TSTP Solution File: BOO013-3 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : BOO013-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:43:33 EDT 2022
% Result : Unsatisfiable 1.81s 2.01s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 39
% Syntax : Number of formulae : 273 ( 157 unt; 10 typ; 0 def)
% Number of atoms : 1837 ( 484 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3896 ( 498 ~; 672 |; 0 &;2726 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 1264 ( 0 ^1264 !; 0 ?;1264 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i > $i > $o ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_an_involution) ).
thf(2,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(3,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(4,axiom,
! [X: $i] : ( product @ X @ ( inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse2) ).
thf(5,axiom,
! [X: $i] : ( product @ ( inverse @ X ) @ X @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
thf(6,axiom,
! [X: $i] : ( sum @ X @ ( inverse @ X ) @ multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
thf(7,axiom,
! [X: $i] : ( sum @ ( inverse @ X ) @ X @ multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
thf(8,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ V3 @ X @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity8) ).
thf(9,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( sum @ V3 @ X @ V4 )
| ( product @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity7) ).
thf(10,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ X @ V3 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity6) ).
thf(11,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( sum @ X @ V3 @ V4 )
| ( product @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
thf(12,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(13,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(14,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(15,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(16,axiom,
! [X: $i] : ( product @ X @ multiplicative_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(17,axiom,
! [X: $i] : ( product @ multiplicative_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(18,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(19,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(20,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
thf(21,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(22,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(23,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
thf(27,negated_conjecture,
product @ x @ z @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity2) ).
thf(28,negated_conjecture,
product @ x @ y @ additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity1) ).
thf(29,negated_conjecture,
sum @ x @ z @ multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
thf(30,negated_conjecture,
sum @ x @ y @ multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
thf(31,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,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)],[2]) ).
thf(34,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)],[3]) ).
thf(35,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(37,plain,
( ( ! [X: $i] : ( sum @ X @ ( inverse @ X ) @ multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ! [X: $i] : ( sum @ ( inverse @ X ) @ X @ multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(39,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ V3 @ X @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( sum @ V3 @ X @ V4 )
| ( product @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ X @ V3 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ~ ( product @ Y @ Z @ V3 )
| ~ ( sum @ X @ V3 @ V4 )
| ( product @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,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)],[12]) ).
thf(44,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)],[13]) ).
thf(45,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)],[14]) ).
thf(46,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)],[15]) ).
thf(47,plain,
( ( ! [X: $i] : ( product @ X @ multiplicative_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(48,plain,
( ( ! [X: $i] : ( product @ multiplicative_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(49,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(50,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(55,plain,
( ( ( y != z ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(56,plain,
( ( product @ x @ z @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(57,plain,
( ( product @ x @ y @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(58,plain,
( ( sum @ x @ z @ multiplicative_identity )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(59,plain,
( ( sum @ x @ y @ multiplicative_identity )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(60,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(61,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)],[33]) ).
thf(62,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)],[34]) ).
thf(63,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ V3 @ X @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(64,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V3 @ X @ V4 )
| ( product @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ X @ V3 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ X @ V3 @ V4 )
| ( product @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(67,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)],[43]) ).
thf(68,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)],[44]) ).
thf(69,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)],[45]) ).
thf(70,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)],[46]) ).
thf(71,plain,
( ( ( y != z ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(72,plain,
( ( sum @ x @ y @ multiplicative_identity )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( sum @ x @ z @ multiplicative_identity )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(74,plain,
( ( product @ x @ y @ additive_identity )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(75,plain,
( ( product @ x @ z @ additive_identity )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(76,plain,
( ( ( y != z ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(81,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(82,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(83,plain,
( ( ! [X: $i] : ( product @ multiplicative_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(84,plain,
( ( ! [X: $i] : ( product @ X @ multiplicative_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(85,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)],[70]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( sum @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(87,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)],[68]) ).
