%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:37:33 AM UTC 2026
% Result : Unsatisfiable 0.61s 0.38s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 31
% Syntax : Number of formulae : 303 ( 184 unt; 0 typ; 0 def)
% Number of atoms : 1899 ( 457 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 4133 ( 553 ~; 682 |; 0 &;2898 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 1352 ( 0 ^;1352 !; 0 ?;1352 :)
% 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_equalish,type,
equalish: $i > $i > $o ).
thf(tp_h,type,
h: $i > $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(1,axiom,
! [X: $i] : ( product @ X @ additive_identity @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(2,axiom,
! [X: $i] : ( product @ additive_identity @ X @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(3,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(4,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(5,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(6,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(11,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(14,axiom,
! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
thf(15,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(16,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(17,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(18,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
thf(19,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).
thf(20,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution1) ).
thf(21,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(22,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).
thf(23,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).
thf(24,axiom,
! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution1) ).
thf(25,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).
thf(26,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_substitution) ).
thf(27,axiom,
product @ a @ b @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
thf(28,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ additive_identity )
| ( product @ X @ ( h @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_property) ).
thf(29,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(30,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,negated_conjecture,
~ ( equalish @ b @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
thf(32,negated_conjecture,
~ ( equalish @ a @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_additive_identity) ).
thf(33,plain,
$false = $false,
inference(unfold_def,[status(thm)],[30]) ).
thf(34,plain,
( ( ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,plain,
( ( ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(38,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(39,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(40,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)],[7]) ).
thf(41,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)],[8]) ).
thf(42,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)],[9]) ).
thf(43,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)],[10]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(45,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)],[12]) ).
thf(46,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)],[13]) ).
thf(47,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(50,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(60,plain,
( ( product @ a @ b @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ additive_identity )
| ( product @ X @ ( h @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(62,plain,
( ( ~ ( equalish @ b @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(63,plain,
( ( ~ ( equalish @ a @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(64,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(65,plain,
( ( ~ ( equalish @ a @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ( equalish @ b @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ additive_identity )
| ( product @ X @ ( h @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(68,plain,
( ( product @ a @ b @ additive_identity )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( add @ X @ W ) @ ( add @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ X @ W @ Z )
| ( sum @ Y @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ X @ Z )
| ( sum @ W @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( sum @ W @ Z @ X )
| ( sum @ W @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ ( multiply @ X @ W ) @ ( multiply @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ X @ W @ Z )
| ( product @ Y @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ X @ Z )
| ( product @ W @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i,W: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( product @ W @ Z @ X )
| ( product @ W @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(81,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(82,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(copy,[status(thm)],[46]) ).
thf(83,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(copy,[status(thm)],[45]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(85,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(copy,[status(thm)],[43]) ).
thf(86,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(copy,[status(thm)],[42]) ).
thf(87,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(copy,[status(thm)],[41]) ).
thf(88,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(copy,[status(thm)],[40]) ).
thf(89,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(90,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( equalish @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( equalish @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(93,plain,
( ( ! [X: $i] : ( product @ additive_identity @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(94,plain,
( ( ! [X: $i] : ( product @ X @ additive_identity @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(95,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[64]) ).
thf(96,plain,
( ( equalish @ a @ additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(97,plain,
( ( equalish @ b @ additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(98,plain,
! [SV1: $i] :
( ( ! [SY105: $i] :
( ~ ( equalish @ SV1 @ additive_identity )
| ( product @ SV1 @ ( h @ SV1 @ SY105 ) @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(99,plain,
! [SV2: $i] :
( ( ! [SY106: $i] :
( ~ ( equalish @ SV2 @ SY106 )
| ( equalish @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(100,plain,
! [SV3: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( equalish @ SV3 @ SY107 )
| ( equalish @ ( add @ SV3 @ SY108 ) @ ( add @ SY107 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(101,plain,
! [SV4: $i] :
( ( ! [SY109: $i,SY110: $i,SY111: $i] :
( ~ ( equalish @ SV4 @ SY109 )
| ~ ( sum @ SV4 @ SY110 @ SY111 )
| ( sum @ SY109 @ SY110 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(102,plain,
! [SV5: $i] :
( ( ! [SY112: $i,SY113: $i,SY114: $i] :
( ~ ( equalish @ SV5 @ SY112 )
| ~ ( sum @ SY113 @ SV5 @ SY114 )
| ( sum @ SY113 @ SY112 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(103,plain,
! [SV6: $i] :
( ( ! [SY115: $i,SY116: $i,SY117: $i] :
( ~ ( equalish @ SV6 @ SY115 )
