%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : RNG038-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 34.25s 6.05s
% Output : CNFRefutation 34.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 22
% Syntax : Number of formulae : 227 ( 128 unt; 0 typ; 0 def)
% Number of atoms : 1553 ( 425 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3240 ( 425 ~; 560 |; 0 &;2255 @)
% ( 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 : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 1088 ( 0 ^;1088 !; 0 ?;1088 :)
% 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_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,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,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
thf(4,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
thf(5,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(6,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(7,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(8,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(9,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(10,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(11,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(12,axiom,
! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(13,axiom,
! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(14,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(15,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(16,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(17,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(18,axiom,
product @ a @ b @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
thf(19,axiom,
! [X: $i,Y: $i] :
( ( X != additive_identity )
| ( product @ X @ ( h @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',some_property) ).
thf(20,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(21,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
thf(23,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_additive_identity) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[21]) ).
thf(25,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(26,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(27,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)],[3]) ).
thf(28,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)],[4]) ).
thf(29,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)],[5]) ).
thf(30,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)],[6]) ).
thf(31,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)],[7]) ).
thf(32,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)],[8]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,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)],[10]) ).
thf(35,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)],[11]) ).
thf(36,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( product @ a @ b @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( X != additive_identity )
| ( product @ X @ ( h @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( b != additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(45,plain,
( ( a != additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,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)],[25]) ).
thf(48,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)],[26]) ).
thf(49,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(50,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(51,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)],[29]) ).
thf(52,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)],[30]) ).
thf(53,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)],[31]) ).
thf(54,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)],[32]) ).
thf(55,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)],[34]) ).
thf(56,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)],[35]) ).
thf(57,plain,
( ( ! [X: $i] :
( ( X != additive_identity )
| ! [Y: $i] : ( product @ X @ ( h @ X @ Y ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(58,plain,
( ( b != additive_identity )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(59,plain,
( ( a != additive_identity )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(60,plain,
( ( a != additive_identity )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(61,plain,
( ( b != additive_identity )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( X != additive_identity )
| ! [Y: $i] : ( product @ X @ ( h @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(63,plain,
( ( product @ a @ b @ additive_identity )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(64,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(65,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(68,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(69,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(70,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)],[56]) ).
thf(71,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)],[55]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(73,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)],[54]) ).
thf(74,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)],[53]) ).
thf(75,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)],[52]) ).
thf(76,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)],[51]) ).
thf(77,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(78,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(81,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[46]) ).