thf(88,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)],[67]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ X @ V3 @ V4 )
| ( product @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(90,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ X @ Y @ V1 )
| ~ ( sum @ X @ Z @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ X @ V3 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(91,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( sum @ V3 @ X @ V4 )
| ( product @ V1 @ V2 @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(92,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i] :
( ~ ( sum @ Y @ X @ V1 )
| ~ ( sum @ Z @ X @ V2 )
| ! [V3: $i] :
( ~ ( product @ Y @ Z @ V3 )
| ! [V4: $i] :
( ~ ( product @ V1 @ V2 @ V4 )
| ( sum @ V3 @ X @ V4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(93,plain,
( ( ! [X: $i] : ( sum @ ( inverse @ X ) @ X @ multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(94,plain,
( ( ! [X: $i] : ( sum @ X @ ( inverse @ X ) @ multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(95,plain,
( ( ! [X: $i] : ( product @ ( inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(96,plain,
( ( ! [X: $i] : ( product @ X @ ( inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(98,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(99,plain,
( ( ! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(100,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(101,plain,
( ( y = z )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(102,plain,
! [SV1: $i] :
( ( ! [SY83: $i] : ( sum @ SV1 @ SY83 @ ( add @ SV1 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(103,plain,
! [SV2: $i] :
( ( ! [SY84: $i] : ( product @ SV2 @ SY84 @ ( multiply @ SV2 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(104,plain,
! [SV3: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( sum @ SV3 @ SY85 @ SY86 )
| ( sum @ SY85 @ SV3 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(105,plain,
! [SV4: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( product @ SV4 @ SY87 @ SY88 )
| ( product @ SY87 @ SV4 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(106,plain,
! [SV5: $i] :
( ( sum @ additive_identity @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(107,plain,
! [SV6: $i] :
( ( sum @ SV6 @ additive_identity @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(108,plain,
! [SV7: $i] :
( ( product @ multiplicative_identity @ SV7 @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(109,plain,
! [SV8: $i] :
( ( product @ SV8 @ multiplicative_identity @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(110,plain,
! [SV9: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i,SY92: $i] :
( ~ ( product @ SV9 @ SY89 @ SY90 )
| ~ ( product @ SV9 @ SY91 @ SY92 )
| ! [SY93: $i] :
( ~ ( sum @ SY89 @ SY91 @ SY93 )
| ! [SY94: $i] :
( ~ ( product @ SV9 @ SY93 @ SY94 )
| ( sum @ SY90 @ SY92 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(111,plain,
! [SV10: $i] :
( ( ! [SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ~ ( product @ SV10 @ SY95 @ SY96 )
| ~ ( product @ SV10 @ SY97 @ SY98 )
| ! [SY99: $i] :
( ~ ( sum @ SY95 @ SY97 @ SY99 )
| ! [SY100: $i] :
( ~ ( sum @ SY96 @ SY98 @ SY100 )
| ( product @ SV10 @ SY99 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(112,plain,
! [SV11: $i] :
( ( ! [SY101: $i,SY102: $i,SY103: $i,SY104: $i] :
( ~ ( product @ SV11 @ SY101 @ SY102 )
| ~ ( product @ SY103 @ SY101 @ SY104 )
| ! [SY105: $i] :
( ~ ( sum @ SV11 @ SY103 @ SY105 )
| ! [V4: $i] :
( ~ ( product @ SY105 @ SY101 @ V4 )
| ( sum @ SY102 @ SY104 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(113,plain,
! [SV12: $i] :
( ( ! [SY107: $i,SY108: $i,SY109: $i,SY110: $i] :
( ~ ( product @ SV12 @ SY107 @ SY108 )
| ~ ( product @ SY109 @ SY107 @ SY110 )
| ! [SY111: $i] :
( ~ ( sum @ SV12 @ SY109 @ SY111 )
| ! [V4: $i] :
( ~ ( sum @ SY108 @ SY110 @ V4 )
| ( product @ SY111 @ SY107 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(114,plain,
! [SV13: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] :
( ~ ( sum @ SV13 @ SY113 @ SY114 )
| ~ ( sum @ SV13 @ SY115 @ SY116 )
| ! [SY117: $i] :
( ~ ( product @ SY113 @ SY115 @ SY117 )
| ! [SY118: $i] :
( ~ ( sum @ SV13 @ SY117 @ SY118 )
| ( product @ SY114 @ SY116 @ SY118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(115,plain,
! [SV14: $i] :
( ( ! [SY119: $i,SY120: $i,SY121: $i,SY122: $i] :
( ~ ( sum @ SV14 @ SY119 @ SY120 )
| ~ ( sum @ SV14 @ SY121 @ SY122 )
| ! [SY123: $i] :
( ~ ( product @ SY119 @ SY121 @ SY123 )
| ! [SY124: $i] :
( ~ ( product @ SY120 @ SY122 @ SY124 )
| ( sum @ SV14 @ SY123 @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(116,plain,
! [SV15: $i] :
( ( ! [SY125: $i,SY126: $i,SY127: $i,SY128: $i] :
( ~ ( sum @ SV15 @ SY125 @ SY126 )
| ~ ( sum @ SY127 @ SY125 @ SY128 )
| ! [SY129: $i] :
( ~ ( product @ SV15 @ SY127 @ SY129 )
| ! [V4: $i] :
( ~ ( sum @ SY129 @ SY125 @ V4 )
| ( product @ SY126 @ SY128 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(117,plain,
! [SV16: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i,SY134: $i] :
( ~ ( sum @ SV16 @ SY131 @ SY132 )
| ~ ( sum @ SY133 @ SY131 @ SY134 )
| ! [SY135: $i] :
( ~ ( product @ SV16 @ SY133 @ SY135 )
| ! [V4: $i] :
( ~ ( product @ SY132 @ SY134 @ V4 )
| ( sum @ SY135 @ SY131 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(118,plain,
! [SV17: $i] :
( ( sum @ ( inverse @ SV17 ) @ SV17 @ multiplicative_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(119,plain,
! [SV18: $i] :
( ( sum @ SV18 @ ( inverse @ SV18 ) @ multiplicative_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(120,plain,
! [SV19: $i] :
( ( product @ ( inverse @ SV19 ) @ SV19 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(121,plain,
! [SV20: $i] :
( ( product @ SV20 @ ( inverse @ SV20 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(122,plain,
! [SV21: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( sum @ SV21 @ SY137 @ SY138 )
| ! [SY139: $i] :
( ~ ( sum @ SV21 @ SY137 @ SY139 )
| ( SY138 = SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(123,plain,
! [SV22: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( product @ SV22 @ SY140 @ SY141 )
| ! [SY142: $i] :
( ~ ( product @ SV22 @ SY140 @ SY142 )
| ( SY141 = SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(124,plain,
! [SV23: $i] :
( ( ( inverse @ ( inverse @ SV23 ) )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(125,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(126,plain,
! [SV24: $i,SV1: $i] :
( ( sum @ SV1 @ SV24 @ ( add @ SV1 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(127,plain,