| ~ ( sum @ SY116 @ SY117 @ SV6 )
| ( sum @ SY116 @ SY117 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(104,plain,
! [SV7: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( equalish @ SV7 @ SY118 )
| ( equalish @ ( multiply @ SV7 @ SY119 ) @ ( multiply @ SY118 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(105,plain,
! [SV8: $i] :
( ( ! [SY120: $i,SY121: $i,SY122: $i] :
( ~ ( equalish @ SV8 @ SY120 )
| ~ ( product @ SV8 @ SY121 @ SY122 )
| ( product @ SY120 @ SY121 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(106,plain,
! [SV9: $i] :
( ( ! [SY123: $i,SY124: $i,SY125: $i] :
( ~ ( equalish @ SV9 @ SY123 )
| ~ ( product @ SY124 @ SV9 @ SY125 )
| ( product @ SY124 @ SY123 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(107,plain,
! [SV10: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i] :
( ~ ( equalish @ SV10 @ SY126 )
| ~ ( product @ SY127 @ SY128 @ SV10 )
| ( product @ SY127 @ SY128 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(108,plain,
! [SV11: $i] :
( ( sum @ SV11 @ additive_identity @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(109,plain,
! [SV12: $i] :
( ( ! [SY129: $i] : ( product @ SV12 @ SY129 @ ( multiply @ SV12 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(110,plain,
! [SV13: $i] :
( ( ! [SY130: $i] : ( sum @ SV13 @ SY130 @ ( add @ SV13 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(111,plain,
! [SV14: $i] :
( ( sum @ SV14 @ ( additive_inverse @ SV14 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(112,plain,
! [SV15: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ~ ( sum @ SV15 @ SY131 @ SY132 )
| ~ ( sum @ SY131 @ SY133 @ SY134 )
| ~ ( sum @ SY132 @ SY133 @ SY135 )
| ( sum @ SV15 @ SY134 @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(113,plain,
! [SV16: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i,SY139: $i,SY140: $i] :
( ~ ( sum @ SV16 @ SY136 @ SY137 )
| ~ ( sum @ SY136 @ SY138 @ SY139 )
| ~ ( sum @ SV16 @ SY139 @ SY140 )
| ( sum @ SY137 @ SY138 @ SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(114,plain,
! [SV17: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ( sum @ SV17 @ SY141 @ SY142 )
| ( sum @ SY141 @ SV17 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(115,plain,
! [SV18: $i] :
( ( ! [SY143: $i,SY144: $i,SY145: $i,SY146: $i,SY147: $i] :
( ~ ( product @ SV18 @ SY143 @ SY144 )
| ~ ( product @ SY143 @ SY145 @ SY146 )
| ~ ( product @ SY144 @ SY145 @ SY147 )
| ( product @ SV18 @ SY146 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(116,plain,
! [SV19: $i] :
( ( ! [SY148: $i,SY149: $i,SY150: $i,SY151: $i,SY152: $i] :
( ~ ( product @ SV19 @ SY148 @ SY149 )
| ~ ( product @ SY148 @ SY150 @ SY151 )
| ~ ( product @ SV19 @ SY151 @ SY152 )
| ( product @ SY149 @ SY150 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(117,plain,
! [SV20: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i,SY156: $i,SY157: $i,SY158: $i] :
( ~ ( product @ SV20 @ SY153 @ SY154 )
| ~ ( product @ SV20 @ SY155 @ SY156 )
| ~ ( sum @ SY153 @ SY155 @ SY157 )
| ~ ( product @ SV20 @ SY157 @ SY158 )
| ( sum @ SY154 @ SY156 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(118,plain,
! [SV21: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i,SY162: $i,SY163: $i,SY164: $i] :
( ~ ( product @ SV21 @ SY159 @ SY160 )
| ~ ( product @ SV21 @ SY161 @ SY162 )
| ~ ( sum @ SY159 @ SY161 @ SY163 )
| ~ ( sum @ SY160 @ SY162 @ SY164 )
| ( product @ SV21 @ SY163 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(119,plain,
! [SV22: $i] :
( ( ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i,SY169: $i,SY170: $i] :
( ~ ( product @ SV22 @ SY165 @ SY166 )
| ~ ( product @ SY167 @ SY165 @ SY168 )
| ~ ( sum @ SV22 @ SY167 @ SY169 )
| ~ ( product @ SY169 @ SY165 @ SY170 )
| ( sum @ SY166 @ SY168 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(120,plain,
! [SV23: $i] :
( ( ! [SY171: $i,SY172: $i,SY173: $i,SY174: $i,SY175: $i,SY176: $i] :
( ~ ( product @ SV23 @ SY171 @ SY172 )
| ~ ( product @ SY173 @ SY171 @ SY174 )
| ~ ( sum @ SV23 @ SY173 @ SY175 )
| ~ ( sum @ SY172 @ SY174 @ SY176 )
| ( product @ SY175 @ SY171 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(121,plain,
! [SV24: $i] :
( ( ! [SY177: $i,SY178: $i,SY179: $i] :
( ~ ( sum @ SV24 @ SY177 @ SY178 )
| ~ ( sum @ SV24 @ SY177 @ SY179 )
| ( equalish @ SY178 @ SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(122,plain,
! [SV25: $i] :
( ( ! [SY180: $i,SY181: $i,SY182: $i] :
( ~ ( product @ SV25 @ SY180 @ SY181 )
| ~ ( product @ SV25 @ SY180 @ SY182 )
| ( equalish @ SY181 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(123,plain,
! [SV26: $i] :
( ( product @ additive_identity @ SV26 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(124,plain,
! [SV27: $i] :
( ( product @ SV27 @ additive_identity @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(125,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(126,plain,
! [SV28: $i,SV1: $i] :
( ( ~ ( equalish @ SV1 @ additive_identity )
| ( product @ SV1 @ ( h @ SV1 @ SV28 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(127,plain,
! [SV29: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV29 )
| ( equalish @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(128,plain,
! [SV30: $i,SV3: $i] :
( ( ! [SY183: $i] :
( ~ ( equalish @ SV3 @ SV30 )
| ( equalish @ ( add @ SV3 @ SY183 ) @ ( add @ SV30 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(129,plain,
! [SV31: $i,SV4: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ~ ( equalish @ SV4 @ SV31 )
| ~ ( sum @ SV4 @ SY184 @ SY185 )
| ( sum @ SV31 @ SY184 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(130,plain,
! [SV32: $i,SV5: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ~ ( equalish @ SV5 @ SV32 )
| ~ ( sum @ SY186 @ SV5 @ SY187 )
| ( sum @ SY186 @ SV32 @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(131,plain,
! [SV33: $i,SV6: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ~ ( equalish @ SV6 @ SV33 )
| ~ ( sum @ SY188 @ SY189 @ SV6 )
| ( sum @ SY188 @ SY189 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(132,plain,
! [SV34: $i,SV7: $i] :
( ( ! [SY190: $i] :
( ~ ( equalish @ SV7 @ SV34 )
| ( equalish @ ( multiply @ SV7 @ SY190 ) @ ( multiply @ SV34 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(133,plain,
! [SV35: $i,SV8: $i] :
( ( ! [SY191: $i,SY192: $i] :
( ~ ( equalish @ SV8 @ SV35 )
| ~ ( product @ SV8 @ SY191 @ SY192 )
| ( product @ SV35 @ SY191 @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(134,plain,
! [SV36: $i,SV9: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( equalish @ SV9 @ SV36 )
| ~ ( product @ SY193 @ SV9 @ SY194 )
| ( product @ SY193 @ SV36 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(135,plain,
! [SV37: $i,SV10: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ~ ( equalish @ SV10 @ SV37 )
| ~ ( product @ SY195 @ SY196 @ SV10 )
| ( product @ SY195 @ SY196 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(136,plain,
! [SV38: $i,SV12: $i] :
( ( product @ SV12 @ SV38 @ ( multiply @ SV12 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(137,plain,
! [SV39: $i,SV13: $i] :
( ( sum @ SV13 @ SV39 @ ( add @ SV13 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(138,plain,
! [SV40: $i,SV15: $i] :
( ( ! [SY197: $i,SY198: $i,SY199: $i,SY200: $i] :
( ~ ( sum @ SV15 @ SV40 @ SY197 )