thf(82,plain,
( ( a = additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(83,plain,
( ( b = additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV1: $i] :
( ( ( SV1 != additive_identity )
| ! [SY73: $i] : ( product @ SV1 @ ( h @ SV1 @ SY73 ) @ SY73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV2: $i] :
( ( sum @ additive_identity @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV3: $i] :
( ( sum @ SV3 @ additive_identity @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV4: $i] :
( ( ! [SY74: $i] : ( product @ SV4 @ SY74 @ ( multiply @ SV4 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV5: $i] :
( ( ! [SY75: $i] : ( sum @ SV5 @ SY75 @ ( add @ SV5 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV6: $i] :
( ( sum @ ( additive_inverse @ SV6 ) @ SV6 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV7: $i] :
( ( sum @ SV7 @ ( additive_inverse @ SV7 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV8: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ( sum @ SV8 @ SY76 @ SY77 )
| ! [SY79: $i] :
( ~ ( sum @ SY76 @ SY78 @ SY79 )
| ! [SY80: $i] :
( ~ ( sum @ SY77 @ SY78 @ SY80 )
| ( sum @ SV8 @ SY79 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV9: $i] :
( ( ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ( sum @ SV9 @ SY81 @ SY82 )
| ! [SY84: $i] :
( ~ ( sum @ SY81 @ SY83 @ SY84 )
| ! [SY85: $i] :
( ~ ( sum @ SV9 @ SY84 @ SY85 )
| ( sum @ SY82 @ SY83 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV10: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( sum @ SV10 @ SY86 @ SY87 )
| ( sum @ SY86 @ SV10 @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV11: $i] :
( ( ! [SY88: $i,SY89: $i,SY90: $i] :
( ~ ( product @ SV11 @ SY88 @ SY89 )
| ! [SY91: $i] :
( ~ ( product @ SY88 @ SY90 @ SY91 )
| ! [SY92: $i] :
( ~ ( product @ SY89 @ SY90 @ SY92 )
| ( product @ SV11 @ SY91 @ SY92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV12: $i] :
( ( ! [SY93: $i,SY94: $i,SY95: $i] :
( ~ ( product @ SV12 @ SY93 @ SY94 )
| ! [SY96: $i] :
( ~ ( product @ SY93 @ SY95 @ SY96 )
| ! [SY97: $i] :
( ~ ( product @ SV12 @ SY96 @ SY97 )
| ( product @ SY94 @ SY95 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV13: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i,SY101: $i] :
( ~ ( product @ SV13 @ SY98 @ SY99 )
| ~ ( product @ SV13 @ SY100 @ SY101 )
| ! [SY102: $i] :
( ~ ( sum @ SY98 @ SY100 @ SY102 )
| ! [SY103: $i] :
( ~ ( product @ SV13 @ SY102 @ SY103 )
| ( sum @ SY99 @ SY101 @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV14: $i] :
( ( ! [SY104: $i,SY105: $i,SY106: $i,SY107: $i] :
( ~ ( product @ SV14 @ SY104 @ SY105 )
| ~ ( product @ SV14 @ SY106 @ SY107 )
| ! [SY108: $i] :
( ~ ( sum @ SY104 @ SY106 @ SY108 )
| ! [SY109: $i] :
( ~ ( sum @ SY105 @ SY107 @ SY109 )
| ( product @ SV14 @ SY108 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV15: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i,SY113: $i] :
( ~ ( product @ SV15 @ SY110 @ SY111 )
| ~ ( product @ SY112 @ SY110 @ SY113 )
| ! [SY114: $i] :
( ~ ( sum @ SV15 @ SY112 @ SY114 )
| ! [V4: $i] :
( ~ ( product @ SY114 @ SY110 @ V4 )
| ( sum @ SY111 @ SY113 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV16: $i] :
( ( ! [SY116: $i,SY117: $i,SY118: $i,SY119: $i] :
( ~ ( product @ SV16 @ SY116 @ SY117 )
| ~ ( product @ SY118 @ SY116 @ SY119 )
| ! [SY120: $i] :
( ~ ( sum @ SV16 @ SY118 @ SY120 )
| ! [V4: $i] :
( ~ ( sum @ SY117 @ SY119 @ V4 )
| ( product @ SY120 @ SY116 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV17: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( sum @ SV17 @ SY122 @ SY123 )
| ! [SY124: $i] :
( ~ ( sum @ SV17 @ SY122 @ SY124 )
| ( SY123 = SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV18: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( product @ SV18 @ SY125 @ SY126 )
| ! [SY127: $i] :
( ~ ( product @ SV18 @ SY125 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( SV1 != additive_identity )
= $true )
| ( ( ! [SY73: $i] : ( product @ SV1 @ ( h @ SV1 @ SY73 ) @ SY73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV19: $i,SV4: $i] :
( ( product @ SV4 @ SV19 @ ( multiply @ SV4 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV20: $i,SV5: $i] :
( ( sum @ SV5 @ SV20 @ ( add @ SV5 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( sum @ SV8 @ SV21 @ SY128 )
| ! [SY130: $i] :
( ~ ( sum @ SV21 @ SY129 @ SY130 )
| ! [SY80: $i] :
( ~ ( sum @ SY128 @ SY129 @ SY80 )
| ( sum @ SV8 @ SY130 @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV22: $i,SV9: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ~ ( sum @ SV9 @ SV22 @ SY132 )
| ! [SY134: $i] :
( ~ ( sum @ SV22 @ SY133 @ SY134 )
| ! [SY85: $i] :
( ~ ( sum @ SV9 @ SY134 @ SY85 )
| ( sum @ SY132 @ SY133 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV23: $i,SV10: $i] :
( ( ! [SY136: $i] :
( ~ ( sum @ SV10 @ SV23 @ SY136 )
| ( sum @ SV23 @ SV10 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( product @ SV11 @ SV24 @ SY137 )
| ! [SY139: $i] :
( ~ ( product @ SV24 @ SY138 @ SY139 )
| ! [SY92: $i] :
( ~ ( product @ SY137 @ SY138 @ SY92 )
| ( product @ SV11 @ SY139 @ SY92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ( product @ SV12 @ SV25 @ SY141 )
| ! [SY143: $i] :
( ~ ( product @ SV25 @ SY142 @ SY143 )
| ! [SY97: $i] :
( ~ ( product @ SV12 @ SY143 @ SY97 )