! [SV25: $i,SV2: $i] :
( ( product @ SV2 @ SV25 @ ( multiply @ SV2 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(128,plain,
! [SV26: $i,SV3: $i] :
( ( ! [SY143: $i] :
( ~ ( sum @ SV3 @ SV26 @ SY143 )
| ( sum @ SV26 @ SV3 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(129,plain,
! [SV27: $i,SV4: $i] :
( ( ! [SY144: $i] :
( ~ ( product @ SV4 @ SV27 @ SY144 )
| ( product @ SV27 @ SV4 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV28: $i,SV9: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i] :
( ~ ( product @ SV9 @ SV28 @ SY145 )
| ~ ( product @ SV9 @ SY146 @ SY147 )
| ! [SY148: $i] :
( ~ ( sum @ SV28 @ SY146 @ SY148 )
| ! [SY94: $i] :
( ~ ( product @ SV9 @ SY148 @ SY94 )
| ( sum @ SY145 @ SY147 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(131,plain,
! [SV29: $i,SV10: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i] :
( ~ ( product @ SV10 @ SV29 @ SY150 )
| ~ ( product @ SV10 @ SY151 @ SY152 )
| ! [SY153: $i] :
( ~ ( sum @ SV29 @ SY151 @ SY153 )
| ! [SY100: $i] :
( ~ ( sum @ SY150 @ SY152 @ SY100 )
| ( product @ SV10 @ SY153 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(132,plain,
! [SV30: $i,SV11: $i] :
( ( ! [SY155: $i,SY156: $i,SY157: $i] :
( ~ ( product @ SV11 @ SV30 @ SY155 )
| ~ ( product @ SY156 @ SV30 @ SY157 )
| ! [SY158: $i] :
( ~ ( sum @ SV11 @ SY156 @ SY158 )
| ! [SY159: $i] :
( ~ ( product @ SY158 @ SV30 @ SY159 )
| ( sum @ SY155 @ SY157 @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(133,plain,
! [SV31: $i,SV12: $i] :
( ( ! [SY160: $i,SY161: $i,SY162: $i] :
( ~ ( product @ SV12 @ SV31 @ SY160 )
| ~ ( product @ SY161 @ SV31 @ SY162 )
| ! [SY163: $i] :
( ~ ( sum @ SV12 @ SY161 @ SY163 )
| ! [SY164: $i] :
( ~ ( sum @ SY160 @ SY162 @ SY164 )
| ( product @ SY163 @ SV31 @ SY164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(134,plain,
! [SV32: $i,SV13: $i] :
( ( ! [SY165: $i,SY166: $i,SY167: $i] :
( ~ ( sum @ SV13 @ SV32 @ SY165 )
| ~ ( sum @ SV13 @ SY166 @ SY167 )
| ! [SY168: $i] :
( ~ ( product @ SV32 @ SY166 @ SY168 )
| ! [SY118: $i] :
( ~ ( sum @ SV13 @ SY168 @ SY118 )
| ( product @ SY165 @ SY167 @ SY118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(135,plain,
! [SV33: $i,SV14: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ~ ( sum @ SV14 @ SV33 @ SY170 )
| ~ ( sum @ SV14 @ SY171 @ SY172 )
| ! [SY173: $i] :
( ~ ( product @ SV33 @ SY171 @ SY173 )
| ! [SY124: $i] :
( ~ ( product @ SY170 @ SY172 @ SY124 )
| ( sum @ SV14 @ SY173 @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(136,plain,
! [SV34: $i,SV15: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i] :
( ~ ( sum @ SV15 @ SV34 @ SY175 )
| ~ ( sum @ SY176 @ SV34 @ SY177 )
| ! [SY178: $i] :
( ~ ( product @ SV15 @ SY176 @ SY178 )
| ! [SY179: $i] :
( ~ ( sum @ SY178 @ SV34 @ SY179 )
| ( product @ SY175 @ SY177 @ SY179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(137,plain,
! [SV35: $i,SV16: $i] :
( ( ! [SY180: $i,SY181: $i,SY182: $i] :
( ~ ( sum @ SV16 @ SV35 @ SY180 )
| ~ ( sum @ SY181 @ SV35 @ SY182 )
| ! [SY183: $i] :
( ~ ( product @ SV16 @ SY181 @ SY183 )
| ! [SY184: $i] :
( ~ ( product @ SY180 @ SY182 @ SY184 )
| ( sum @ SY183 @ SV35 @ SY184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(138,plain,
! [SV36: $i,SV21: $i] :
( ( ! [SY185: $i] :
( ~ ( sum @ SV21 @ SV36 @ SY185 )
| ! [SY186: $i] :
( ~ ( sum @ SV21 @ SV36 @ SY186 )
| ( SY185 = SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV37: $i,SV22: $i] :
( ( ! [SY187: $i] :
( ~ ( product @ SV22 @ SV37 @ SY187 )
| ! [SY188: $i] :
( ~ ( product @ SV22 @ SV37 @ SY188 )
| ( SY187 = SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV38: $i,SV26: $i,SV3: $i] :
( ( ~ ( sum @ SV3 @ SV26 @ SV38 )
| ( sum @ SV26 @ SV3 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV39: $i,SV27: $i,SV4: $i] :
( ( ~ ( product @ SV4 @ SV27 @ SV39 )
| ( product @ SV27 @ SV4 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV40: $i,SV28: $i,SV9: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ~ ( product @ SV9 @ SV28 @ SV40 )
| ~ ( product @ SV9 @ SY189 @ SY190 )
| ! [SY191: $i] :
( ~ ( sum @ SV28 @ SY189 @ SY191 )
| ! [SY192: $i] :
( ~ ( product @ SV9 @ SY191 @ SY192 )
| ( sum @ SV40 @ SY190 @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV41: $i,SV29: $i,SV10: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( product @ SV10 @ SV29 @ SV41 )
| ~ ( product @ SV10 @ SY193 @ SY194 )
| ! [SY195: $i] :
( ~ ( sum @ SV29 @ SY193 @ SY195 )
| ! [SY196: $i] :
( ~ ( sum @ SV41 @ SY194 @ SY196 )
| ( product @ SV10 @ SY195 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV42: $i,SV30: $i,SV11: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( product @ SV11 @ SV30 @ SV42 )
| ~ ( product @ SY197 @ SV30 @ SY198 )
| ! [SY199: $i] :
( ~ ( sum @ SV11 @ SY197 @ SY199 )
| ! [SY200: $i] :
( ~ ( product @ SY199 @ SV30 @ SY200 )
| ( sum @ SV42 @ SY198 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV43: $i,SV31: $i,SV12: $i] :
( ( ! [SY201: $i,SY202: $i] :
( ~ ( product @ SV12 @ SV31 @ SV43 )
| ~ ( product @ SY201 @ SV31 @ SY202 )
| ! [SY203: $i] :
( ~ ( sum @ SV12 @ SY201 @ SY203 )
| ! [SY204: $i] :
( ~ ( sum @ SV43 @ SY202 @ SY204 )
| ( product @ SY203 @ SV31 @ SY204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV44: $i,SV32: $i,SV13: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( sum @ SV13 @ SV32 @ SV44 )
| ~ ( sum @ SV13 @ SY205 @ SY206 )
| ! [SY207: $i] :
( ~ ( product @ SV32 @ SY205 @ SY207 )
| ! [SY208: $i] :
( ~ ( sum @ SV13 @ SY207 @ SY208 )
| ( product @ SV44 @ SY206 @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV45: $i,SV33: $i,SV14: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ( sum @ SV14 @ SV33 @ SV45 )
| ~ ( sum @ SV14 @ SY209 @ SY210 )
| ! [SY211: $i] :
( ~ ( product @ SV33 @ SY209 @ SY211 )
| ! [SY212: $i] :
( ~ ( product @ SV45 @ SY210 @ SY212 )
| ( sum @ SV14 @ SY211 @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV46: $i,SV34: $i,SV15: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ~ ( sum @ SV15 @ SV34 @ SV46 )
| ~ ( sum @ SY213 @ SV34 @ SY214 )
| ! [SY215: $i] :
( ~ ( product @ SV15 @ SY213 @ SY215 )
| ! [SY216: $i] :
( ~ ( sum @ SY215 @ SV34 @ SY216 )
| ( product @ SV46 @ SY214 @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV47: $i,SV35: $i,SV16: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( sum @ SV16 @ SV35 @ SV47 )
| ~ ( sum @ SY217 @ SV35 @ SY218 )
| ! [SY219: $i] :
( ~ ( product @ SV16 @ SY217 @ SY219 )
| ! [SY220: $i] :
( ~ ( product @ SV47 @ SY218 @ SY220 )
| ( sum @ SY219 @ SV35 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV48: $i,SV36: $i,SV21: $i] :
( ( ~ ( sum @ SV21 @ SV36 @ SV48 )
| ! [SY221: $i] :
( ~ ( sum @ SV21 @ SV36 @ SY221 )
| ( SV48 = SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV49: $i,SV37: $i,SV22: $i] :
( ( ~ ( product @ SV22 @ SV37 @ SV49 )