| ~ ( sum @ SV40 @ SY198 @ SY199 )
| ~ ( sum @ SY197 @ SY198 @ SY200 )
| ( sum @ SV15 @ SY199 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(139,plain,
! [SV41: $i,SV16: $i] :
( ( ! [SY201: $i,SY202: $i,SY203: $i,SY204: $i] :
( ~ ( sum @ SV16 @ SV41 @ SY201 )
| ~ ( sum @ SV41 @ SY202 @ SY203 )
| ~ ( sum @ SV16 @ SY203 @ SY204 )
| ( sum @ SY201 @ SY202 @ SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(140,plain,
! [SV42: $i,SV17: $i] :
( ( ! [SY205: $i] :
( ~ ( sum @ SV17 @ SV42 @ SY205 )
| ( sum @ SV42 @ SV17 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(141,plain,
! [SV43: $i,SV18: $i] :
( ( ! [SY206: $i,SY207: $i,SY208: $i,SY209: $i] :
( ~ ( product @ SV18 @ SV43 @ SY206 )
| ~ ( product @ SV43 @ SY207 @ SY208 )
| ~ ( product @ SY206 @ SY207 @ SY209 )
| ( product @ SV18 @ SY208 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(142,plain,
! [SV44: $i,SV19: $i] :
( ( ! [SY210: $i,SY211: $i,SY212: $i,SY213: $i] :
( ~ ( product @ SV19 @ SV44 @ SY210 )
| ~ ( product @ SV44 @ SY211 @ SY212 )
| ~ ( product @ SV19 @ SY212 @ SY213 )
| ( product @ SY210 @ SY211 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV45: $i,SV20: $i] :
( ( ! [SY214: $i,SY215: $i,SY216: $i,SY217: $i,SY218: $i] :
( ~ ( product @ SV20 @ SV45 @ SY214 )
| ~ ( product @ SV20 @ SY215 @ SY216 )
| ~ ( sum @ SV45 @ SY215 @ SY217 )
| ~ ( product @ SV20 @ SY217 @ SY218 )
| ( sum @ SY214 @ SY216 @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
! [SV46: $i,SV21: $i] :
( ( ! [SY219: $i,SY220: $i,SY221: $i,SY222: $i,SY223: $i] :
( ~ ( product @ SV21 @ SV46 @ SY219 )
| ~ ( product @ SV21 @ SY220 @ SY221 )
| ~ ( sum @ SV46 @ SY220 @ SY222 )
| ~ ( sum @ SY219 @ SY221 @ SY223 )
| ( product @ SV21 @ SY222 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(145,plain,
! [SV47: $i,SV22: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i,SY227: $i,SY228: $i] :
( ~ ( product @ SV22 @ SV47 @ SY224 )
| ~ ( product @ SY225 @ SV47 @ SY226 )
| ~ ( sum @ SV22 @ SY225 @ SY227 )
| ~ ( product @ SY227 @ SV47 @ SY228 )
| ( sum @ SY224 @ SY226 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(146,plain,
! [SV48: $i,SV23: $i] :
( ( ! [SY229: $i,SY230: $i,SY231: $i,SY232: $i,SY233: $i] :
( ~ ( product @ SV23 @ SV48 @ SY229 )
| ~ ( product @ SY230 @ SV48 @ SY231 )
| ~ ( sum @ SV23 @ SY230 @ SY232 )
| ~ ( sum @ SY229 @ SY231 @ SY233 )
| ( product @ SY232 @ SV48 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(147,plain,
! [SV49: $i,SV24: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ~ ( sum @ SV24 @ SV49 @ SY234 )
| ~ ( sum @ SV24 @ SV49 @ SY235 )
| ( equalish @ SY234 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(148,plain,
! [SV50: $i,SV25: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ~ ( product @ SV25 @ SV50 @ SY236 )
| ~ ( product @ SV25 @ SV50 @ SY237 )
| ( equalish @ SY236 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(149,plain,
! [SV28: $i,SV1: $i] :
( ( ( ~ ( equalish @ SV1 @ additive_identity ) )
= $true )
| ( ( product @ SV1 @ ( h @ SV1 @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(150,plain,
! [SV29: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV29 ) )
= $true )
| ( ( equalish @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(151,plain,
! [SV51: $i,SV30: $i,SV3: $i] :
( ( ~ ( equalish @ SV3 @ SV30 )
| ( equalish @ ( add @ SV3 @ SV51 ) @ ( add @ SV30 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(152,plain,
! [SV52: $i,SV31: $i,SV4: $i] :
( ( ! [SY238: $i] :
( ~ ( equalish @ SV4 @ SV31 )
| ~ ( sum @ SV4 @ SV52 @ SY238 )
| ( sum @ SV31 @ SV52 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(153,plain,
! [SV53: $i,SV32: $i,SV5: $i] :
( ( ! [SY239: $i] :
( ~ ( equalish @ SV5 @ SV32 )
| ~ ( sum @ SV53 @ SV5 @ SY239 )
| ( sum @ SV53 @ SV32 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV54: $i,SV33: $i,SV6: $i] :
( ( ! [SY240: $i] :
( ~ ( equalish @ SV6 @ SV33 )
| ~ ( sum @ SV54 @ SY240 @ SV6 )
| ( sum @ SV54 @ SY240 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(155,plain,
! [SV55: $i,SV34: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV34 )
| ( equalish @ ( multiply @ SV7 @ SV55 ) @ ( multiply @ SV34 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(156,plain,
! [SV56: $i,SV35: $i,SV8: $i] :
( ( ! [SY241: $i] :
( ~ ( equalish @ SV8 @ SV35 )
| ~ ( product @ SV8 @ SV56 @ SY241 )
| ( product @ SV35 @ SV56 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(157,plain,
! [SV57: $i,SV36: $i,SV9: $i] :
( ( ! [SY242: $i] :
( ~ ( equalish @ SV9 @ SV36 )
| ~ ( product @ SV57 @ SV9 @ SY242 )
| ( product @ SV57 @ SV36 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV58: $i,SV37: $i,SV10: $i] :
( ( ! [SY243: $i] :
( ~ ( equalish @ SV10 @ SV37 )
| ~ ( product @ SV58 @ SY243 @ SV10 )
| ( product @ SV58 @ SY243 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV59: $i,SV40: $i,SV15: $i] :
( ( ! [SY244: $i,SY245: $i,SY246: $i] :
( ~ ( sum @ SV15 @ SV40 @ SV59 )
| ~ ( sum @ SV40 @ SY244 @ SY245 )
| ~ ( sum @ SV59 @ SY244 @ SY246 )
| ( sum @ SV15 @ SY245 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(160,plain,
! [SV60: $i,SV41: $i,SV16: $i] :
( ( ! [SY247: $i,SY248: $i,SY249: $i] :
( ~ ( sum @ SV16 @ SV41 @ SV60 )
| ~ ( sum @ SV41 @ SY247 @ SY248 )
| ~ ( sum @ SV16 @ SY248 @ SY249 )
| ( sum @ SV60 @ SY247 @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(161,plain,
! [SV61: $i,SV42: $i,SV17: $i] :
( ( ~ ( sum @ SV17 @ SV42 @ SV61 )
| ( sum @ SV42 @ SV17 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(162,plain,
! [SV62: $i,SV43: $i,SV18: $i] :
( ( ! [SY250: $i,SY251: $i,SY252: $i] :
( ~ ( product @ SV18 @ SV43 @ SV62 )
| ~ ( product @ SV43 @ SY250 @ SY251 )
| ~ ( product @ SV62 @ SY250 @ SY252 )
| ( product @ SV18 @ SY251 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(163,plain,
! [SV63: $i,SV44: $i,SV19: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i] :
( ~ ( product @ SV19 @ SV44 @ SV63 )
| ~ ( product @ SV44 @ SY253 @ SY254 )
| ~ ( product @ SV19 @ SY254 @ SY255 )
| ( product @ SV63 @ SY253 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(164,plain,
! [SV64: $i,SV45: $i,SV20: $i] :
( ( ! [SY256: $i,SY257: $i,SY258: $i,SY259: $i] :
( ~ ( product @ SV20 @ SV45 @ SV64 )
| ~ ( product @ SV20 @ SY256 @ SY257 )
| ~ ( sum @ SV45 @ SY256 @ SY258 )
| ~ ( product @ SV20 @ SY258 @ SY259 )
| ( sum @ SV64 @ SY257 @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(165,plain,
! [SV65: $i,SV46: $i,SV21: $i] :
( ( ! [SY260: $i,SY261: $i,SY262: $i,SY263: $i] :
( ~ ( product @ SV21 @ SV46 @ SV65 )
| ~ ( product @ SV21 @ SY260 @ SY261 )
| ~ ( sum @ SV46 @ SY260 @ SY262 )
| ~ ( sum @ SV65 @ SY261 @ SY263 )
| ( product @ SV21 @ SY262 @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(166,plain,
! [SV66: $i,SV47: $i,SV22: $i] :
( ( ! [SY264: $i,SY265: $i,SY266: $i,SY267: $i] :
( ~ ( product @ SV22 @ SV47 @ SV66 )
| ~ ( product @ SY264 @ SV47 @ SY265 )
| ~ ( sum @ SV22 @ SY264 @ SY266 )
| ~ ( product @ SY266 @ SV47 @ SY267 )
| ( sum @ SV66 @ SY265 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(167,plain,
! [SV67: $i,SV48: $i,SV23: $i] :
( ( ! [SY268: $i,SY269: $i,SY270: $i,SY271: $i] :
( ~ ( product @ SV23 @ SV48 @ SV67 )
| ~ ( product @ SY268 @ SV48 @ SY269 )
| ~ ( sum @ SV23 @ SY268 @ SY270 )
| ~ ( sum @ SV67 @ SY269 @ SY271 )
| ( product @ SY270 @ SV48 @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV68: $i,SV49: $i,SV24: $i] :