| ( product @ SY141 @ SY142 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ( product @ SV13 @ SV26 @ SY145 )
| ~ ( product @ SV13 @ SY146 @ SY147 )
| ! [SY148: $i] :
( ~ ( sum @ SV26 @ SY146 @ SY148 )
| ! [SY103: $i] :
( ~ ( product @ SV13 @ SY148 @ SY103 )
| ( sum @ SY145 @ SY147 @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i] :
( ~ ( product @ SV14 @ SV27 @ SY150 )
| ~ ( product @ SV14 @ SY151 @ SY152 )
| ! [SY153: $i] :
( ~ ( sum @ SV27 @ SY151 @ SY153 )
| ! [SY109: $i] :
( ~ ( sum @ SY150 @ SY152 @ SY109 )
| ( product @ SV14 @ SY153 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV28: $i,SV15: $i] :
( ( ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ( product @ SV15 @ SV28 @ SY155 )
| ~ ( product @ SY156 @ SV28 @ SY157 )
| ! [SY158: $i] :
( ~ ( sum @ SV15 @ SY156 @ SY158 )
| ! [SY159: $i] :
( ~ ( product @ SY158 @ SV28 @ SY159 )
| ( sum @ SY155 @ SY157 @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV29: $i,SV16: $i] :
( ( ! [SY160: $i,SY161: $i,SY162: $i] :
( ~ ( product @ SV16 @ SV29 @ SY160 )
| ~ ( product @ SY161 @ SV29 @ SY162 )
| ! [SY163: $i] :
( ~ ( sum @ SV16 @ SY161 @ SY163 )
| ! [SY164: $i] :
( ~ ( sum @ SY160 @ SY162 @ SY164 )
| ( product @ SY163 @ SV29 @ SY164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV30: $i,SV17: $i] :
( ( ! [SY165: $i] :
( ~ ( sum @ SV17 @ SV30 @ SY165 )
| ! [SY166: $i] :
( ~ ( sum @ SV17 @ SV30 @ SY166 )
| ( SY165 = SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV31: $i,SV18: $i] :
( ( ! [SY167: $i] :
( ~ ( product @ SV18 @ SV31 @ SY167 )
| ! [SY168: $i] :
( ~ ( product @ SV18 @ SV31 @ SY168 )
| ( SY167 = SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV1: $i] :
( ( ( SV1 = additive_identity )
= $false )
| ( ( ! [SY73: $i] : ( product @ SV1 @ ( h @ SV1 @ SY73 ) @ SY73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV32: $i,SV21: $i,SV8: $i] :
( ( ! [SY169: $i] :
( ~ ( sum @ SV8 @ SV21 @ SV32 )
| ! [SY170: $i] :
( ~ ( sum @ SV21 @ SY169 @ SY170 )
| ! [SY171: $i] :
( ~ ( sum @ SV32 @ SY169 @ SY171 )
| ( sum @ SV8 @ SY170 @ SY171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV33: $i,SV22: $i,SV9: $i] :
( ( ! [SY172: $i] :
( ~ ( sum @ SV9 @ SV22 @ SV33 )
| ! [SY173: $i] :
( ~ ( sum @ SV22 @ SY172 @ SY173 )
| ! [SY174: $i] :
( ~ ( sum @ SV9 @ SY173 @ SY174 )
| ( sum @ SV33 @ SY172 @ SY174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV34: $i,SV23: $i,SV10: $i] :
( ( ~ ( sum @ SV10 @ SV23 @ SV34 )
| ( sum @ SV23 @ SV10 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV35: $i,SV24: $i,SV11: $i] :
( ( ! [SY175: $i] :
( ~ ( product @ SV11 @ SV24 @ SV35 )
| ! [SY176: $i] :
( ~ ( product @ SV24 @ SY175 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV35 @ SY175 @ SY177 )
| ( product @ SV11 @ SY176 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV36: $i,SV25: $i,SV12: $i] :
( ( ! [SY178: $i] :
( ~ ( product @ SV12 @ SV25 @ SV36 )
| ! [SY179: $i] :
( ~ ( product @ SV25 @ SY178 @ SY179 )
| ! [SY180: $i] :
( ~ ( product @ SV12 @ SY179 @ SY180 )
| ( product @ SV36 @ SY178 @ SY180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV37: $i,SV26: $i,SV13: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( product @ SV13 @ SV26 @ SV37 )
| ~ ( product @ SV13 @ SY181 @ SY182 )
| ! [SY183: $i] :
( ~ ( sum @ SV26 @ SY181 @ SY183 )
| ! [SY184: $i] :
( ~ ( product @ SV13 @ SY183 @ SY184 )
| ( sum @ SV37 @ SY182 @ SY184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV38: $i,SV27: $i,SV14: $i] :
( ( ! [SY185: $i,SY186: $i] :
( ~ ( product @ SV14 @ SV27 @ SV38 )
| ~ ( product @ SV14 @ SY185 @ SY186 )
| ! [SY187: $i] :
( ~ ( sum @ SV27 @ SY185 @ SY187 )
| ! [SY188: $i] :
( ~ ( sum @ SV38 @ SY186 @ SY188 )
| ( product @ SV14 @ SY187 @ SY188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV39: $i,SV28: $i,SV15: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ~ ( product @ SV15 @ SV28 @ SV39 )
| ~ ( product @ SY189 @ SV28 @ SY190 )
| ! [SY191: $i] :
( ~ ( sum @ SV15 @ SY189 @ SY191 )
| ! [SY192: $i] :
( ~ ( product @ SY191 @ SV28 @ SY192 )
| ( sum @ SV39 @ SY190 @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( product @ SV16 @ SV29 @ SV40 )
| ~ ( product @ SY193 @ SV29 @ SY194 )
| ! [SY195: $i] :
( ~ ( sum @ SV16 @ SY193 @ SY195 )
| ! [SY196: $i] :
( ~ ( sum @ SV40 @ SY194 @ SY196 )
| ( product @ SY195 @ SV29 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV41: $i,SV30: $i,SV17: $i] :
( ( ~ ( sum @ SV17 @ SV30 @ SV41 )
| ! [SY197: $i] :
( ~ ( sum @ SV17 @ SV30 @ SY197 )
| ( SV41 = SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV42: $i,SV31: $i,SV18: $i] :
( ( ~ ( product @ SV18 @ SV31 @ SV42 )
| ! [SY198: $i] :
( ~ ( product @ SV18 @ SV31 @ SY198 )
| ( SV42 = SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV43: $i,SV1: $i] :
( ( ( product @ SV1 @ ( h @ SV1 @ SV43 ) @ SV43 )
= $true )
| ( ( SV1 = additive_identity )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV44: $i,SV32: $i,SV21: $i,SV8: $i] :
( ( ~ ( sum @ SV8 @ SV21 @ SV32 )
| ! [SY199: $i] :
( ~ ( sum @ SV21 @ SV44 @ SY199 )
| ! [SY200: $i] :
( ~ ( sum @ SV32 @ SV44 @ SY200 )
| ( sum @ SV8 @ SY199 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV45: $i,SV33: $i,SV22: $i,SV9: $i] :
( ( ~ ( sum @ SV9 @ SV22 @ SV33 )
| ! [SY201: $i] :
( ~ ( sum @ SV22 @ SV45 @ SY201 )
| ! [SY202: $i] :
( ~ ( sum @ SV9 @ SY201 @ SY202 )
| ( sum @ SV33 @ SV45 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV34: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( sum @ SV10 @ SV23 @ SV34 ) )