| ! [SY222: $i] :
( ~ ( product @ SV22 @ SV37 @ SY222 )
| ( SV49 = SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV38: $i,SV26: $i,SV3: $i] :
( ( ( ~ ( sum @ SV3 @ SV26 @ SV38 ) )
= $true )
| ( ( sum @ SV26 @ SV3 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV39: $i,SV27: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV27 @ SV39 ) )
= $true )
| ( ( product @ SV27 @ SV4 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV50: $i,SV40: $i,SV28: $i,SV9: $i] :
( ( ! [SY223: $i] :
( ~ ( product @ SV9 @ SV28 @ SV40 )
| ~ ( product @ SV9 @ SV50 @ SY223 )
| ! [SY224: $i] :
( ~ ( sum @ SV28 @ SV50 @ SY224 )
| ! [SY192: $i] :
( ~ ( product @ SV9 @ SY224 @ SY192 )
| ( sum @ SV40 @ SY223 @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV51: $i,SV41: $i,SV29: $i,SV10: $i] :
( ( ! [SY226: $i] :
( ~ ( product @ SV10 @ SV29 @ SV41 )
| ~ ( product @ SV10 @ SV51 @ SY226 )
| ! [SY227: $i] :
( ~ ( sum @ SV29 @ SV51 @ SY227 )
| ! [SY196: $i] :
( ~ ( sum @ SV41 @ SY226 @ SY196 )
| ( product @ SV10 @ SY227 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV52: $i,SV42: $i,SV30: $i,SV11: $i] :
( ( ! [SY229: $i] :
( ~ ( product @ SV11 @ SV30 @ SV42 )
| ~ ( product @ SV52 @ SV30 @ SY229 )
| ! [SY230: $i] :
( ~ ( sum @ SV11 @ SV52 @ SY230 )
| ! [SY200: $i] :
( ~ ( product @ SY230 @ SV30 @ SY200 )
| ( sum @ SV42 @ SY229 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV53: $i,SV43: $i,SV31: $i,SV12: $i] :
( ( ! [SY232: $i] :
( ~ ( product @ SV12 @ SV31 @ SV43 )
| ~ ( product @ SV53 @ SV31 @ SY232 )
| ! [SY233: $i] :
( ~ ( sum @ SV12 @ SV53 @ SY233 )
| ! [SY204: $i] :
( ~ ( sum @ SV43 @ SY232 @ SY204 )
| ( product @ SY233 @ SV31 @ SY204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV54: $i,SV44: $i,SV32: $i,SV13: $i] :
( ( ! [SY235: $i] :
( ~ ( sum @ SV13 @ SV32 @ SV44 )
| ~ ( sum @ SV13 @ SV54 @ SY235 )
| ! [SY236: $i] :
( ~ ( product @ SV32 @ SV54 @ SY236 )
| ! [SY208: $i] :
( ~ ( sum @ SV13 @ SY236 @ SY208 )
| ( product @ SV44 @ SY235 @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV55: $i,SV45: $i,SV33: $i,SV14: $i] :
( ( ! [SY238: $i] :
( ~ ( sum @ SV14 @ SV33 @ SV45 )
| ~ ( sum @ SV14 @ SV55 @ SY238 )
| ! [SY239: $i] :
( ~ ( product @ SV33 @ SV55 @ SY239 )
| ! [SY212: $i] :
( ~ ( product @ SV45 @ SY238 @ SY212 )
| ( sum @ SV14 @ SY239 @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV56: $i,SV46: $i,SV34: $i,SV15: $i] :
( ( ! [SY241: $i] :
( ~ ( sum @ SV15 @ SV34 @ SV46 )
| ~ ( sum @ SV56 @ SV34 @ SY241 )
| ! [SY242: $i] :
( ~ ( product @ SV15 @ SV56 @ SY242 )
| ! [SY216: $i] :
( ~ ( sum @ SY242 @ SV34 @ SY216 )
| ( product @ SV46 @ SY241 @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV57: $i,SV47: $i,SV35: $i,SV16: $i] :
( ( ! [SY244: $i] :
( ~ ( sum @ SV16 @ SV35 @ SV47 )
| ~ ( sum @ SV57 @ SV35 @ SY244 )
| ! [SY245: $i] :
( ~ ( product @ SV16 @ SV57 @ SY245 )
| ! [SY220: $i] :
( ~ ( product @ SV47 @ SY244 @ SY220 )
| ( sum @ SY245 @ SV35 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(162,plain,
! [SV48: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV36 @ SV48 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( sum @ SV21 @ SV36 @ SY221 )
| ( SV48 = SY221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV49: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV37 @ SV49 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( product @ SV22 @ SV37 @ SY222 )
| ( SV49 = SY222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(164,plain,
! [SV38: $i,SV26: $i,SV3: $i] :
( ( ( sum @ SV3 @ SV26 @ SV38 )
= $false )
| ( ( sum @ SV26 @ SV3 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(165,plain,
! [SV39: $i,SV27: $i,SV4: $i] :
( ( ( product @ SV4 @ SV27 @ SV39 )
= $false )
| ( ( product @ SV27 @ SV4 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(166,plain,
! [SV58: $i,SV50: $i,SV40: $i,SV28: $i,SV9: $i] :
( ( ~ ( product @ SV9 @ SV28 @ SV40 )
| ~ ( product @ SV9 @ SV50 @ SV58 )
| ! [SY247: $i] :
( ~ ( sum @ SV28 @ SV50 @ SY247 )
| ! [SY248: $i] :
( ~ ( product @ SV9 @ SY247 @ SY248 )
| ( sum @ SV40 @ SV58 @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(167,plain,
! [SV59: $i,SV51: $i,SV41: $i,SV29: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV29 @ SV41 )
| ~ ( product @ SV10 @ SV51 @ SV59 )
| ! [SY249: $i] :
( ~ ( sum @ SV29 @ SV51 @ SY249 )
| ! [SY250: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY250 )
| ( product @ SV10 @ SY249 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV60: $i,SV52: $i,SV42: $i,SV30: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV30 @ SV42 )
| ~ ( product @ SV52 @ SV30 @ SV60 )
| ! [SY251: $i] :
( ~ ( sum @ SV11 @ SV52 @ SY251 )
| ! [SY252: $i] :
( ~ ( product @ SY251 @ SV30 @ SY252 )
| ( sum @ SV42 @ SV60 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV61: $i,SV53: $i,SV43: $i,SV31: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV31 @ SV43 )
| ~ ( product @ SV53 @ SV31 @ SV61 )
| ! [SY253: $i] :
( ~ ( sum @ SV12 @ SV53 @ SY253 )
| ! [SY254: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY254 )
| ( product @ SY253 @ SV31 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV62: $i,SV54: $i,SV44: $i,SV32: $i,SV13: $i] :
( ( ~ ( sum @ SV13 @ SV32 @ SV44 )
| ~ ( sum @ SV13 @ SV54 @ SV62 )
| ! [SY255: $i] :
( ~ ( product @ SV32 @ SV54 @ SY255 )
| ! [SY256: $i] :
( ~ ( sum @ SV13 @ SY255 @ SY256 )
| ( product @ SV44 @ SV62 @ SY256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV63: $i,SV55: $i,SV45: $i,SV33: $i,SV14: $i] :
( ( ~ ( sum @ SV14 @ SV33 @ SV45 )
| ~ ( sum @ SV14 @ SV55 @ SV63 )
| ! [SY257: $i] :
( ~ ( product @ SV33 @ SV55 @ SY257 )
| ! [SY258: $i] :
( ~ ( product @ SV45 @ SV63 @ SY258 )
| ( sum @ SV14 @ SY257 @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV64: $i,SV56: $i,SV46: $i,SV34: $i,SV15: $i] :
( ( ~ ( sum @ SV15 @ SV34 @ SV46 )
| ~ ( sum @ SV56 @ SV34 @ SV64 )
| ! [SY259: $i] :
( ~ ( product @ SV15 @ SV56 @ SY259 )
| ! [SY260: $i] :
( ~ ( sum @ SY259 @ SV34 @ SY260 )
| ( product @ SV46 @ SV64 @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV65: $i,SV57: $i,SV47: $i,SV35: $i,SV16: $i] :
( ( ~ ( sum @ SV16 @ SV35 @ SV47 )
| ~ ( sum @ SV57 @ SV35 @ SV65 )
| ! [SY261: $i] :
( ~ ( product @ SV16 @ SV57 @ SY261 )
| ! [SY262: $i] :
( ~ ( product @ SV47 @ SV65 @ SY262 )
| ( sum @ SY261 @ SV35 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV48: $i,SV36: $i,SV21: $i] :
( ( ( sum @ SV21 @ SV36 @ SV48 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( sum @ SV21 @ SV36 @ SY221 )
| ( SV48 = SY221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV49: $i,SV37: $i,SV22: $i] :
( ( ( product @ SV22 @ SV37 @ SV49 )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( product @ SV22 @ SV37 @ SY222 )