( ( ! [SY272: $i] :
( ~ ( sum @ SV24 @ SV49 @ SV68 )
| ~ ( sum @ SV24 @ SV49 @ SY272 )
| ( equalish @ SV68 @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV69: $i,SV50: $i,SV25: $i] :
( ( ! [SY273: $i] :
( ~ ( product @ SV25 @ SV50 @ SV69 )
| ~ ( product @ SV25 @ SV50 @ SY273 )
| ( equalish @ SV69 @ SY273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV28: $i,SV1: $i] :
( ( ( equalish @ SV1 @ additive_identity )
= $false )
| ( ( product @ SV1 @ ( h @ SV1 @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(171,plain,
! [SV29: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV29 )
= $false )
| ( ( equalish @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(172,plain,
! [SV51: $i,SV30: $i,SV3: $i] :
( ( ( ~ ( equalish @ SV3 @ SV30 ) )
= $true )
| ( ( equalish @ ( add @ SV3 @ SV51 ) @ ( add @ SV30 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(173,plain,
! [SV70: $i,SV52: $i,SV31: $i,SV4: $i] :
( ( ~ ( equalish @ SV4 @ SV31 )
| ~ ( sum @ SV4 @ SV52 @ SV70 )
| ( sum @ SV31 @ SV52 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(174,plain,
! [SV71: $i,SV53: $i,SV32: $i,SV5: $i] :
( ( ~ ( equalish @ SV5 @ SV32 )
| ~ ( sum @ SV53 @ SV5 @ SV71 )
| ( sum @ SV53 @ SV32 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(175,plain,
! [SV72: $i,SV54: $i,SV33: $i,SV6: $i] :
( ( ~ ( equalish @ SV6 @ SV33 )
| ~ ( sum @ SV54 @ SV72 @ SV6 )
| ( sum @ SV54 @ SV72 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(176,plain,
! [SV55: $i,SV34: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV34 ) )
= $true )
| ( ( equalish @ ( multiply @ SV7 @ SV55 ) @ ( multiply @ SV34 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV73: $i,SV56: $i,SV35: $i,SV8: $i] :
( ( ~ ( equalish @ SV8 @ SV35 )
| ~ ( product @ SV8 @ SV56 @ SV73 )
| ( product @ SV35 @ SV56 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(178,plain,
! [SV74: $i,SV57: $i,SV36: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV36 )
| ~ ( product @ SV57 @ SV9 @ SV74 )
| ( product @ SV57 @ SV36 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(179,plain,
! [SV75: $i,SV58: $i,SV37: $i,SV10: $i] :
( ( ~ ( equalish @ SV10 @ SV37 )
| ~ ( product @ SV58 @ SV75 @ SV10 )
| ( product @ SV58 @ SV75 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(180,plain,
! [SV76: $i,SV59: $i,SV40: $i,SV15: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ( sum @ SV15 @ SV40 @ SV59 )
| ~ ( sum @ SV40 @ SV76 @ SY274 )
| ~ ( sum @ SV59 @ SV76 @ SY275 )
| ( sum @ SV15 @ SY274 @ SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(181,plain,
! [SV77: $i,SV60: $i,SV41: $i,SV16: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( sum @ SV16 @ SV41 @ SV60 )
| ~ ( sum @ SV41 @ SV77 @ SY276 )
| ~ ( sum @ SV16 @ SY276 @ SY277 )
| ( sum @ SV60 @ SV77 @ SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(182,plain,
! [SV61: $i,SV42: $i,SV17: $i] :
( ( ( ~ ( sum @ SV17 @ SV42 @ SV61 ) )
= $true )
| ( ( sum @ SV42 @ SV17 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(183,plain,
! [SV78: $i,SV62: $i,SV43: $i,SV18: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ( product @ SV18 @ SV43 @ SV62 )
| ~ ( product @ SV43 @ SV78 @ SY278 )
| ~ ( product @ SV62 @ SV78 @ SY279 )
| ( product @ SV18 @ SY278 @ SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(184,plain,
! [SV79: $i,SV63: $i,SV44: $i,SV19: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( product @ SV19 @ SV44 @ SV63 )
| ~ ( product @ SV44 @ SV79 @ SY280 )
| ~ ( product @ SV19 @ SY280 @ SY281 )
| ( product @ SV63 @ SV79 @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(185,plain,
! [SV80: $i,SV64: $i,SV45: $i,SV20: $i] :
( ( ! [SY282: $i,SY283: $i,SY284: $i] :
( ~ ( product @ SV20 @ SV45 @ SV64 )
| ~ ( product @ SV20 @ SV80 @ SY282 )
| ~ ( sum @ SV45 @ SV80 @ SY283 )
| ~ ( product @ SV20 @ SY283 @ SY284 )
| ( sum @ SV64 @ SY282 @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(186,plain,
! [SV81: $i,SV65: $i,SV46: $i,SV21: $i] :
( ( ! [SY285: $i,SY286: $i,SY287: $i] :
( ~ ( product @ SV21 @ SV46 @ SV65 )
| ~ ( product @ SV21 @ SV81 @ SY285 )
| ~ ( sum @ SV46 @ SV81 @ SY286 )
| ~ ( sum @ SV65 @ SY285 @ SY287 )
| ( product @ SV21 @ SY286 @ SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(187,plain,
! [SV82: $i,SV66: $i,SV47: $i,SV22: $i] :
( ( ! [SY288: $i,SY289: $i,SY290: $i] :
( ~ ( product @ SV22 @ SV47 @ SV66 )
| ~ ( product @ SV82 @ SV47 @ SY288 )
| ~ ( sum @ SV22 @ SV82 @ SY289 )
| ~ ( product @ SY289 @ SV47 @ SY290 )
| ( sum @ SV66 @ SY288 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(188,plain,
! [SV83: $i,SV67: $i,SV48: $i,SV23: $i] :
( ( ! [SY291: $i,SY292: $i,SY293: $i] :
( ~ ( product @ SV23 @ SV48 @ SV67 )
| ~ ( product @ SV83 @ SV48 @ SY291 )
| ~ ( sum @ SV23 @ SV83 @ SY292 )
| ~ ( sum @ SV67 @ SY291 @ SY293 )
| ( product @ SY292 @ SV48 @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(189,plain,
! [SV84: $i,SV68: $i,SV49: $i,SV24: $i] :
( ( ~ ( sum @ SV24 @ SV49 @ SV68 )
| ~ ( sum @ SV24 @ SV49 @ SV84 )
| ( equalish @ SV68 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(190,plain,
! [SV85: $i,SV69: $i,SV50: $i,SV25: $i] :
( ( ~ ( product @ SV25 @ SV50 @ SV69 )
| ~ ( product @ SV25 @ SV50 @ SV85 )
| ( equalish @ SV69 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(191,plain,
! [SV51: $i,SV30: $i,SV3: $i] :
( ( ( equalish @ SV3 @ SV30 )
= $false )
| ( ( equalish @ ( add @ SV3 @ SV51 ) @ ( add @ SV30 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(192,plain,
! [SV70: $i,SV52: $i,SV31: $i,SV4: $i] :
( ( ( ~ ( equalish @ SV4 @ SV31 ) )
= $true )
| ( ( ~ ( sum @ SV4 @ SV52 @ SV70 )
| ( sum @ SV31 @ SV52 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(193,plain,
! [SV71: $i,SV53: $i,SV32: $i,SV5: $i] :
( ( ( ~ ( equalish @ SV5 @ SV32 ) )
= $true )
| ( ( ~ ( sum @ SV53 @ SV5 @ SV71 )
| ( sum @ SV53 @ SV32 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(194,plain,
! [SV72: $i,SV54: $i,SV33: $i,SV6: $i] :
( ( ( ~ ( equalish @ SV6 @ SV33 ) )
= $true )
| ( ( ~ ( sum @ SV54 @ SV72 @ SV6 )
| ( sum @ SV54 @ SV72 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(195,plain,
! [SV55: $i,SV34: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV34 )
= $false )
| ( ( equalish @ ( multiply @ SV7 @ SV55 ) @ ( multiply @ SV34 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(196,plain,
! [SV73: $i,SV56: $i,SV35: $i,SV8: $i] :
( ( ( ~ ( equalish @ SV8 @ SV35 ) )
= $true )
| ( ( ~ ( product @ SV8 @ SV56 @ SV73 )
| ( product @ SV35 @ SV56 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(197,plain,
! [SV74: $i,SV57: $i,SV36: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV36 ) )
= $true )
| ( ( ~ ( product @ SV57 @ SV9 @ SV74 )
| ( product @ SV57 @ SV36 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV75: $i,SV58: $i,SV37: $i,SV10: $i] :
( ( ( ~ ( equalish @ SV10 @ SV37 ) )
= $true )
| ( ( ~ ( product @ SV58 @ SV75 @ SV10 )
| ( product @ SV58 @ SV75 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(199,plain,
! [SV86: $i,SV76: $i,SV59: $i,SV40: $i,SV15: $i] :
( ( ! [SY294: $i] :
( ~ ( sum @ SV15 @ SV40 @ SV59 )
| ~ ( sum @ SV40 @ SV76 @ SV86 )
| ~ ( sum @ SV59 @ SV76 @ SY294 )
| ( sum @ SV15 @ SV86 @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV87: $i,SV77: $i,SV60: $i,SV41: $i,SV16: $i] :
( ( ! [SY295: $i] :