= $true )
| ( ( sum @ SV23 @ SV10 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV46: $i,SV35: $i,SV24: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV24 @ SV35 )
| ! [SY203: $i] :
( ~ ( product @ SV24 @ SV46 @ SY203 )
| ! [SY204: $i] :
( ~ ( product @ SV35 @ SV46 @ SY204 )
| ( product @ SV11 @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV47: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV25 @ SV36 )
| ! [SY205: $i] :
( ~ ( product @ SV25 @ SV47 @ SY205 )
| ! [SY206: $i] :
( ~ ( product @ SV12 @ SY205 @ SY206 )
| ( product @ SV36 @ SV47 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV48: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ! [SY207: $i] :
( ~ ( product @ SV13 @ SV26 @ SV37 )
| ~ ( product @ SV13 @ SV48 @ SY207 )
| ! [SY208: $i] :
( ~ ( sum @ SV26 @ SV48 @ SY208 )
| ! [SY184: $i] :
( ~ ( product @ SV13 @ SY208 @ SY184 )
| ( sum @ SV37 @ SY207 @ SY184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV49: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ! [SY210: $i] :
( ~ ( product @ SV14 @ SV27 @ SV38 )
| ~ ( product @ SV14 @ SV49 @ SY210 )
| ! [SY211: $i] :
( ~ ( sum @ SV27 @ SV49 @ SY211 )
| ! [SY188: $i] :
( ~ ( sum @ SV38 @ SY210 @ SY188 )
| ( product @ SV14 @ SY211 @ SY188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV50: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ! [SY213: $i] :
( ~ ( product @ SV15 @ SV28 @ SV39 )
| ~ ( product @ SV50 @ SV28 @ SY213 )
| ! [SY214: $i] :
( ~ ( sum @ SV15 @ SV50 @ SY214 )
| ! [SY192: $i] :
( ~ ( product @ SY214 @ SV28 @ SY192 )
| ( sum @ SV39 @ SY213 @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV51: $i,SV40: $i,SV29: $i,SV16: $i] :
( ( ! [SY216: $i] :
( ~ ( product @ SV16 @ SV29 @ SV40 )
| ~ ( product @ SV51 @ SV29 @ SY216 )
| ! [SY217: $i] :
( ~ ( sum @ SV16 @ SV51 @ SY217 )
| ! [SY196: $i] :
( ~ ( sum @ SV40 @ SY216 @ SY196 )
| ( product @ SY217 @ SV29 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV41: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( sum @ SV17 @ SV30 @ SV41 ) )
= $true )
| ( ( ! [SY197: $i] :
( ~ ( sum @ SV17 @ SV30 @ SY197 )
| ( SV41 = SY197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV42: $i,SV31: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV31 @ SV42 ) )
= $true )
| ( ( ! [SY198: $i] :
( ~ ( product @ SV18 @ SV31 @ SY198 )
| ( SV42 = SY198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV44: $i,SV32: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV21 @ SV32 ) )
= $true )
| ( ( ! [SY199: $i] :
( ~ ( sum @ SV21 @ SV44 @ SY199 )
| ! [SY200: $i] :
( ~ ( sum @ SV32 @ SV44 @ SY200 )
| ( sum @ SV8 @ SY199 @ SY200 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV45: $i,SV33: $i,SV22: $i,SV9: $i] :
( ( ( ~ ( sum @ SV9 @ SV22 @ SV33 ) )
= $true )
| ( ( ! [SY201: $i] :
( ~ ( sum @ SV22 @ SV45 @ SY201 )
| ! [SY202: $i] :
( ~ ( sum @ SV9 @ SY201 @ SY202 )
| ( sum @ SV33 @ SV45 @ SY202 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV34: $i,SV23: $i,SV10: $i] :
( ( ( sum @ SV10 @ SV23 @ SV34 )
= $false )
| ( ( sum @ SV23 @ SV10 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV46: $i,SV35: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV24 @ SV35 ) )
= $true )
| ( ( ! [SY203: $i] :
( ~ ( product @ SV24 @ SV46 @ SY203 )
| ! [SY204: $i] :
( ~ ( product @ SV35 @ SV46 @ SY204 )
| ( product @ SV11 @ SY203 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV47: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV25 @ SV36 ) )
= $true )
| ( ( ! [SY205: $i] :
( ~ ( product @ SV25 @ SV47 @ SY205 )
| ! [SY206: $i] :
( ~ ( product @ SV12 @ SY205 @ SY206 )
| ( product @ SV36 @ SV47 @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV52: $i,SV48: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ~ ( product @ SV13 @ SV26 @ SV37 )
| ~ ( product @ SV13 @ SV48 @ SV52 )
| ! [SY219: $i] :
( ~ ( sum @ SV26 @ SV48 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV13 @ SY219 @ SY220 )
| ( sum @ SV37 @ SV52 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(147,plain,
! [SV53: $i,SV49: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ~ ( product @ SV14 @ SV27 @ SV38 )
| ~ ( product @ SV14 @ SV49 @ SV53 )
| ! [SY221: $i] :
( ~ ( sum @ SV27 @ SV49 @ SY221 )
| ! [SY222: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY222 )
| ( product @ SV14 @ SY221 @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV54: $i,SV50: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ~ ( product @ SV15 @ SV28 @ SV39 )
| ~ ( product @ SV50 @ SV28 @ SV54 )
| ! [SY223: $i] :
( ~ ( sum @ SV15 @ SV50 @ SY223 )
| ! [SY224: $i] :
( ~ ( product @ SY223 @ SV28 @ SY224 )
| ( sum @ SV39 @ SV54 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(149,plain,
! [SV55: $i,SV51: $i,SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ( product @ SV16 @ SV29 @ SV40 )
| ~ ( product @ SV51 @ SV29 @ SV55 )
| ! [SY225: $i] :
( ~ ( sum @ SV16 @ SV51 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY226 )
| ( product @ SY225 @ SV29 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV41: $i,SV30: $i,SV17: $i] :
( ( ( sum @ SV17 @ SV30 @ SV41 )
= $false )
| ( ( ! [SY197: $i] :
( ~ ( sum @ SV17 @ SV30 @ SY197 )
| ( SV41 = SY197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV42: $i,SV31: $i,SV18: $i] :
( ( ( product @ SV18 @ SV31 @ SV42 )
= $false )
| ( ( ! [SY198: $i] :