| ( SV49 = SY222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV58: $i,SV50: $i,SV40: $i,SV28: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV28 @ SV40 ) )
= $true )
| ( ( ~ ( product @ SV9 @ SV50 @ SV58 )
| ! [SY247: $i] :
( ~ ( sum @ SV28 @ SV50 @ SY247 )
| ! [SY248: $i] :
( ~ ( product @ SV9 @ SY247 @ SY248 )
| ( sum @ SV40 @ SV58 @ SY248 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV59: $i,SV51: $i,SV41: $i,SV29: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV29 @ SV41 ) )
= $true )
| ( ( ~ ( product @ SV10 @ SV51 @ SV59 )
| ! [SY249: $i] :
( ~ ( sum @ SV29 @ SV51 @ SY249 )
| ! [SY250: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY250 )
| ( product @ SV10 @ SY249 @ SY250 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV60: $i,SV52: $i,SV42: $i,SV30: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV30 @ SV42 ) )
= $true )
| ( ( ~ ( product @ SV52 @ SV30 @ SV60 )
| ! [SY251: $i] :
( ~ ( sum @ SV11 @ SV52 @ SY251 )
| ! [SY252: $i] :
( ~ ( product @ SY251 @ SV30 @ SY252 )
| ( sum @ SV42 @ SV60 @ SY252 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV61: $i,SV53: $i,SV43: $i,SV31: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV31 @ SV43 ) )
= $true )
| ( ( ~ ( product @ SV53 @ SV31 @ SV61 )
| ! [SY253: $i] :
( ~ ( sum @ SV12 @ SV53 @ SY253 )
| ! [SY254: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY254 )
| ( product @ SY253 @ SV31 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV62: $i,SV54: $i,SV44: $i,SV32: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV32 @ SV44 ) )
= $true )
| ( ( ~ ( sum @ SV13 @ SV54 @ SV62 )
| ! [SY255: $i] :
( ~ ( product @ SV32 @ SV54 @ SY255 )
| ! [SY256: $i] :
( ~ ( sum @ SV13 @ SY255 @ SY256 )
| ( product @ SV44 @ SV62 @ SY256 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV63: $i,SV55: $i,SV45: $i,SV33: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV33 @ SV45 ) )
= $true )
| ( ( ~ ( sum @ SV14 @ SV55 @ SV63 )
| ! [SY257: $i] :
( ~ ( product @ SV33 @ SV55 @ SY257 )
| ! [SY258: $i] :
( ~ ( product @ SV45 @ SV63 @ SY258 )
| ( sum @ SV14 @ SY257 @ SY258 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV64: $i,SV56: $i,SV46: $i,SV34: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV34 @ SV46 ) )
= $true )
| ( ( ~ ( sum @ SV56 @ SV34 @ SV64 )
| ! [SY259: $i] :
( ~ ( product @ SV15 @ SV56 @ SY259 )
| ! [SY260: $i] :
( ~ ( sum @ SY259 @ SV34 @ SY260 )
| ( product @ SV46 @ SV64 @ SY260 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV65: $i,SV57: $i,SV47: $i,SV35: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV35 @ SV47 ) )
= $true )
| ( ( ~ ( sum @ SV57 @ SV35 @ SV65 )
| ! [SY261: $i] :
( ~ ( product @ SV16 @ SV57 @ SY261 )
| ! [SY262: $i] :
( ~ ( product @ SV47 @ SV65 @ SY262 )
| ( sum @ SY261 @ SV35 @ SY262 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV48: $i,SV66: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV36 @ SV66 )
| ( SV48 = SV66 ) )
= $true )
| ( ( sum @ SV21 @ SV36 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV49: $i,SV67: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV37 @ SV67 )
| ( SV49 = SV67 ) )
= $true )
| ( ( product @ SV22 @ SV37 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV58: $i,SV50: $i,SV40: $i,SV28: $i,SV9: $i] :
( ( ( product @ SV9 @ SV28 @ SV40 )
= $false )
| ( ( ~ ( product @ SV9 @ SV50 @ SV58 )
| ! [SY247: $i] :
( ~ ( sum @ SV28 @ SV50 @ SY247 )
| ! [SY248: $i] :
( ~ ( product @ SV9 @ SY247 @ SY248 )
| ( sum @ SV40 @ SV58 @ SY248 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV59: $i,SV51: $i,SV41: $i,SV29: $i,SV10: $i] :
( ( ( product @ SV10 @ SV29 @ SV41 )
= $false )
| ( ( ~ ( product @ SV10 @ SV51 @ SV59 )
| ! [SY249: $i] :
( ~ ( sum @ SV29 @ SV51 @ SY249 )
| ! [SY250: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY250 )
| ( product @ SV10 @ SY249 @ SY250 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV60: $i,SV52: $i,SV42: $i,SV30: $i,SV11: $i] :
( ( ( product @ SV11 @ SV30 @ SV42 )
= $false )
| ( ( ~ ( product @ SV52 @ SV30 @ SV60 )
| ! [SY251: $i] :
( ~ ( sum @ SV11 @ SV52 @ SY251 )
| ! [SY252: $i] :
( ~ ( product @ SY251 @ SV30 @ SY252 )
| ( sum @ SV42 @ SV60 @ SY252 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV61: $i,SV53: $i,SV43: $i,SV31: $i,SV12: $i] :
( ( ( product @ SV12 @ SV31 @ SV43 )
= $false )
| ( ( ~ ( product @ SV53 @ SV31 @ SV61 )
| ! [SY253: $i] :
( ~ ( sum @ SV12 @ SV53 @ SY253 )
| ! [SY254: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY254 )
| ( product @ SY253 @ SV31 @ SY254 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(190,plain,
! [SV62: $i,SV54: $i,SV44: $i,SV32: $i,SV13: $i] :
( ( ( sum @ SV13 @ SV32 @ SV44 )
= $false )
| ( ( ~ ( sum @ SV13 @ SV54 @ SV62 )
| ! [SY255: $i] :
( ~ ( product @ SV32 @ SV54 @ SY255 )
| ! [SY256: $i] :
( ~ ( sum @ SV13 @ SY255 @ SY256 )
| ( product @ SV44 @ SV62 @ SY256 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(191,plain,
! [SV63: $i,SV55: $i,SV45: $i,SV33: $i,SV14: $i] :
( ( ( sum @ SV14 @ SV33 @ SV45 )
= $false )
| ( ( ~ ( sum @ SV14 @ SV55 @ SV63 )
| ! [SY257: $i] :
( ~ ( product @ SV33 @ SV55 @ SY257 )
| ! [SY258: $i] :
( ~ ( product @ SV45 @ SV63 @ SY258 )
| ( sum @ SV14 @ SY257 @ SY258 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV64: $i,SV56: $i,SV46: $i,SV34: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV34 @ SV46 )
= $false )
| ( ( ~ ( sum @ SV56 @ SV34 @ SV64 )
| ! [SY259: $i] :
( ~ ( product @ SV15 @ SV56 @ SY259 )
| ! [SY260: $i] :
( ~ ( sum @ SY259 @ SV34 @ SY260 )
| ( product @ SV46 @ SV64 @ SY260 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(193,plain,
! [SV65: $i,SV57: $i,SV47: $i,SV35: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV35 @ SV47 )
= $false )
| ( ( ~ ( sum @ SV57 @ SV35 @ SV65 )
| ! [SY261: $i] :
( ~ ( product @ SV16 @ SV57 @ SY261 )
| ! [SY262: $i] :
( ~ ( product @ SV47 @ SV65 @ SY262 )
| ( sum @ SY261 @ SV35 @ SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV48: $i,SV66: $i,SV36: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV36 @ SV66 ) )
= $true )
| ( ( SV48 = SV66 )
= $true )
| ( ( sum @ SV21 @ SV36 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(195,plain,
! [SV49: $i,SV67: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( product @ SV22 @ SV37 @ SV67 ) )
= $true )
| ( ( SV49 = SV67 )
= $true )
| ( ( product @ SV22 @ SV37 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(196,plain,
! [SV40: $i,SV28: $i,SV58: $i,SV50: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV50 @ SV58 ) )
= $true )
| ( ( ! [SY247: $i] :
( ~ ( sum @ SV28 @ SV50 @ SY247 )
| ! [SY248: $i] :
( ~ ( product @ SV9 @ SY247 @ SY248 )
| ( sum @ SV40 @ SV58 @ SY248 ) ) ) )
= $true )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(197,plain,
! [SV41: $i,SV29: $i,SV59: $i,SV51: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV51 @ SV59 ) )
= $true )