( ~ ( sum @ SV16 @ SV41 @ SV60 )
| ~ ( sum @ SV41 @ SV77 @ SV87 )
| ~ ( sum @ SV16 @ SV87 @ SY295 )
| ( sum @ SV60 @ SV77 @ SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(201,plain,
! [SV61: $i,SV42: $i,SV17: $i] :
( ( ( sum @ SV17 @ SV42 @ SV61 )
= $false )
| ( ( sum @ SV42 @ SV17 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV88: $i,SV78: $i,SV62: $i,SV43: $i,SV18: $i] :
( ( ! [SY296: $i] :
( ~ ( product @ SV18 @ SV43 @ SV62 )
| ~ ( product @ SV43 @ SV78 @ SV88 )
| ~ ( product @ SV62 @ SV78 @ SY296 )
| ( product @ SV18 @ SV88 @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(203,plain,
! [SV89: $i,SV79: $i,SV63: $i,SV44: $i,SV19: $i] :
( ( ! [SY297: $i] :
( ~ ( product @ SV19 @ SV44 @ SV63 )
| ~ ( product @ SV44 @ SV79 @ SV89 )
| ~ ( product @ SV19 @ SV89 @ SY297 )
| ( product @ SV63 @ SV79 @ SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(204,plain,
! [SV90: $i,SV80: $i,SV64: $i,SV45: $i,SV20: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ~ ( product @ SV20 @ SV45 @ SV64 )
| ~ ( product @ SV20 @ SV80 @ SV90 )
| ~ ( sum @ SV45 @ SV80 @ SY298 )
| ~ ( product @ SV20 @ SY298 @ SY299 )
| ( sum @ SV64 @ SV90 @ SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(205,plain,
! [SV91: $i,SV81: $i,SV65: $i,SV46: $i,SV21: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ~ ( product @ SV21 @ SV46 @ SV65 )
| ~ ( product @ SV21 @ SV81 @ SV91 )
| ~ ( sum @ SV46 @ SV81 @ SY300 )
| ~ ( sum @ SV65 @ SV91 @ SY301 )
| ( product @ SV21 @ SY300 @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(206,plain,
! [SV92: $i,SV82: $i,SV66: $i,SV47: $i,SV22: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ~ ( product @ SV22 @ SV47 @ SV66 )
| ~ ( product @ SV82 @ SV47 @ SV92 )
| ~ ( sum @ SV22 @ SV82 @ SY302 )
| ~ ( product @ SY302 @ SV47 @ SY303 )
| ( sum @ SV66 @ SV92 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(207,plain,
! [SV93: $i,SV83: $i,SV67: $i,SV48: $i,SV23: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ~ ( product @ SV23 @ SV48 @ SV67 )
| ~ ( product @ SV83 @ SV48 @ SV93 )
| ~ ( sum @ SV23 @ SV83 @ SY304 )
| ~ ( sum @ SV67 @ SV93 @ SY305 )
| ( product @ SY304 @ SV48 @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(208,plain,
! [SV84: $i,SV68: $i,SV49: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV49 @ SV68 ) )
= $true )
| ( ( ~ ( sum @ SV24 @ SV49 @ SV84 )
| ( equalish @ SV68 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(209,plain,
! [SV85: $i,SV69: $i,SV50: $i,SV25: $i] :
( ( ( ~ ( product @ SV25 @ SV50 @ SV69 ) )
= $true )
| ( ( ~ ( product @ SV25 @ SV50 @ SV85 )
| ( equalish @ SV69 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(210,plain,
! [SV70: $i,SV52: $i,SV31: $i,SV4: $i] :
( ( ( equalish @ SV4 @ SV31 )
= $false )
| ( ( ~ ( sum @ SV4 @ SV52 @ SV70 )
| ( sum @ SV31 @ SV52 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(211,plain,
! [SV71: $i,SV53: $i,SV32: $i,SV5: $i] :
( ( ( equalish @ SV5 @ SV32 )
= $false )
| ( ( ~ ( sum @ SV53 @ SV5 @ SV71 )
| ( sum @ SV53 @ SV32 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(212,plain,
! [SV72: $i,SV54: $i,SV33: $i,SV6: $i] :
( ( ( equalish @ SV6 @ SV33 )
= $false )
| ( ( ~ ( sum @ SV54 @ SV72 @ SV6 )
| ( sum @ SV54 @ SV72 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(213,plain,
! [SV73: $i,SV56: $i,SV35: $i,SV8: $i] :
( ( ( equalish @ SV8 @ SV35 )
= $false )
| ( ( ~ ( product @ SV8 @ SV56 @ SV73 )
| ( product @ SV35 @ SV56 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV74: $i,SV57: $i,SV36: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV36 )
= $false )
| ( ( ~ ( product @ SV57 @ SV9 @ SV74 )
| ( product @ SV57 @ SV36 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV75: $i,SV58: $i,SV37: $i,SV10: $i] :
( ( ( equalish @ SV10 @ SV37 )
= $false )
| ( ( ~ ( product @ SV58 @ SV75 @ SV10 )
| ( product @ SV58 @ SV75 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(216,plain,
! [SV94: $i,SV86: $i,SV76: $i,SV59: $i,SV40: $i,SV15: $i] :
( ( ~ ( sum @ SV15 @ SV40 @ SV59 )
| ~ ( sum @ SV40 @ SV76 @ SV86 )
| ~ ( sum @ SV59 @ SV76 @ SV94 )
| ( sum @ SV15 @ SV86 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(217,plain,
! [SV95: $i,SV87: $i,SV77: $i,SV60: $i,SV41: $i,SV16: $i] :
( ( ~ ( sum @ SV16 @ SV41 @ SV60 )
| ~ ( sum @ SV41 @ SV77 @ SV87 )
| ~ ( sum @ SV16 @ SV87 @ SV95 )
| ( sum @ SV60 @ SV77 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(218,plain,
! [SV96: $i,SV88: $i,SV78: $i,SV62: $i,SV43: $i,SV18: $i] :
( ( ~ ( product @ SV18 @ SV43 @ SV62 )
| ~ ( product @ SV43 @ SV78 @ SV88 )
| ~ ( product @ SV62 @ SV78 @ SV96 )
| ( product @ SV18 @ SV88 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(219,plain,
! [SV97: $i,SV89: $i,SV79: $i,SV63: $i,SV44: $i,SV19: $i] :
( ( ~ ( product @ SV19 @ SV44 @ SV63 )
| ~ ( product @ SV44 @ SV79 @ SV89 )
| ~ ( product @ SV19 @ SV89 @ SV97 )
| ( product @ SV63 @ SV79 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV98: $i,SV90: $i,SV80: $i,SV64: $i,SV45: $i,SV20: $i] :
( ( ! [SY306: $i] :
( ~ ( product @ SV20 @ SV45 @ SV64 )
| ~ ( product @ SV20 @ SV80 @ SV90 )
| ~ ( sum @ SV45 @ SV80 @ SV98 )
| ~ ( product @ SV20 @ SV98 @ SY306 )
| ( sum @ SV64 @ SV90 @ SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV99: $i,SV91: $i,SV81: $i,SV65: $i,SV46: $i,SV21: $i] :
( ( ! [SY307: $i] :
( ~ ( product @ SV21 @ SV46 @ SV65 )
| ~ ( product @ SV21 @ SV81 @ SV91 )
| ~ ( sum @ SV46 @ SV81 @ SV99 )
| ~ ( sum @ SV65 @ SV91 @ SY307 )
| ( product @ SV21 @ SV99 @ SY307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(222,plain,
! [SV100: $i,SV92: $i,SV82: $i,SV66: $i,SV47: $i,SV22: $i] :
( ( ! [SY308: $i] :
( ~ ( product @ SV22 @ SV47 @ SV66 )
| ~ ( product @ SV82 @ SV47 @ SV92 )
| ~ ( sum @ SV22 @ SV82 @ SV100 )
| ~ ( product @ SV100 @ SV47 @ SY308 )
| ( sum @ SV66 @ SV92 @ SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(223,plain,
! [SV101: $i,SV93: $i,SV83: $i,SV67: $i,SV48: $i,SV23: $i] :
( ( ! [SY309: $i] :
( ~ ( product @ SV23 @ SV48 @ SV67 )
| ~ ( product @ SV83 @ SV48 @ SV93 )
| ~ ( sum @ SV23 @ SV83 @ SV101 )
| ~ ( sum @ SV67 @ SV93 @ SY309 )
| ( product @ SV101 @ SV48 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(224,plain,
! [SV84: $i,SV68: $i,SV49: $i,SV24: $i] :
( ( ( sum @ SV24 @ SV49 @ SV68 )
= $false )
| ( ( ~ ( sum @ SV24 @ SV49 @ SV84 )
| ( equalish @ SV68 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(225,plain,
! [SV85: $i,SV69: $i,SV50: $i,SV25: $i] :
( ( ( product @ SV25 @ SV50 @ SV69 )
= $false )
| ( ( ~ ( product @ SV25 @ SV50 @ SV85 )
| ( equalish @ SV69 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(226,plain,
! [SV31: $i,SV70: $i,SV52: $i,SV4: $i] :
( ( ( ~ ( sum @ SV4 @ SV52 @ SV70 ) )
= $true )
| ( ( sum @ SV31 @ SV52 @ SV70 )
= $true )
| ( ( equalish @ SV4 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(227,plain,
! [SV32: $i,SV71: $i,SV5: $i,SV53: $i] :
( ( ( ~ ( sum @ SV53 @ SV5 @ SV71 ) )
= $true )
| ( ( sum @ SV53 @ SV32 @ SV71 )
= $true )
| ( ( equalish @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(228,plain,
! [SV33: $i,SV6: $i,SV72: $i,SV54: $i] :
( ( ( ~ ( sum @ SV54 @ SV72 @ SV6 ) )
= $true )
| ( ( sum @ SV54 @ SV72 @ SV33 )
= $true )
| ( ( equalish @ SV6 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(229,plain,
! [SV35: $i,SV73: $i,SV56: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV56 @ SV73 ) )