( ~ ( product @ SV18 @ SV31 @ SY198 )
| ( SV42 = SY198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV44: $i,SV32: $i,SV21: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV21 @ SV32 )
= $false )
| ( ( ! [SY199: $i] :
( ~ ( sum @ SV21 @ SV44 @ SY199 )
| ! [SY200: $i] :
( ~ ( sum @ SV32 @ SV44 @ SY200 )
| ( sum @ SV8 @ SY199 @ SY200 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV45: $i,SV33: $i,SV22: $i,SV9: $i] :
( ( ( sum @ SV9 @ SV22 @ SV33 )
= $false )
| ( ( ! [SY201: $i] :
( ~ ( sum @ SV22 @ SV45 @ SY201 )
| ! [SY202: $i] :
( ~ ( sum @ SV9 @ SY201 @ SY202 )
| ( sum @ SV33 @ SV45 @ SY202 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV46: $i,SV35: $i,SV24: $i,SV11: $i] :
( ( ( product @ SV11 @ SV24 @ SV35 )
= $false )
| ( ( ! [SY203: $i] :
( ~ ( product @ SV24 @ SV46 @ SY203 )
| ! [SY204: $i] :
( ~ ( product @ SV35 @ SV46 @ SY204 )
| ( product @ SV11 @ SY203 @ SY204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV47: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ( product @ SV12 @ SV25 @ SV36 )
= $false )
| ( ( ! [SY205: $i] :
( ~ ( product @ SV25 @ SV47 @ SY205 )
| ! [SY206: $i] :
( ~ ( product @ SV12 @ SY205 @ SY206 )
| ( product @ SV36 @ SV47 @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV52: $i,SV48: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV26 @ SV37 ) )
= $true )
| ( ( ~ ( product @ SV13 @ SV48 @ SV52 )
| ! [SY219: $i] :
( ~ ( sum @ SV26 @ SV48 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV13 @ SY219 @ SY220 )
| ( sum @ SV37 @ SV52 @ SY220 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV53: $i,SV49: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV27 @ SV38 ) )
= $true )
| ( ( ~ ( product @ SV14 @ SV49 @ SV53 )
| ! [SY221: $i] :
( ~ ( sum @ SV27 @ SV49 @ SY221 )
| ! [SY222: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY222 )
| ( product @ SV14 @ SY221 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV54: $i,SV50: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV28 @ SV39 ) )
= $true )
| ( ( ~ ( product @ SV50 @ SV28 @ SV54 )
| ! [SY223: $i] :
( ~ ( sum @ SV15 @ SV50 @ SY223 )
| ! [SY224: $i] :
( ~ ( product @ SY223 @ SV28 @ SY224 )
| ( sum @ SV39 @ SV54 @ SY224 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV55: $i,SV51: $i,SV40: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV29 @ SV40 ) )
= $true )
| ( ( ~ ( product @ SV51 @ SV29 @ SV55 )
| ! [SY225: $i] :
( ~ ( sum @ SV16 @ SV51 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY226 )
| ( product @ SY225 @ SV29 @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV41: $i,SV56: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( sum @ SV17 @ SV30 @ SV56 )
| ( SV41 = SV56 ) )
= $true )
| ( ( sum @ SV17 @ SV30 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV42: $i,SV57: $i,SV31: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV31 @ SV57 )
| ( SV42 = SV57 ) )
= $true )
| ( ( product @ SV18 @ SV31 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV8: $i,SV32: $i,SV58: $i,SV44: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV44 @ SV58 )
| ! [SY227: $i] :
( ~ ( sum @ SV32 @ SV44 @ SY227 )
| ( sum @ SV8 @ SV58 @ SY227 ) ) )
= $true )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV33: $i,SV9: $i,SV59: $i,SV45: $i,SV22: $i] :
( ( ( ~ ( sum @ SV22 @ SV45 @ SV59 )
| ! [SY228: $i] :
( ~ ( sum @ SV9 @ SV59 @ SY228 )
| ( sum @ SV33 @ SV45 @ SY228 ) ) )
= $true )
| ( ( sum @ SV9 @ SV22 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV11: $i,SV35: $i,SV60: $i,SV46: $i,SV24: $i] :
( ( ( ~ ( product @ SV24 @ SV46 @ SV60 )
| ! [SY229: $i] :
( ~ ( product @ SV35 @ SV46 @ SY229 )
| ( product @ SV11 @ SV60 @ SY229 ) ) )
= $true )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV36: $i,SV12: $i,SV61: $i,SV47: $i,SV25: $i] :
( ( ( ~ ( product @ SV25 @ SV47 @ SV61 )
| ! [SY230: $i] :
( ~ ( product @ SV12 @ SV61 @ SY230 )
| ( product @ SV36 @ SV47 @ SY230 ) ) )
= $true )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV52: $i,SV48: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ( product @ SV13 @ SV26 @ SV37 )
= $false )
| ( ( ~ ( product @ SV13 @ SV48 @ SV52 )
| ! [SY219: $i] :
( ~ ( sum @ SV26 @ SV48 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV13 @ SY219 @ SY220 )
| ( sum @ SV37 @ SV52 @ SY220 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV53: $i,SV49: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ( product @ SV14 @ SV27 @ SV38 )
= $false )
| ( ( ~ ( product @ SV14 @ SV49 @ SV53 )
| ! [SY221: $i] :
( ~ ( sum @ SV27 @ SV49 @ SY221 )
| ! [SY222: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY222 )
| ( product @ SV14 @ SY221 @ SY222 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV54: $i,SV50: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ( product @ SV15 @ SV28 @ SV39 )
= $false )
| ( ( ~ ( product @ SV50 @ SV28 @ SV54 )
| ! [SY223: $i] :
( ~ ( sum @ SV15 @ SV50 @ SY223 )
| ! [SY224: $i] :
( ~ ( product @ SY223 @ SV28 @ SY224 )
| ( sum @ SV39 @ SV54 @ SY224 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV55: $i,SV51: $i,SV40: $i,SV29: $i,SV16: $i] :
( ( ( product @ SV16 @ SV29 @ SV40 )
= $false )
| ( ( ~ ( product @ SV51 @ SV29 @ SV55 )
| ! [SY225: $i] :
( ~ ( sum @ SV16 @ SV51 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY226 )
| ( product @ SY225 @ SV29 @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV41: $i,SV56: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( sum @ SV17 @ SV30 @ SV56 ) )