| ( ( ! [SY249: $i] :
( ~ ( sum @ SV29 @ SV51 @ SY249 )
| ! [SY250: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY250 )
| ( product @ SV10 @ SY249 @ SY250 ) ) ) )
= $true )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(198,plain,
! [SV42: $i,SV11: $i,SV60: $i,SV30: $i,SV52: $i] :
( ( ( ~ ( product @ SV52 @ SV30 @ SV60 ) )
= $true )
| ( ( ! [SY251: $i] :
( ~ ( sum @ SV11 @ SV52 @ SY251 )
| ! [SY252: $i] :
( ~ ( product @ SY251 @ SV30 @ SY252 )
| ( sum @ SV42 @ SV60 @ SY252 ) ) ) )
= $true )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(199,plain,
! [SV43: $i,SV12: $i,SV61: $i,SV31: $i,SV53: $i] :
( ( ( ~ ( product @ SV53 @ SV31 @ SV61 ) )
= $true )
| ( ( ! [SY253: $i] :
( ~ ( sum @ SV12 @ SV53 @ SY253 )
| ! [SY254: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY254 )
| ( product @ SY253 @ SV31 @ SY254 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(200,plain,
! [SV44: $i,SV32: $i,SV62: $i,SV54: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV54 @ SV62 ) )
= $true )
| ( ( ! [SY255: $i] :
( ~ ( product @ SV32 @ SV54 @ SY255 )
| ! [SY256: $i] :
( ~ ( sum @ SV13 @ SY255 @ SY256 )
| ( product @ SV44 @ SV62 @ SY256 ) ) ) )
= $true )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(201,plain,
! [SV45: $i,SV33: $i,SV63: $i,SV55: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV55 @ SV63 ) )
= $true )
| ( ( ! [SY257: $i] :
( ~ ( product @ SV33 @ SV55 @ SY257 )
| ! [SY258: $i] :
( ~ ( product @ SV45 @ SV63 @ SY258 )
| ( sum @ SV14 @ SY257 @ SY258 ) ) ) )
= $true )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(202,plain,
! [SV46: $i,SV15: $i,SV64: $i,SV34: $i,SV56: $i] :
( ( ( ~ ( sum @ SV56 @ SV34 @ SV64 ) )
= $true )
| ( ( ! [SY259: $i] :
( ~ ( product @ SV15 @ SV56 @ SY259 )
| ! [SY260: $i] :
( ~ ( sum @ SY259 @ SV34 @ SY260 )
| ( product @ SV46 @ SV64 @ SY260 ) ) ) )
= $true )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(203,plain,
! [SV47: $i,SV16: $i,SV65: $i,SV35: $i,SV57: $i] :
( ( ( ~ ( sum @ SV57 @ SV35 @ SV65 ) )
= $true )
| ( ( ! [SY261: $i] :
( ~ ( product @ SV16 @ SV57 @ SY261 )
| ! [SY262: $i] :
( ~ ( product @ SV47 @ SV65 @ SY262 )
| ( sum @ SY261 @ SV35 @ SY262 ) ) ) )
= $true )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(204,plain,
! [SV48: $i,SV66: $i,SV36: $i,SV21: $i] :
( ( ( sum @ SV21 @ SV36 @ SV66 )
= $false )
| ( ( SV48 = SV66 )
= $true )
| ( ( sum @ SV21 @ SV36 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(205,plain,
! [SV49: $i,SV67: $i,SV37: $i,SV22: $i] :
( ( ( product @ SV22 @ SV37 @ SV67 )
= $false )
| ( ( SV49 = SV67 )
= $true )
| ( ( product @ SV22 @ SV37 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(206,plain,
! [SV40: $i,SV28: $i,SV58: $i,SV50: $i,SV9: $i] :
( ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( ! [SY247: $i] :
( ~ ( sum @ SV28 @ SV50 @ SY247 )
| ! [SY248: $i] :
( ~ ( product @ SV9 @ SY247 @ SY248 )
| ( sum @ SV40 @ SV58 @ SY248 ) ) ) )
= $true )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(207,plain,
! [SV41: $i,SV29: $i,SV59: $i,SV51: $i,SV10: $i] :
( ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( ! [SY249: $i] :
( ~ ( sum @ SV29 @ SV51 @ SY249 )
| ! [SY250: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY250 )
| ( product @ SV10 @ SY249 @ SY250 ) ) ) )
= $true )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(208,plain,
! [SV42: $i,SV11: $i,SV60: $i,SV30: $i,SV52: $i] :
( ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( ! [SY251: $i] :
( ~ ( sum @ SV11 @ SV52 @ SY251 )
| ! [SY252: $i] :
( ~ ( product @ SY251 @ SV30 @ SY252 )
| ( sum @ SV42 @ SV60 @ SY252 ) ) ) )
= $true )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(209,plain,
! [SV43: $i,SV12: $i,SV61: $i,SV31: $i,SV53: $i] :
( ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( ! [SY253: $i] :
( ~ ( sum @ SV12 @ SV53 @ SY253 )
| ! [SY254: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY254 )
| ( product @ SY253 @ SV31 @ SY254 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(210,plain,
! [SV44: $i,SV32: $i,SV62: $i,SV54: $i,SV13: $i] :
( ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( ! [SY255: $i] :
( ~ ( product @ SV32 @ SV54 @ SY255 )
| ! [SY256: $i] :
( ~ ( sum @ SV13 @ SY255 @ SY256 )
| ( product @ SV44 @ SV62 @ SY256 ) ) ) )
= $true )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(211,plain,
! [SV45: $i,SV33: $i,SV63: $i,SV55: $i,SV14: $i] :
( ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( ! [SY257: $i] :
( ~ ( product @ SV33 @ SV55 @ SY257 )
| ! [SY258: $i] :
( ~ ( product @ SV45 @ SV63 @ SY258 )
| ( sum @ SV14 @ SY257 @ SY258 ) ) ) )
= $true )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV46: $i,SV15: $i,SV64: $i,SV34: $i,SV56: $i] :
( ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( ! [SY259: $i] :
( ~ ( product @ SV15 @ SV56 @ SY259 )
| ! [SY260: $i] :
( ~ ( sum @ SY259 @ SV34 @ SY260 )
| ( product @ SV46 @ SV64 @ SY260 ) ) ) )
= $true )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV47: $i,SV16: $i,SV65: $i,SV35: $i,SV57: $i] :
( ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( ! [SY261: $i] :
( ~ ( product @ SV16 @ SV57 @ SY261 )
| ! [SY262: $i] :
( ~ ( product @ SV47 @ SV65 @ SY262 )
| ( sum @ SY261 @ SV35 @ SY262 ) ) ) )
= $true )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV58: $i,SV40: $i,SV9: $i,SV68: $i,SV50: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV50 @ SV68 )
| ! [SY263: $i] :
( ~ ( product @ SV9 @ SV68 @ SY263 )
| ( sum @ SV40 @ SV58 @ SY263 ) ) )
= $true )
| ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(215,plain,
! [SV10: $i,SV59: $i,SV41: $i,SV69: $i,SV51: $i,SV29: $i] :
( ( ( ~ ( sum @ SV29 @ SV51 @ SV69 )
| ! [SY264: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY264 )
| ( product @ SV10 @ SV69 @ SY264 ) ) )
= $true )
| ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(216,plain,
! [SV60: $i,SV42: $i,SV30: $i,SV70: $i,SV52: $i,SV11: $i] :
( ( ( ~ ( sum @ SV11 @ SV52 @ SV70 )
| ! [SY265: $i] :
( ~ ( product @ SV70 @ SV30 @ SY265 )
| ( sum @ SV42 @ SV60 @ SY265 ) ) )
= $true )
| ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(217,plain,
! [SV31: $i,SV61: $i,SV43: $i,SV71: $i,SV53: $i,SV12: $i] :
( ( ( ~ ( sum @ SV12 @ SV53 @ SV71 )
| ! [SY266: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY266 )
| ( product @ SV71 @ SV31 @ SY266 ) ) )
= $true )
| ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(218,plain,
! [SV62: $i,SV44: $i,SV13: $i,SV72: $i,SV54: $i,SV32: $i] :
( ( ( ~ ( product @ SV32 @ SV54 @ SV72 )
| ! [SY267: $i] :
( ~ ( sum @ SV13 @ SV72 @ SY267 )
| ( product @ SV44 @ SV62 @ SY267 ) ) )
= $true )
| ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV14: $i,SV63: $i,SV45: $i,SV73: $i,SV55: $i,SV33: $i] :
( ( ( ~ ( product @ SV33 @ SV55 @ SV73 )
| ! [SY268: $i] :