= $true )
| ( ( product @ SV35 @ SV56 @ SV73 )
= $true )
| ( ( equalish @ SV8 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(230,plain,
! [SV36: $i,SV74: $i,SV9: $i,SV57: $i] :
( ( ( ~ ( product @ SV57 @ SV9 @ SV74 ) )
= $true )
| ( ( product @ SV57 @ SV36 @ SV74 )
= $true )
| ( ( equalish @ SV9 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(231,plain,
! [SV37: $i,SV10: $i,SV75: $i,SV58: $i] :
( ( ( ~ ( product @ SV58 @ SV75 @ SV10 ) )
= $true )
| ( ( product @ SV58 @ SV75 @ SV37 )
= $true )
| ( ( equalish @ SV10 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV94: $i,SV86: $i,SV76: $i,SV59: $i,SV40: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV40 @ SV59 ) )
= $true )
| ( ( ~ ( sum @ SV40 @ SV76 @ SV86 )
| ~ ( sum @ SV59 @ SV76 @ SV94 )
| ( sum @ SV15 @ SV86 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV95: $i,SV87: $i,SV77: $i,SV60: $i,SV41: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV41 @ SV60 ) )
= $true )
| ( ( ~ ( sum @ SV41 @ SV77 @ SV87 )
| ~ ( sum @ SV16 @ SV87 @ SV95 )
| ( sum @ SV60 @ SV77 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(234,plain,
! [SV96: $i,SV88: $i,SV78: $i,SV62: $i,SV43: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV43 @ SV62 ) )
= $true )
| ( ( ~ ( product @ SV43 @ SV78 @ SV88 )
| ~ ( product @ SV62 @ SV78 @ SV96 )
| ( product @ SV18 @ SV88 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV97: $i,SV89: $i,SV79: $i,SV63: $i,SV44: $i,SV19: $i] :
( ( ( ~ ( product @ SV19 @ SV44 @ SV63 ) )
= $true )
| ( ( ~ ( product @ SV44 @ SV79 @ SV89 )
| ~ ( product @ SV19 @ SV89 @ SV97 )
| ( product @ SV63 @ SV79 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(236,plain,
! [SV102: $i,SV98: $i,SV90: $i,SV80: $i,SV64: $i,SV45: $i,SV20: $i] :
( ( ~ ( product @ SV20 @ SV45 @ SV64 )
| ~ ( product @ SV20 @ SV80 @ SV90 )
| ~ ( sum @ SV45 @ SV80 @ SV98 )
| ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(237,plain,
! [SV103: $i,SV99: $i,SV91: $i,SV81: $i,SV65: $i,SV46: $i,SV21: $i] :
( ( ~ ( product @ SV21 @ SV46 @ SV65 )
| ~ ( product @ SV21 @ SV81 @ SV91 )
| ~ ( sum @ SV46 @ SV81 @ SV99 )
| ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(238,plain,
! [SV104: $i,SV100: $i,SV92: $i,SV82: $i,SV66: $i,SV47: $i,SV22: $i] :
( ( ~ ( product @ SV22 @ SV47 @ SV66 )
| ~ ( product @ SV82 @ SV47 @ SV92 )
| ~ ( sum @ SV22 @ SV82 @ SV100 )
| ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(239,plain,
! [SV105: $i,SV101: $i,SV93: $i,SV83: $i,SV67: $i,SV48: $i,SV23: $i] :
( ( ~ ( product @ SV23 @ SV48 @ SV67 )
| ~ ( product @ SV83 @ SV48 @ SV93 )
| ~ ( sum @ SV23 @ SV83 @ SV101 )
| ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(240,plain,
! [SV68: $i,SV84: $i,SV49: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV49 @ SV84 ) )
= $true )
| ( ( equalish @ SV68 @ SV84 )
= $true )
| ( ( sum @ SV24 @ SV49 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(241,plain,
! [SV69: $i,SV85: $i,SV50: $i,SV25: $i] :
( ( ( ~ ( product @ SV25 @ SV50 @ SV85 ) )
= $true )
| ( ( equalish @ SV69 @ SV85 )
= $true )
| ( ( product @ SV25 @ SV50 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(242,plain,
! [SV31: $i,SV70: $i,SV52: $i,SV4: $i] :
( ( ( sum @ SV4 @ SV52 @ SV70 )
= $false )
| ( ( sum @ SV31 @ SV52 @ SV70 )
= $true )
| ( ( equalish @ SV4 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(243,plain,
! [SV32: $i,SV71: $i,SV5: $i,SV53: $i] :
( ( ( sum @ SV53 @ SV5 @ SV71 )
= $false )
| ( ( sum @ SV53 @ SV32 @ SV71 )
= $true )
| ( ( equalish @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(244,plain,
! [SV33: $i,SV6: $i,SV72: $i,SV54: $i] :
( ( ( sum @ SV54 @ SV72 @ SV6 )
= $false )
| ( ( sum @ SV54 @ SV72 @ SV33 )
= $true )
| ( ( equalish @ SV6 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(245,plain,
! [SV35: $i,SV73: $i,SV56: $i,SV8: $i] :
( ( ( product @ SV8 @ SV56 @ SV73 )
= $false )
| ( ( product @ SV35 @ SV56 @ SV73 )
= $true )
| ( ( equalish @ SV8 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(246,plain,
! [SV36: $i,SV74: $i,SV9: $i,SV57: $i] :
( ( ( product @ SV57 @ SV9 @ SV74 )
= $false )
| ( ( product @ SV57 @ SV36 @ SV74 )
= $true )
| ( ( equalish @ SV9 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(247,plain,
! [SV37: $i,SV10: $i,SV75: $i,SV58: $i] :
( ( ( product @ SV58 @ SV75 @ SV10 )
= $false )
| ( ( product @ SV58 @ SV75 @ SV37 )
= $true )
| ( ( equalish @ SV10 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(248,plain,
! [SV94: $i,SV86: $i,SV76: $i,SV59: $i,SV40: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV40 @ SV59 )
= $false )
| ( ( ~ ( sum @ SV40 @ SV76 @ SV86 )
| ~ ( sum @ SV59 @ SV76 @ SV94 )
| ( sum @ SV15 @ SV86 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(249,plain,
! [SV95: $i,SV87: $i,SV77: $i,SV60: $i,SV41: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV41 @ SV60 )
= $false )
| ( ( ~ ( sum @ SV41 @ SV77 @ SV87 )
| ~ ( sum @ SV16 @ SV87 @ SV95 )
| ( sum @ SV60 @ SV77 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(250,plain,
! [SV96: $i,SV88: $i,SV78: $i,SV62: $i,SV43: $i,SV18: $i] :
( ( ( product @ SV18 @ SV43 @ SV62 )
= $false )
| ( ( ~ ( product @ SV43 @ SV78 @ SV88 )
| ~ ( product @ SV62 @ SV78 @ SV96 )
| ( product @ SV18 @ SV88 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(251,plain,
! [SV97: $i,SV89: $i,SV79: $i,SV63: $i,SV44: $i,SV19: $i] :
( ( ( product @ SV19 @ SV44 @ SV63 )
= $false )
| ( ( ~ ( product @ SV44 @ SV79 @ SV89 )
| ~ ( product @ SV19 @ SV89 @ SV97 )
| ( product @ SV63 @ SV79 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(252,plain,
! [SV102: $i,SV98: $i,SV90: $i,SV80: $i,SV64: $i,SV45: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV45 @ SV64 ) )
= $true )
| ( ( ~ ( product @ SV20 @ SV80 @ SV90 )
| ~ ( sum @ SV45 @ SV80 @ SV98 )
| ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(253,plain,
! [SV103: $i,SV99: $i,SV91: $i,SV81: $i,SV65: $i,SV46: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV46 @ SV65 ) )
= $true )
| ( ( ~ ( product @ SV21 @ SV81 @ SV91 )
| ~ ( sum @ SV46 @ SV81 @ SV99 )
| ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(254,plain,
! [SV104: $i,SV100: $i,SV92: $i,SV82: $i,SV66: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV47 @ SV66 ) )
= $true )
| ( ( ~ ( product @ SV82 @ SV47 @ SV92 )
| ~ ( sum @ SV22 @ SV82 @ SV100 )
| ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(255,plain,
! [SV105: $i,SV101: $i,SV93: $i,SV83: $i,SV67: $i,SV48: $i,SV23: $i] :
( ( ( ~ ( product @ SV23 @ SV48 @ SV67 ) )
= $true )
| ( ( ~ ( product @ SV83 @ SV48 @ SV93 )
| ~ ( sum @ SV23 @ SV83 @ SV101 )
| ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(256,plain,
! [SV68: $i,SV84: $i,SV49: $i,SV24: $i] :
( ( ( sum @ SV24 @ SV49 @ SV84 )
= $false )
| ( ( equalish @ SV68 @ SV84 )
= $true )
| ( ( sum @ SV24 @ SV49 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(257,plain,
! [SV69: $i,SV85: $i,SV50: $i,SV25: $i] :
( ( ( product @ SV25 @ SV50 @ SV85 )
= $false )
| ( ( equalish @ SV69 @ SV85 )
= $true )
| ( ( product @ SV25 @ SV50 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(258,plain,
! [SV15: $i,SV94: $i,SV59: $i,SV86: $i,SV76: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV76 @ SV86 ) )
= $true )
| ( ( ~ ( sum @ SV59 @ SV76 @ SV94 )
| ( sum @ SV15 @ SV86 @ SV94 ) )
= $true )
| ( ( sum @ SV15 @ SV40 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(259,plain,