= $true )
| ( ( SV41 = SV56 )
= $true )
| ( ( sum @ SV17 @ SV30 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV42: $i,SV57: $i,SV31: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV31 @ SV57 ) )
= $true )
| ( ( SV42 = SV57 )
= $true )
| ( ( product @ SV18 @ SV31 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV8: $i,SV32: $i,SV58: $i,SV44: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV44 @ SV58 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( sum @ SV32 @ SV44 @ SY227 )
| ( sum @ SV8 @ SV58 @ SY227 ) ) )
= $true )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV33: $i,SV9: $i,SV59: $i,SV45: $i,SV22: $i] :
( ( ( ~ ( sum @ SV22 @ SV45 @ SV59 ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( sum @ SV9 @ SV59 @ SY228 )
| ( sum @ SV33 @ SV45 @ SY228 ) ) )
= $true )
| ( ( sum @ SV9 @ SV22 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV11: $i,SV35: $i,SV60: $i,SV46: $i,SV24: $i] :
( ( ( ~ ( product @ SV24 @ SV46 @ SV60 ) )
= $true )
| ( ( ! [SY229: $i] :
( ~ ( product @ SV35 @ SV46 @ SY229 )
| ( product @ SV11 @ SV60 @ SY229 ) ) )
= $true )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV36: $i,SV12: $i,SV61: $i,SV47: $i,SV25: $i] :
( ( ( ~ ( product @ SV25 @ SV47 @ SV61 ) )
= $true )
| ( ( ! [SY230: $i] :
( ~ ( product @ SV12 @ SV61 @ SY230 )
| ( product @ SV36 @ SV47 @ SY230 ) ) )
= $true )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV37: $i,SV26: $i,SV52: $i,SV48: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV48 @ SV52 ) )
= $true )
| ( ( ! [SY219: $i] :
( ~ ( sum @ SV26 @ SV48 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV13 @ SY219 @ SY220 )
| ( sum @ SV37 @ SV52 @ SY220 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV38: $i,SV27: $i,SV53: $i,SV49: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV49 @ SV53 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( sum @ SV27 @ SV49 @ SY221 )
| ! [SY222: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY222 )
| ( product @ SV14 @ SY221 @ SY222 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV39: $i,SV15: $i,SV54: $i,SV28: $i,SV50: $i] :
( ( ( ~ ( product @ SV50 @ SV28 @ SV54 ) )
= $true )
| ( ( ! [SY223: $i] :
( ~ ( sum @ SV15 @ SV50 @ SY223 )
| ! [SY224: $i] :
( ~ ( product @ SY223 @ SV28 @ SY224 )
| ( sum @ SV39 @ SV54 @ SY224 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV40: $i,SV16: $i,SV55: $i,SV29: $i,SV51: $i] :
( ( ( ~ ( product @ SV51 @ SV29 @ SV55 ) )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( sum @ SV16 @ SV51 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY226 )
| ( product @ SY225 @ SV29 @ SY226 ) ) ) )
= $true )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV41: $i,SV56: $i,SV30: $i,SV17: $i] :
( ( ( sum @ SV17 @ SV30 @ SV56 )
= $false )
| ( ( SV41 = SV56 )
= $true )
| ( ( sum @ SV17 @ SV30 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV42: $i,SV57: $i,SV31: $i,SV18: $i] :
( ( ( product @ SV18 @ SV31 @ SV57 )
= $false )
| ( ( SV42 = SV57 )
= $true )
| ( ( product @ SV18 @ SV31 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV8: $i,SV32: $i,SV58: $i,SV44: $i,SV21: $i] :
( ( ( sum @ SV21 @ SV44 @ SV58 )
= $false )
| ( ( ! [SY227: $i] :
( ~ ( sum @ SV32 @ SV44 @ SY227 )
| ( sum @ SV8 @ SV58 @ SY227 ) ) )
= $true )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV33: $i,SV9: $i,SV59: $i,SV45: $i,SV22: $i] :
( ( ( sum @ SV22 @ SV45 @ SV59 )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( sum @ SV9 @ SV59 @ SY228 )
| ( sum @ SV33 @ SV45 @ SY228 ) ) )
= $true )
| ( ( sum @ SV9 @ SV22 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV11: $i,SV35: $i,SV60: $i,SV46: $i,SV24: $i] :
( ( ( product @ SV24 @ SV46 @ SV60 )
= $false )
| ( ( ! [SY229: $i] :
( ~ ( product @ SV35 @ SV46 @ SY229 )
| ( product @ SV11 @ SV60 @ SY229 ) ) )
= $true )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV36: $i,SV12: $i,SV61: $i,SV47: $i,SV25: $i] :
( ( ( product @ SV25 @ SV47 @ SV61 )
= $false )
| ( ( ! [SY230: $i] :
( ~ ( product @ SV12 @ SV61 @ SY230 )
| ( product @ SV36 @ SV47 @ SY230 ) ) )
= $true )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV37: $i,SV26: $i,SV52: $i,SV48: $i,SV13: $i] :
( ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( ! [SY219: $i] :
( ~ ( sum @ SV26 @ SV48 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV13 @ SY219 @ SY220 )
| ( sum @ SV37 @ SV52 @ SY220 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV38: $i,SV27: $i,SV53: $i,SV49: $i,SV14: $i] :
( ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( sum @ SV27 @ SV49 @ SY221 )
| ! [SY222: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY222 )
| ( product @ SV14 @ SY221 @ SY222 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV39: $i,SV15: $i,SV54: $i,SV28: $i,SV50: $i] :
( ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( ! [SY223: $i] :
( ~ ( sum @ SV15 @ SV50 @ SY223 )
| ! [SY224: $i] :
( ~ ( product @ SY223 @ SV28 @ SY224 )
| ( sum @ SV39 @ SV54 @ SY224 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV40: $i,SV16: $i,SV55: $i,SV29: $i,SV51: $i] :
( ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( ! [SY225: $i] :
( ~ ( sum @ SV16 @ SV51 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY226 )
| ( product @ SY225 @ SV29 @ SY226 ) ) ) )
= $true )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(190,plain,
! [SV21: $i,SV58: $i,SV8: $i,SV62: $i,SV44: $i,SV32: $i] :
