25
% 0.12/0.37
% 0.12/0.37 Length.of.Defs: 0
% 0.12/0.37
% 0.12/0.37 Contains.Choice.Funs: false
% 0.12/0.39 .
% 0.12/0.39 (rf:0,axioms:25,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:27,loop_count:0,foatp_calls:0,translation:fof_full).............
% 2.39/2.57
% 2.39/2.57 ********************************
% 2.39/2.57 * All subproblems solved! *
% 2.39/2.57 ********************************
% 2.39/2.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:211,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.39/2.59
% 2.39/2.59 %**** Beginning of derivation protocol ****
% 2.39/2.59 % SZS output start CNFRefutation
% See solution above
% 2.39/2.59
% 2.39/2.59 %**** End of derivation protocol ****
% 2.39/2.59 %**** no. of clauses in derivation: 212 ****
% 2.39/2.59 %**** clause counter: 211 ****
% 2.39/2.59
% 2.39/2.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,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:211,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------