! [SV60: $i,SV95: $i,SV16: $i,SV87: $i,SV77: $i,SV41: $i] :
( ( ( ~ ( sum @ SV41 @ SV77 @ SV87 ) )
= $true )
| ( ( ~ ( sum @ SV16 @ SV87 @ SV95 )
| ( sum @ SV60 @ SV77 @ SV95 ) )
= $true )
| ( ( sum @ SV16 @ SV41 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(260,plain,
! [SV18: $i,SV96: $i,SV62: $i,SV88: $i,SV78: $i,SV43: $i] :
( ( ( ~ ( product @ SV43 @ SV78 @ SV88 ) )
= $true )
| ( ( ~ ( product @ SV62 @ SV78 @ SV96 )
| ( product @ SV18 @ SV88 @ SV96 ) )
= $true )
| ( ( product @ SV18 @ SV43 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(261,plain,
! [SV63: $i,SV97: $i,SV19: $i,SV89: $i,SV79: $i,SV44: $i] :
( ( ( ~ ( product @ SV44 @ SV79 @ SV89 ) )
= $true )
| ( ( ~ ( product @ SV19 @ SV89 @ SV97 )
| ( product @ SV63 @ SV79 @ SV97 ) )
= $true )
| ( ( product @ SV19 @ SV44 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(262,plain,
! [SV102: $i,SV98: $i,SV90: $i,SV80: $i,SV64: $i,SV45: $i,SV20: $i] :
( ( ( product @ SV20 @ SV45 @ SV64 )
= $false )
| ( ( ~ ( product @ SV20 @ SV80 @ SV90 )
| ~ ( sum @ SV45 @ SV80 @ SV98 )
| ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV103: $i,SV99: $i,SV91: $i,SV81: $i,SV65: $i,SV46: $i,SV21: $i] :
( ( ( product @ SV21 @ SV46 @ SV65 )
= $false )
| ( ( ~ ( product @ SV21 @ SV81 @ SV91 )
| ~ ( sum @ SV46 @ SV81 @ SV99 )
| ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(264,plain,
! [SV104: $i,SV100: $i,SV92: $i,SV82: $i,SV66: $i,SV47: $i,SV22: $i] :
( ( ( product @ SV22 @ SV47 @ SV66 )
= $false )
| ( ( ~ ( product @ SV82 @ SV47 @ SV92 )
| ~ ( sum @ SV22 @ SV82 @ SV100 )
| ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(265,plain,
! [SV105: $i,SV101: $i,SV93: $i,SV83: $i,SV67: $i,SV48: $i,SV23: $i] :
( ( ( product @ SV23 @ SV48 @ SV67 )
= $false )
| ( ( ~ ( product @ SV83 @ SV48 @ SV93 )
| ~ ( sum @ SV23 @ SV83 @ SV101 )
| ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(266,plain,
! [SV15: $i,SV94: $i,SV59: $i,SV86: $i,SV76: $i,SV40: $i] :
( ( ( sum @ SV40 @ SV76 @ SV86 )
= $false )
| ( ( ~ ( sum @ SV59 @ SV76 @ SV94 )
| ( sum @ SV15 @ SV86 @ SV94 ) )
= $true )
| ( ( sum @ SV15 @ SV40 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV60: $i,SV95: $i,SV16: $i,SV87: $i,SV77: $i,SV41: $i] :
( ( ( sum @ SV41 @ SV77 @ SV87 )
= $false )
| ( ( ~ ( sum @ SV16 @ SV87 @ SV95 )
| ( sum @ SV60 @ SV77 @ SV95 ) )
= $true )
| ( ( sum @ SV16 @ SV41 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV18: $i,SV96: $i,SV62: $i,SV88: $i,SV78: $i,SV43: $i] :
( ( ( product @ SV43 @ SV78 @ SV88 )
= $false )
| ( ( ~ ( product @ SV62 @ SV78 @ SV96 )
| ( product @ SV18 @ SV88 @ SV96 ) )
= $true )
| ( ( product @ SV18 @ SV43 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(269,plain,
! [SV63: $i,SV97: $i,SV19: $i,SV89: $i,SV79: $i,SV44: $i] :
( ( ( product @ SV44 @ SV79 @ SV89 )
= $false )
| ( ( ~ ( product @ SV19 @ SV89 @ SV97 )
| ( product @ SV63 @ SV79 @ SV97 ) )
= $true )
| ( ( product @ SV19 @ SV44 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(270,plain,
! [SV64: $i,SV102: $i,SV98: $i,SV45: $i,SV90: $i,SV80: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV80 @ SV90 ) )
= $true )
| ( ( ~ ( sum @ SV45 @ SV80 @ SV98 )
| ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true )
| ( ( product @ SV20 @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(271,plain,
! [SV103: $i,SV65: $i,SV99: $i,SV46: $i,SV91: $i,SV81: $i,SV21: $i] :
( ( ( ~ ( product @ SV21 @ SV81 @ SV91 ) )
= $true )
| ( ( ~ ( sum @ SV46 @ SV81 @ SV99 )
| ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true )
| ( ( product @ SV21 @ SV46 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV66: $i,SV104: $i,SV100: $i,SV22: $i,SV92: $i,SV47: $i,SV82: $i] :
( ( ( ~ ( product @ SV82 @ SV47 @ SV92 ) )
= $true )
| ( ( ~ ( sum @ SV22 @ SV82 @ SV100 )
| ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true )
| ( ( product @ SV22 @ SV47 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV105: $i,SV67: $i,SV101: $i,SV23: $i,SV93: $i,SV48: $i,SV83: $i] :
( ( ( ~ ( product @ SV83 @ SV48 @ SV93 ) )
= $true )
| ( ( ~ ( sum @ SV23 @ SV83 @ SV101 )
| ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true )
| ( ( product @ SV23 @ SV48 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV40: $i,SV86: $i,SV15: $i,SV94: $i,SV76: $i,SV59: $i] :
( ( ( ~ ( sum @ SV59 @ SV76 @ SV94 ) )
= $true )
| ( ( sum @ SV15 @ SV86 @ SV94 )
= $true )
| ( ( sum @ SV40 @ SV76 @ SV86 )
= $false )
| ( ( sum @ SV15 @ SV40 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(275,plain,
! [SV41: $i,SV77: $i,SV60: $i,SV95: $i,SV87: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV87 @ SV95 ) )
= $true )
| ( ( sum @ SV60 @ SV77 @ SV95 )
= $true )
| ( ( sum @ SV41 @ SV77 @ SV87 )
= $false )
| ( ( sum @ SV16 @ SV41 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV43: $i,SV88: $i,SV18: $i,SV96: $i,SV78: $i,SV62: $i] :
( ( ( ~ ( product @ SV62 @ SV78 @ SV96 ) )
= $true )
| ( ( product @ SV18 @ SV88 @ SV96 )
= $true )
| ( ( product @ SV43 @ SV78 @ SV88 )
= $false )
| ( ( product @ SV18 @ SV43 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV44: $i,SV79: $i,SV63: $i,SV97: $i,SV89: $i,SV19: $i] :
( ( ( ~ ( product @ SV19 @ SV89 @ SV97 ) )
= $true )
| ( ( product @ SV63 @ SV79 @ SV97 )
= $true )
| ( ( product @ SV44 @ SV79 @ SV89 )
= $false )
| ( ( product @ SV19 @ SV44 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(278,plain,
! [SV64: $i,SV102: $i,SV98: $i,SV45: $i,SV90: $i,SV80: $i,SV20: $i] :
( ( ( product @ SV20 @ SV80 @ SV90 )
= $false )
| ( ( ~ ( sum @ SV45 @ SV80 @ SV98 )
| ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true )
| ( ( product @ SV20 @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(279,plain,
! [SV103: $i,SV65: $i,SV99: $i,SV46: $i,SV91: $i,SV81: $i,SV21: $i] :
( ( ( product @ SV21 @ SV81 @ SV91 )
= $false )
| ( ( ~ ( sum @ SV46 @ SV81 @ SV99 )
| ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true )
| ( ( product @ SV21 @ SV46 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(280,plain,
! [SV66: $i,SV104: $i,SV100: $i,SV22: $i,SV92: $i,SV47: $i,SV82: $i] :
( ( ( product @ SV82 @ SV47 @ SV92 )
= $false )
| ( ( ~ ( sum @ SV22 @ SV82 @ SV100 )
| ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true )
| ( ( product @ SV22 @ SV47 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(281,plain,
! [SV105: $i,SV67: $i,SV101: $i,SV23: $i,SV93: $i,SV48: $i,SV83: $i] :
( ( ( product @ SV83 @ SV48 @ SV93 )
= $false )
| ( ( ~ ( sum @ SV23 @ SV83 @ SV101 )
| ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true )
| ( ( product @ SV23 @ SV48 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(282,plain,
! [SV40: $i,SV86: $i,SV15: $i,SV94: $i,SV76: $i,SV59: $i] :
( ( ( sum @ SV59 @ SV76 @ SV94 )
= $false )
| ( ( sum @ SV15 @ SV86 @ SV94 )
= $true )
| ( ( sum @ SV40 @ SV76 @ SV86 )
= $false )
| ( ( sum @ SV15 @ SV40 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(283,plain,
! [SV41: $i,SV77: $i,SV60: $i,SV95: $i,SV87: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV87 @ SV95 )
= $false )
| ( ( sum @ SV60 @ SV77 @ SV95 )
= $true )
| ( ( sum @ SV41 @ SV77 @ SV87 )
= $false )
| ( ( sum @ SV16 @ SV41 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(284,plain,
! [SV43: $i,SV88: $i,SV18: $i,SV96: $i,SV78: $i,SV62: $i] :
( ( ( product @ SV62 @ SV78 @ SV96 )
= $false )