( ~ ( product @ SV45 @ SV63 @ SY268 )
| ( sum @ SV14 @ SV73 @ SY268 ) ) )
= $true )
| ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV64: $i,SV46: $i,SV34: $i,SV74: $i,SV56: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV56 @ SV74 )
| ! [SY269: $i] :
( ~ ( sum @ SV74 @ SV34 @ SY269 )
| ( product @ SV46 @ SV64 @ SY269 ) ) )
= $true )
| ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV35: $i,SV65: $i,SV47: $i,SV75: $i,SV57: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV57 @ SV75 )
| ! [SY270: $i] :
( ~ ( product @ SV47 @ SV65 @ SY270 )
| ( sum @ SV75 @ SV35 @ SY270 ) ) )
= $true )
| ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(222,plain,
! [SV58: $i,SV40: $i,SV9: $i,SV68: $i,SV50: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV50 @ SV68 ) )
= $true )
| ( ( ! [SY263: $i] :
( ~ ( product @ SV9 @ SV68 @ SY263 )
| ( sum @ SV40 @ SV58 @ SY263 ) ) )
= $true )
| ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(223,plain,
! [SV10: $i,SV59: $i,SV41: $i,SV69: $i,SV51: $i,SV29: $i] :
( ( ( ~ ( sum @ SV29 @ SV51 @ SV69 ) )
= $true )
| ( ( ! [SY264: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY264 )
| ( product @ SV10 @ SV69 @ SY264 ) ) )
= $true )
| ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV60: $i,SV42: $i,SV30: $i,SV70: $i,SV52: $i,SV11: $i] :
( ( ( ~ ( sum @ SV11 @ SV52 @ SV70 ) )
= $true )
| ( ( ! [SY265: $i] :
( ~ ( product @ SV70 @ SV30 @ SY265 )
| ( sum @ SV42 @ SV60 @ SY265 ) ) )
= $true )
| ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV31: $i,SV61: $i,SV43: $i,SV71: $i,SV53: $i,SV12: $i] :
( ( ( ~ ( sum @ SV12 @ SV53 @ SV71 ) )
= $true )
| ( ( ! [SY266: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY266 )
| ( product @ SV71 @ SV31 @ SY266 ) ) )
= $true )
| ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV62: $i,SV44: $i,SV13: $i,SV72: $i,SV54: $i,SV32: $i] :
( ( ( ~ ( product @ SV32 @ SV54 @ SV72 ) )
= $true )
| ( ( ! [SY267: $i] :
( ~ ( sum @ SV13 @ SV72 @ SY267 )
| ( product @ SV44 @ SV62 @ SY267 ) ) )
= $true )
| ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV14: $i,SV63: $i,SV45: $i,SV73: $i,SV55: $i,SV33: $i] :
( ( ( ~ ( product @ SV33 @ SV55 @ SV73 ) )
= $true )
| ( ( ! [SY268: $i] :
( ~ ( product @ SV45 @ SV63 @ SY268 )
| ( sum @ SV14 @ SV73 @ SY268 ) ) )
= $true )
| ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV64: $i,SV46: $i,SV34: $i,SV74: $i,SV56: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV56 @ SV74 ) )
= $true )
| ( ( ! [SY269: $i] :
( ~ ( sum @ SV74 @ SV34 @ SY269 )
| ( product @ SV46 @ SV64 @ SY269 ) ) )
= $true )
| ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV35: $i,SV65: $i,SV47: $i,SV75: $i,SV57: $i,SV16: $i] :
( ( ( ~ ( product @ SV16 @ SV57 @ SV75 ) )
= $true )
| ( ( ! [SY270: $i] :
( ~ ( product @ SV47 @ SV65 @ SY270 )
| ( sum @ SV75 @ SV35 @ SY270 ) ) )
= $true )
| ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV58: $i,SV40: $i,SV9: $i,SV68: $i,SV50: $i,SV28: $i] :
( ( ( sum @ SV28 @ SV50 @ SV68 )
= $false )
| ( ( ! [SY263: $i] :
( ~ ( product @ SV9 @ SV68 @ SY263 )
| ( sum @ SV40 @ SV58 @ SY263 ) ) )
= $true )
| ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV10: $i,SV59: $i,SV41: $i,SV69: $i,SV51: $i,SV29: $i] :
( ( ( sum @ SV29 @ SV51 @ SV69 )
= $false )
| ( ( ! [SY264: $i] :
( ~ ( sum @ SV41 @ SV59 @ SY264 )
| ( product @ SV10 @ SV69 @ SY264 ) ) )
= $true )
| ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV60: $i,SV42: $i,SV30: $i,SV70: $i,SV52: $i,SV11: $i] :
( ( ( sum @ SV11 @ SV52 @ SV70 )
= $false )
| ( ( ! [SY265: $i] :
( ~ ( product @ SV70 @ SV30 @ SY265 )
| ( sum @ SV42 @ SV60 @ SY265 ) ) )
= $true )
| ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(233,plain,
! [SV31: $i,SV61: $i,SV43: $i,SV71: $i,SV53: $i,SV12: $i] :
( ( ( sum @ SV12 @ SV53 @ SV71 )
= $false )
| ( ( ! [SY266: $i] :
( ~ ( sum @ SV43 @ SV61 @ SY266 )
| ( product @ SV71 @ SV31 @ SY266 ) ) )
= $true )
| ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(234,plain,
! [SV62: $i,SV44: $i,SV13: $i,SV72: $i,SV54: $i,SV32: $i] :
( ( ( product @ SV32 @ SV54 @ SV72 )
= $false )
| ( ( ! [SY267: $i] :
( ~ ( sum @ SV13 @ SV72 @ SY267 )
| ( product @ SV44 @ SV62 @ SY267 ) ) )
= $true )
| ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(235,plain,
! [SV14: $i,SV63: $i,SV45: $i,SV73: $i,SV55: $i,SV33: $i] :
( ( ( product @ SV33 @ SV55 @ SV73 )
= $false )
| ( ( ! [SY268: $i] :
( ~ ( product @ SV45 @ SV63 @ SY268 )
| ( sum @ SV14 @ SV73 @ SY268 ) ) )
= $true )
| ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(236,plain,
! [SV64: $i,SV46: $i,SV34: $i,SV74: $i,SV56: $i,SV15: $i] :
( ( ( product @ SV15 @ SV56 @ SV74 )
= $false )
| ( ( ! [SY269: $i] :
( ~ ( sum @ SV74 @ SV34 @ SY269 )
| ( product @ SV46 @ SV64 @ SY269 ) ) )
= $true )
| ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(237,plain,
! [SV35: $i,SV65: $i,SV47: $i,SV75: $i,SV57: $i,SV16: $i] :
( ( ( product @ SV16 @ SV57 @ SV75 )
= $false )
| ( ( ! [SY270: $i] :
( ~ ( product @ SV47 @ SV65 @ SY270 )
| ( sum @ SV75 @ SV35 @ SY270 ) ) )
= $true )
| ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(238,plain,
! [SV50: $i,SV28: $i,SV58: $i,SV40: $i,SV76: $i,SV68: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV68 @ SV76 )
| ( sum @ SV40 @ SV58 @ SV76 ) )
= $true )
| ( ( sum @ SV28 @ SV50 @ SV68 )
= $false )
| ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(239,plain,
! [SV51: $i,SV29: $i,SV69: $i,SV10: $i,SV77: $i,SV59: $i,SV41: $i] :
( ( ( ~ ( sum @ SV41 @ SV59 @ SV77 )
| ( product @ SV10 @ SV69 @ SV77 ) )
= $true )
| ( ( sum @ SV29 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(240,plain,
! [SV52: $i,SV11: $i,SV60: $i,SV42: $i,SV78: $i,SV30: $i,SV70: $i] :
( ( ( ~ ( product @ SV70 @ SV30 @ SV78 )
| ( sum @ SV42 @ SV60 @ SV78 ) )
= $true )
| ( ( sum @ SV11 @ SV52 @ SV70 )
= $false )
| ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(241,plain,
! [SV53: $i,SV12: $i,SV31: $i,SV71: $i,SV79: $i,SV61: $i,SV43: $i] :
( ( ( ~ ( sum @ SV43 @ SV61 @ SV79 )
| ( product @ SV71 @ SV31 @ SV79 ) )
= $true )
| ( ( sum @ SV12 @ SV53 @ SV71 )
= $false )
| ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(242,plain,
! [SV54: $i,SV32: $i,SV62: $i,SV44: $i,SV80: $i,SV72: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV72 @ SV80 )
| ( product @ SV44 @ SV62 @ SV80 ) )
= $true )
| ( ( product @ SV32 @ SV54 @ SV72 )
= $false )
| ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(243,plain,
! [SV55: $i,SV33: $i,SV73: $i,SV14: $i,SV81: $i,SV63: $i,SV45: $i] :
( ( ( ~ ( product @ SV45 @ SV63 @ SV81 )
| ( sum @ SV14 @ SV73 @ SV81 ) )
= $true )
| ( ( product @ SV33 @ SV55 @ SV73 )
= $false )
| ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(244,plain,
! [SV56: $i,SV15: $i,SV64: $i,SV46: $i,SV82: $i,SV34: $i,SV74: $i] :
( ( ( ~ ( sum @ SV74 @ SV34 @ SV82 )