( ( ( ~ ( sum @ SV32 @ SV44 @ SV62 )
| ( sum @ SV8 @ SV58 @ SV62 ) )
= $true )
| ( ( sum @ SV21 @ SV44 @ SV58 )
= $false )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV22: $i,SV45: $i,SV33: $i,SV63: $i,SV59: $i,SV9: $i] :
( ( ( ~ ( sum @ SV9 @ SV59 @ SV63 )
| ( sum @ SV33 @ SV45 @ SV63 ) )
= $true )
| ( ( sum @ SV22 @ SV45 @ SV59 )
= $false )
| ( ( sum @ SV9 @ SV22 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV24: $i,SV60: $i,SV11: $i,SV64: $i,SV46: $i,SV35: $i] :
( ( ( ~ ( product @ SV35 @ SV46 @ SV64 )
| ( product @ SV11 @ SV60 @ SV64 ) )
= $true )
| ( ( product @ SV24 @ SV46 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV25: $i,SV47: $i,SV36: $i,SV65: $i,SV61: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV61 @ SV65 )
| ( product @ SV36 @ SV47 @ SV65 ) )
= $true )
| ( ( product @ SV25 @ SV47 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV52: $i,SV37: $i,SV13: $i,SV66: $i,SV48: $i,SV26: $i] :
( ( ( ~ ( sum @ SV26 @ SV48 @ SV66 )
| ! [SY231: $i] :
( ~ ( product @ SV13 @ SV66 @ SY231 )
| ( sum @ SV37 @ SV52 @ SY231 ) ) )
= $true )
| ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV14: $i,SV53: $i,SV38: $i,SV67: $i,SV49: $i,SV27: $i] :
( ( ( ~ ( sum @ SV27 @ SV49 @ SV67 )
| ! [SY232: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY232 )
| ( product @ SV14 @ SV67 @ SY232 ) ) )
= $true )
| ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV54: $i,SV39: $i,SV28: $i,SV68: $i,SV50: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV50 @ SV68 )
| ! [SY233: $i] :
( ~ ( product @ SV68 @ SV28 @ SY233 )
| ( sum @ SV39 @ SV54 @ SY233 ) ) )
= $true )
| ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV29: $i,SV55: $i,SV40: $i,SV69: $i,SV51: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV51 @ SV69 )
| ! [SY234: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY234 )
| ( product @ SV69 @ SV29 @ SY234 ) ) )
= $true )
| ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV21: $i,SV58: $i,SV8: $i,SV62: $i,SV44: $i,SV32: $i] :
( ( ( ~ ( sum @ SV32 @ SV44 @ SV62 ) )
= $true )
| ( ( sum @ SV8 @ SV58 @ SV62 )
= $true )
| ( ( sum @ SV21 @ SV44 @ SV58 )
= $false )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV22: $i,SV45: $i,SV33: $i,SV63: $i,SV59: $i,SV9: $i] :
( ( ( ~ ( sum @ SV9 @ SV59 @ SV63 ) )
= $true )
| ( ( sum @ SV33 @ SV45 @ SV63 )
= $true )
| ( ( sum @ SV22 @ SV45 @ SV59 )
= $false )
| ( ( sum @ SV9 @ SV22 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV24: $i,SV60: $i,SV11: $i,SV64: $i,SV46: $i,SV35: $i] :
( ( ( ~ ( product @ SV35 @ SV46 @ SV64 ) )
= $true )
| ( ( product @ SV11 @ SV60 @ SV64 )
= $true )
| ( ( product @ SV24 @ SV46 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV25: $i,SV47: $i,SV36: $i,SV65: $i,SV61: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV61 @ SV65 ) )
= $true )
| ( ( product @ SV36 @ SV47 @ SV65 )
= $true )
| ( ( product @ SV25 @ SV47 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV52: $i,SV37: $i,SV13: $i,SV66: $i,SV48: $i,SV26: $i] :
( ( ( ~ ( sum @ SV26 @ SV48 @ SV66 ) )
= $true )
| ( ( ! [SY231: $i] :
( ~ ( product @ SV13 @ SV66 @ SY231 )
| ( sum @ SV37 @ SV52 @ SY231 ) ) )
= $true )
| ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV14: $i,SV53: $i,SV38: $i,SV67: $i,SV49: $i,SV27: $i] :
( ( ( ~ ( sum @ SV27 @ SV49 @ SV67 ) )
= $true )
| ( ( ! [SY232: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY232 )
| ( product @ SV14 @ SV67 @ SY232 ) ) )
= $true )
| ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV54: $i,SV39: $i,SV28: $i,SV68: $i,SV50: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV50 @ SV68 ) )
= $true )
| ( ( ! [SY233: $i] :
( ~ ( product @ SV68 @ SV28 @ SY233 )
| ( sum @ SV39 @ SV54 @ SY233 ) ) )
= $true )
| ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV29: $i,SV55: $i,SV40: $i,SV69: $i,SV51: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV51 @ SV69 ) )
= $true )
| ( ( ! [SY234: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY234 )
| ( product @ SV69 @ SV29 @ SY234 ) ) )
= $true )
| ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV21: $i,SV58: $i,SV8: $i,SV62: $i,SV44: $i,SV32: $i] :
( ( ( sum @ SV32 @ SV44 @ SV62 )
= $false )
| ( ( sum @ SV8 @ SV58 @ SV62 )
= $true )
| ( ( sum @ SV21 @ SV44 @ SV58 )
= $false )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(207,plain,
! [SV22: $i,SV45: $i,SV33: $i,SV63: $i,SV59: $i,SV9: $i] :
( ( ( sum @ SV9 @ SV59 @ SV63 )
= $false )
| ( ( sum @ SV33 @ SV45 @ SV63 )
= $true )
| ( ( sum @ SV22 @ SV45 @ SV59 )
= $false )
| ( ( sum @ SV9 @ SV22 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(208,plain,
! [SV24: $i,SV60: $i,SV11: $i,SV64: $i,SV46: $i,SV35: $i] :
( ( ( product @ SV35 @ SV46 @ SV64 )
= $false )
| ( ( product @ SV11 @ SV60 @ SV64 )
= $true )
| ( ( product @ SV24 @ SV46 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
! [SV25: $i,SV47: $i,SV36: $i,SV65: $i,SV61: $i,SV12: $i] :
( ( ( product @ SV12 @ SV61 @ SV65 )
= $false )
| ( ( product @ SV36 @ SV47 @ SV65 )
= $true )
| ( ( product @ SV25 @ SV47 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV52: $i,SV37: $i,SV13: $i,SV66: $i,SV48: $i,SV26: $i] :
( ( ( sum @ SV26 @ SV48 @ SV66 )
= $false )
| ( ( ! [SY231: $i] :
( ~ ( product @ SV13 @ SV66 @ SY231 )
| ( sum @ SV37 @ SV52 @ SY231 ) ) )
= $true )
| ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV14: $i,SV53: $i,SV38: $i,SV67: $i,SV49: $i,SV27: $i] :