| ( ( product @ SV18 @ SV88 @ SV96 )
= $true )
| ( ( product @ SV43 @ SV78 @ SV88 )
= $false )
| ( ( product @ SV18 @ SV43 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(285,plain,
! [SV44: $i,SV79: $i,SV63: $i,SV97: $i,SV89: $i,SV19: $i] :
( ( ( product @ SV19 @ SV89 @ SV97 )
= $false )
| ( ( product @ SV63 @ SV79 @ SV97 )
= $true )
| ( ( product @ SV44 @ SV79 @ SV89 )
= $false )
| ( ( product @ SV19 @ SV44 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(286,plain,
! [SV90: $i,SV64: $i,SV102: $i,SV20: $i,SV98: $i,SV80: $i,SV45: $i] :
( ( ( ~ ( sum @ SV45 @ SV80 @ SV98 ) )
= $true )
| ( ( ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true )
| ( ( product @ SV20 @ SV80 @ SV90 )
= $false )
| ( ( product @ SV20 @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(287,plain,
! [SV21: $i,SV103: $i,SV91: $i,SV65: $i,SV99: $i,SV81: $i,SV46: $i] :
( ( ( ~ ( sum @ SV46 @ SV81 @ SV99 ) )
= $true )
| ( ( ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true )
| ( ( product @ SV21 @ SV81 @ SV91 )
= $false )
| ( ( product @ SV21 @ SV46 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(288,plain,
! [SV92: $i,SV66: $i,SV104: $i,SV47: $i,SV100: $i,SV82: $i,SV22: $i] :
( ( ( ~ ( sum @ SV22 @ SV82 @ SV100 ) )
= $true )
| ( ( ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true )
| ( ( product @ SV82 @ SV47 @ SV92 )
= $false )
| ( ( product @ SV22 @ SV47 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(289,plain,
! [SV48: $i,SV105: $i,SV93: $i,SV67: $i,SV101: $i,SV83: $i,SV23: $i] :
( ( ( ~ ( sum @ SV23 @ SV83 @ SV101 ) )
= $true )
| ( ( ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true )
| ( ( product @ SV83 @ SV48 @ SV93 )
= $false )
| ( ( product @ SV23 @ SV48 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(290,plain,
! [SV90: $i,SV64: $i,SV102: $i,SV20: $i,SV98: $i,SV80: $i,SV45: $i] :
( ( ( sum @ SV45 @ SV80 @ SV98 )
= $false )
| ( ( ~ ( product @ SV20 @ SV98 @ SV102 )
| ( sum @ SV64 @ SV90 @ SV102 ) )
= $true )
| ( ( product @ SV20 @ SV80 @ SV90 )
= $false )
| ( ( product @ SV20 @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(291,plain,
! [SV21: $i,SV103: $i,SV91: $i,SV65: $i,SV99: $i,SV81: $i,SV46: $i] :
( ( ( sum @ SV46 @ SV81 @ SV99 )
= $false )
| ( ( ~ ( sum @ SV65 @ SV91 @ SV103 )
| ( product @ SV21 @ SV99 @ SV103 ) )
= $true )
| ( ( product @ SV21 @ SV81 @ SV91 )
= $false )
| ( ( product @ SV21 @ SV46 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV92: $i,SV66: $i,SV104: $i,SV47: $i,SV100: $i,SV82: $i,SV22: $i] :
( ( ( sum @ SV22 @ SV82 @ SV100 )
= $false )
| ( ( ~ ( product @ SV100 @ SV47 @ SV104 )
| ( sum @ SV66 @ SV92 @ SV104 ) )
= $true )
| ( ( product @ SV82 @ SV47 @ SV92 )
= $false )
| ( ( product @ SV22 @ SV47 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(293,plain,
! [SV48: $i,SV105: $i,SV93: $i,SV67: $i,SV101: $i,SV83: $i,SV23: $i] :
( ( ( sum @ SV23 @ SV83 @ SV101 )
= $false )
| ( ( ~ ( sum @ SV67 @ SV93 @ SV105 )
| ( product @ SV101 @ SV48 @ SV105 ) )
= $true )
| ( ( product @ SV83 @ SV48 @ SV93 )
= $false )
| ( ( product @ SV23 @ SV48 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV80: $i,SV45: $i,SV90: $i,SV64: $i,SV102: $i,SV98: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV98 @ SV102 ) )
= $true )
| ( ( sum @ SV64 @ SV90 @ SV102 )
= $true )
| ( ( sum @ SV45 @ SV80 @ SV98 )
= $false )
| ( ( product @ SV20 @ SV80 @ SV90 )
= $false )
| ( ( product @ SV20 @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(295,plain,
! [SV81: $i,SV46: $i,SV99: $i,SV21: $i,SV103: $i,SV91: $i,SV65: $i] :
( ( ( ~ ( sum @ SV65 @ SV91 @ SV103 ) )
= $true )
| ( ( product @ SV21 @ SV99 @ SV103 )
= $true )
| ( ( sum @ SV46 @ SV81 @ SV99 )
= $false )
| ( ( product @ SV21 @ SV81 @ SV91 )
= $false )
| ( ( product @ SV21 @ SV46 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(296,plain,
! [SV82: $i,SV22: $i,SV92: $i,SV66: $i,SV104: $i,SV47: $i,SV100: $i] :
( ( ( ~ ( product @ SV100 @ SV47 @ SV104 ) )
= $true )
| ( ( sum @ SV66 @ SV92 @ SV104 )
= $true )
| ( ( sum @ SV22 @ SV82 @ SV100 )
= $false )
| ( ( product @ SV82 @ SV47 @ SV92 )
= $false )
| ( ( product @ SV22 @ SV47 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(297,plain,
! [SV83: $i,SV23: $i,SV48: $i,SV101: $i,SV105: $i,SV93: $i,SV67: $i] :
( ( ( ~ ( sum @ SV67 @ SV93 @ SV105 ) )
= $true )
| ( ( product @ SV101 @ SV48 @ SV105 )
= $true )
| ( ( sum @ SV23 @ SV83 @ SV101 )
= $false )
| ( ( product @ SV83 @ SV48 @ SV93 )
= $false )
| ( ( product @ SV23 @ SV48 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(298,plain,
! [SV80: $i,SV45: $i,SV90: $i,SV64: $i,SV102: $i,SV98: $i,SV20: $i] :
( ( ( product @ SV20 @ SV98 @ SV102 )
= $false )
| ( ( sum @ SV64 @ SV90 @ SV102 )
= $true )
| ( ( sum @ SV45 @ SV80 @ SV98 )
= $false )
| ( ( product @ SV20 @ SV80 @ SV90 )
= $false )
| ( ( product @ SV20 @ SV45 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(299,plain,
! [SV81: $i,SV46: $i,SV99: $i,SV21: $i,SV103: $i,SV91: $i,SV65: $i] :
( ( ( sum @ SV65 @ SV91 @ SV103 )
= $false )
| ( ( product @ SV21 @ SV99 @ SV103 )
= $true )
| ( ( sum @ SV46 @ SV81 @ SV99 )
= $false )
| ( ( product @ SV21 @ SV81 @ SV91 )
= $false )
| ( ( product @ SV21 @ SV46 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV82: $i,SV22: $i,SV92: $i,SV66: $i,SV104: $i,SV47: $i,SV100: $i] :
( ( ( product @ SV100 @ SV47 @ SV104 )
= $false )
| ( ( sum @ SV66 @ SV92 @ SV104 )
= $true )
| ( ( sum @ SV22 @ SV82 @ SV100 )
= $false )
| ( ( product @ SV82 @ SV47 @ SV92 )
= $false )
| ( ( product @ SV22 @ SV47 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(301,plain,
! [SV83: $i,SV23: $i,SV48: $i,SV101: $i,SV105: $i,SV93: $i,SV67: $i] :
( ( ( sum @ SV67 @ SV93 @ SV105 )
= $false )
| ( ( product @ SV101 @ SV48 @ SV105 )
= $true )
| ( ( sum @ SV23 @ SV83 @ SV101 )
= $false )
| ( ( product @ SV83 @ SV48 @ SV93 )
= $false )
| ( ( product @ SV23 @ SV48 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(302,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,301,300,299,298,285,284,283,282,257,256,247,246,245,244,243,242,201,195,191,171,170,137,136,125,124,123,111,108,97,96]) ).
thf(303,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG038-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.20 % Computer : n008.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Tue Oct 6 14:11:39 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.38
% 0.61/0.38 No.of.Axioms: 30
% 0.61/0.38
% 0.61/0.38 Length.of.Defs: 0
% 0.61/0.38
% 0.61/0.38 Contains.Choice.Funs: false
% 0.61/0.38 ........
% 0.61/0.38
% 0.61/0.38 ********************************
% 0.61/0.38 * All subproblems solved! *
% 0.61/0.38 ********************************
% 0.61/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:30,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:302,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.61/0.38
% 0.61/0.38 %**** Beginning of derivation protocol ****
% 0.61/0.38 % SZS output start CNFRefutation
% See solution above
% 0.61/0.38
% 0.61/0.38 %**** End of derivation protocol ****
% 0.61/0.38 %**** no. of clauses in derivation: 303 ****
% 0.61/0.38 %**** clause counter: 302 ****
% 0.61/0.38
% 0.61/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:30,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:302,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------