| ( product @ SV46 @ SV64 @ SV82 ) )
= $true )
| ( ( product @ SV15 @ SV56 @ SV74 )
= $false )
| ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(245,plain,
! [SV57: $i,SV16: $i,SV35: $i,SV75: $i,SV83: $i,SV65: $i,SV47: $i] :
( ( ( ~ ( product @ SV47 @ SV65 @ SV83 )
| ( sum @ SV75 @ SV35 @ SV83 ) )
= $true )
| ( ( product @ SV16 @ SV57 @ SV75 )
= $false )
| ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(246,plain,
! [SV50: $i,SV28: $i,SV58: $i,SV40: $i,SV76: $i,SV68: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV68 @ SV76 ) )
= $true )
| ( ( sum @ SV40 @ SV58 @ SV76 )
= $true )
| ( ( sum @ SV28 @ SV50 @ SV68 )
= $false )
| ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(247,plain,
! [SV51: $i,SV29: $i,SV69: $i,SV10: $i,SV77: $i,SV59: $i,SV41: $i] :
( ( ( ~ ( sum @ SV41 @ SV59 @ SV77 ) )
= $true )
| ( ( product @ SV10 @ SV69 @ SV77 )
= $true )
| ( ( sum @ SV29 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(248,plain,
! [SV52: $i,SV11: $i,SV60: $i,SV42: $i,SV78: $i,SV30: $i,SV70: $i] :
( ( ( ~ ( product @ SV70 @ SV30 @ SV78 ) )
= $true )
| ( ( sum @ SV42 @ SV60 @ SV78 )
= $true )
| ( ( sum @ SV11 @ SV52 @ SV70 )
= $false )
| ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(249,plain,
! [SV53: $i,SV12: $i,SV31: $i,SV71: $i,SV79: $i,SV61: $i,SV43: $i] :
( ( ( ~ ( sum @ SV43 @ SV61 @ SV79 ) )
= $true )
| ( ( product @ SV71 @ SV31 @ SV79 )
= $true )
| ( ( sum @ SV12 @ SV53 @ SV71 )
= $false )
| ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(250,plain,
! [SV54: $i,SV32: $i,SV62: $i,SV44: $i,SV80: $i,SV72: $i,SV13: $i] :
( ( ( ~ ( sum @ SV13 @ SV72 @ SV80 ) )
= $true )
| ( ( product @ SV44 @ SV62 @ SV80 )
= $true )
| ( ( product @ SV32 @ SV54 @ SV72 )
= $false )
| ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(251,plain,
! [SV55: $i,SV33: $i,SV73: $i,SV14: $i,SV81: $i,SV63: $i,SV45: $i] :
( ( ( ~ ( product @ SV45 @ SV63 @ SV81 ) )
= $true )
| ( ( sum @ SV14 @ SV73 @ SV81 )
= $true )
| ( ( product @ SV33 @ SV55 @ SV73 )
= $false )
| ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV56: $i,SV15: $i,SV64: $i,SV46: $i,SV82: $i,SV34: $i,SV74: $i] :
( ( ( ~ ( sum @ SV74 @ SV34 @ SV82 ) )
= $true )
| ( ( product @ SV46 @ SV64 @ SV82 )
= $true )
| ( ( product @ SV15 @ SV56 @ SV74 )
= $false )
| ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(253,plain,
! [SV57: $i,SV16: $i,SV35: $i,SV75: $i,SV83: $i,SV65: $i,SV47: $i] :
( ( ( ~ ( product @ SV47 @ SV65 @ SV83 ) )
= $true )
| ( ( sum @ SV75 @ SV35 @ SV83 )
= $true )
| ( ( product @ SV16 @ SV57 @ SV75 )
= $false )
| ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV50: $i,SV28: $i,SV58: $i,SV40: $i,SV76: $i,SV68: $i,SV9: $i] :
( ( ( product @ SV9 @ SV68 @ SV76 )
= $false )
| ( ( sum @ SV40 @ SV58 @ SV76 )
= $true )
| ( ( sum @ SV28 @ SV50 @ SV68 )
= $false )
| ( ( product @ SV9 @ SV50 @ SV58 )
= $false )
| ( ( product @ SV9 @ SV28 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(255,plain,
! [SV51: $i,SV29: $i,SV69: $i,SV10: $i,SV77: $i,SV59: $i,SV41: $i] :
( ( ( sum @ SV41 @ SV59 @ SV77 )
= $false )
| ( ( product @ SV10 @ SV69 @ SV77 )
= $true )
| ( ( sum @ SV29 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV10 @ SV51 @ SV59 )
= $false )
| ( ( product @ SV10 @ SV29 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(256,plain,
! [SV52: $i,SV11: $i,SV60: $i,SV42: $i,SV78: $i,SV30: $i,SV70: $i] :
( ( ( product @ SV70 @ SV30 @ SV78 )
= $false )
| ( ( sum @ SV42 @ SV60 @ SV78 )
= $true )
| ( ( sum @ SV11 @ SV52 @ SV70 )
= $false )
| ( ( product @ SV52 @ SV30 @ SV60 )
= $false )
| ( ( product @ SV11 @ SV30 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(257,plain,
! [SV53: $i,SV12: $i,SV31: $i,SV71: $i,SV79: $i,SV61: $i,SV43: $i] :
( ( ( sum @ SV43 @ SV61 @ SV79 )
= $false )
| ( ( product @ SV71 @ SV31 @ SV79 )
= $true )
| ( ( sum @ SV12 @ SV53 @ SV71 )
= $false )
| ( ( product @ SV53 @ SV31 @ SV61 )
= $false )
| ( ( product @ SV12 @ SV31 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(258,plain,
! [SV54: $i,SV32: $i,SV62: $i,SV44: $i,SV80: $i,SV72: $i,SV13: $i] :
( ( ( sum @ SV13 @ SV72 @ SV80 )
= $false )
| ( ( product @ SV44 @ SV62 @ SV80 )
= $true )
| ( ( product @ SV32 @ SV54 @ SV72 )
= $false )
| ( ( sum @ SV13 @ SV54 @ SV62 )
= $false )
| ( ( sum @ SV13 @ SV32 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(259,plain,
! [SV55: $i,SV33: $i,SV73: $i,SV14: $i,SV81: $i,SV63: $i,SV45: $i] :
( ( ( product @ SV45 @ SV63 @ SV81 )
= $false )
| ( ( sum @ SV14 @ SV73 @ SV81 )
= $true )
| ( ( product @ SV33 @ SV55 @ SV73 )
= $false )
| ( ( sum @ SV14 @ SV55 @ SV63 )
= $false )
| ( ( sum @ SV14 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(260,plain,
! [SV56: $i,SV15: $i,SV64: $i,SV46: $i,SV82: $i,SV34: $i,SV74: $i] :
( ( ( sum @ SV74 @ SV34 @ SV82 )
= $false )
| ( ( product @ SV46 @ SV64 @ SV82 )
= $true )
| ( ( product @ SV15 @ SV56 @ SV74 )
= $false )
| ( ( sum @ SV56 @ SV34 @ SV64 )
= $false )
| ( ( sum @ SV15 @ SV34 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(261,plain,
! [SV57: $i,SV16: $i,SV35: $i,SV75: $i,SV83: $i,SV65: $i,SV47: $i] :
( ( ( product @ SV47 @ SV65 @ SV83 )
= $false )
| ( ( sum @ SV75 @ SV35 @ SV83 )
= $true )
| ( ( product @ SV16 @ SV57 @ SV75 )
= $false )
| ( ( sum @ SV57 @ SV35 @ SV65 )
= $false )
| ( ( sum @ SV16 @ SV35 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(262,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[72,261,260,259,258,257,256,255,254,205,204,165,164,127,126,125,124,121,120,119,118,109,108,107,106,101,75,74,73]) ).
thf(263,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : BOO013-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 23:18:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.38
% 0.12/0.38 No.of.Axioms: 28
% 0.12/0.38
% 0.12/0.38 Length.of.Defs: 0
% 0.12/0.38
% 0.12/0.38 Contains.Choice.Funs: false
% 0.19/0.42 .
% 0.19/0.42 (rf:0,axioms:28,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:30,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 1.81/2.01
% 1.81/2.01 ********************************
% 1.81/2.01 * All subproblems solved! *
% 1.81/2.01 ********************************
% 1.81/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:28,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:262,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.81/2.04
% 1.81/2.04 %**** Beginning of derivation protocol ****
% 1.81/2.04 % SZS output start CNFRefutation
% See solution above
% 1.81/2.04
% 1.81/2.04 %**** End of derivation protocol ****
% 1.81/2.04 %**** no. of clauses in derivation: 263 ****
% 1.81/2.04 %**** clause counter: 262 ****
% 1.81/2.04
% 1.81/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:28,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:262,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------