( ( ( sum @ SV27 @ SV49 @ SV67 )
= $false )
| ( ( ! [SY232: $i] :
( ~ ( sum @ SV38 @ SV53 @ SY232 )
| ( product @ SV14 @ SV67 @ SY232 ) ) )
= $true )
| ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV54: $i,SV39: $i,SV28: $i,SV68: $i,SV50: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV50 @ SV68 )
= $false )
| ( ( ! [SY233: $i] :
( ~ ( product @ SV68 @ SV28 @ SY233 )
| ( sum @ SV39 @ SV54 @ SY233 ) ) )
= $true )
| ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV29: $i,SV55: $i,SV40: $i,SV69: $i,SV51: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV51 @ SV69 )
= $false )
| ( ( ! [SY234: $i] :
( ~ ( sum @ SV40 @ SV55 @ SY234 )
| ( product @ SV69 @ SV29 @ SY234 ) ) )
= $true )
| ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(214,plain,
! [SV48: $i,SV26: $i,SV52: $i,SV37: $i,SV70: $i,SV66: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV66 @ SV70 )
| ( sum @ SV37 @ SV52 @ SV70 ) )
= $true )
| ( ( sum @ SV26 @ SV48 @ SV66 )
= $false )
| ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV49: $i,SV27: $i,SV67: $i,SV14: $i,SV71: $i,SV53: $i,SV38: $i] :
( ( ( ~ ( sum @ SV38 @ SV53 @ SV71 )
| ( product @ SV14 @ SV67 @ SV71 ) )
= $true )
| ( ( sum @ SV27 @ SV49 @ SV67 )
= $false )
| ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(216,plain,
! [SV50: $i,SV15: $i,SV54: $i,SV39: $i,SV72: $i,SV28: $i,SV68: $i] :
( ( ( ~ ( product @ SV68 @ SV28 @ SV72 )
| ( sum @ SV39 @ SV54 @ SV72 ) )
= $true )
| ( ( sum @ SV15 @ SV50 @ SV68 )
= $false )
| ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(217,plain,
! [SV51: $i,SV16: $i,SV29: $i,SV69: $i,SV73: $i,SV55: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV55 @ SV73 )
| ( product @ SV69 @ SV29 @ SV73 ) )
= $true )
| ( ( sum @ SV16 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV48: $i,SV26: $i,SV52: $i,SV37: $i,SV70: $i,SV66: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV66 @ SV70 ) )
= $true )
| ( ( sum @ SV37 @ SV52 @ SV70 )
= $true )
| ( ( sum @ SV26 @ SV48 @ SV66 )
= $false )
| ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV49: $i,SV27: $i,SV67: $i,SV14: $i,SV71: $i,SV53: $i,SV38: $i] :
( ( ( ~ ( sum @ SV38 @ SV53 @ SV71 ) )
= $true )
| ( ( product @ SV14 @ SV67 @ SV71 )
= $true )
| ( ( sum @ SV27 @ SV49 @ SV67 )
= $false )
| ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV50: $i,SV15: $i,SV54: $i,SV39: $i,SV72: $i,SV28: $i,SV68: $i] :
( ( ( ~ ( product @ SV68 @ SV28 @ SV72 ) )
= $true )
| ( ( sum @ SV39 @ SV54 @ SV72 )
= $true )
| ( ( sum @ SV15 @ SV50 @ SV68 )
= $false )
| ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(221,plain,
! [SV51: $i,SV16: $i,SV29: $i,SV69: $i,SV73: $i,SV55: $i,SV40: $i] :
( ( ( ~ ( sum @ SV40 @ SV55 @ SV73 ) )
= $true )
| ( ( product @ SV69 @ SV29 @ SV73 )
= $true )
| ( ( sum @ SV16 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(222,plain,
! [SV48: $i,SV26: $i,SV52: $i,SV37: $i,SV70: $i,SV66: $i,SV13: $i] :
( ( ( product @ SV13 @ SV66 @ SV70 )
= $false )
| ( ( sum @ SV37 @ SV52 @ SV70 )
= $true )
| ( ( sum @ SV26 @ SV48 @ SV66 )
= $false )
| ( ( product @ SV13 @ SV48 @ SV52 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(223,plain,
! [SV49: $i,SV27: $i,SV67: $i,SV14: $i,SV71: $i,SV53: $i,SV38: $i] :
( ( ( sum @ SV38 @ SV53 @ SV71 )
= $false )
| ( ( product @ SV14 @ SV67 @ SV71 )
= $true )
| ( ( sum @ SV27 @ SV49 @ SV67 )
= $false )
| ( ( product @ SV14 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(224,plain,
! [SV50: $i,SV15: $i,SV54: $i,SV39: $i,SV72: $i,SV28: $i,SV68: $i] :
( ( ( product @ SV68 @ SV28 @ SV72 )
= $false )
| ( ( sum @ SV39 @ SV54 @ SV72 )
= $true )
| ( ( sum @ SV15 @ SV50 @ SV68 )
= $false )
| ( ( product @ SV50 @ SV28 @ SV54 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(225,plain,
! [SV51: $i,SV16: $i,SV29: $i,SV69: $i,SV73: $i,SV55: $i,SV40: $i] :
( ( ( sum @ SV40 @ SV55 @ SV73 )
= $false )
| ( ( product @ SV69 @ SV29 @ SV73 )
= $true )
| ( ( sum @ SV16 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV51 @ SV29 @ SV55 )
= $false )
| ( ( product @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(226,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,225,224,223,222,209,208,207,206,181,180,143,129,105,104,102,90,89,86,85,83,82]) ).
thf(227,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG038-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n017.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 14:06:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.25/6.05
% 34.25/6.05 No.of.Axioms: 21
% 34.25/6.05
% 34.25/6.05 Length.of.Defs: 0
% 34.25/6.05
% 34.25/6.05 Contains.Choice.Funs: false
% 34.25/6.05 ........
% 34.25/6.05
% 34.25/6.05 ********************************
% 34.25/6.05 * All subproblems solved! *
% 34.25/6.05 ********************************
% 34.25/6.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:226,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 34.25/6.05
% 34.25/6.05 %**** Beginning of derivation protocol ****
% 34.25/6.05 % SZS output start CNFRefutation
% See solution above
% 34.25/6.05
% 34.25/6.05 %**** End of derivation protocol ****
% 34.25/6.05 %**** no. of clauses in derivation: 227 ****
% 34.25/6.05 %**** clause counter: 226 ****
% 34.25/6.05
% 34.25/6.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:21,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:226,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------