TSTP Solution File: RNG006-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG006-1 : 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 : Mon Jul 18 20:33:55 EDT 2022
% Result : Unsatisfiable 23.26s 23.49s
% Output : CNFRefutation 23.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 39
% Syntax : Number of formulae : 259 ( 142 unt; 13 typ; 0 def)
% Number of atoms : 1624 ( 425 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3463 ( 435 ~; 576 |; 0 &;2452 @)
% ( 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 : 16 ( 13 usr; 10 con; 0-3 aty)
% Number of variables : 1144 ( 0 ^1144 !; 0 ?;1144 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aPb,type,
aPb: $i ).
thf(tp_aPb_S_IaPc,type,
aPb_S_IaPc: $i ).
thf(tp_aPc,type,
aPc: $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_bS_Ic,type,
bS_Ic: $i ).
thf(tp_c,type,
c: $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,
! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma3) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ ( additive_inverse @ A ) @ B @ ( additive_inverse @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma2) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ A @ ( additive_inverse @ B ) @ ( additive_inverse @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma1) ).
thf(4,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(5,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(6,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
thf(7,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(8,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(9,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(10,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(11,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(12,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(13,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(14,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(15,axiom,
! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
thf(16,axiom,
! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(17,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
thf(18,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(19,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
thf(20,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
thf(21,axiom,
sum @ aPb @ ( additive_inverse @ aPc ) @ aPb_S_IaPc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
thf(22,axiom,
product @ a @ c @ aPc,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
thf(23,axiom,
product @ a @ b @ aPb,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
thf(24,axiom,
sum @ b @ ( additive_inverse @ c ) @ bS_Ic,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
thf(25,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(26,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[25]) ).
thf(27,negated_conjecture,
~ ( product @ a @ bS_Ic @ aPb_S_IaPc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
thf(28,plain,
$false = $false,
inference(unfold_def,[status(thm)],[26]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ ( additive_inverse @ A ) @ B @ ( additive_inverse @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ A @ ( additive_inverse @ B ) @ ( additive_inverse @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(32,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)],[4]) ).
thf(33,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)],[5]) ).
thf(34,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)],[6]) ).
thf(35,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)],[7]) ).
thf(36,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)],[8]) ).
thf(37,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)],[9]) ).
thf(38,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)],[10]) ).
thf(39,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)],[11]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(41,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)],[13]) ).
thf(42,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)],[14]) ).
thf(43,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(47,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(48,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(49,plain,
( ( sum @ aPb @ ( additive_inverse @ aPc ) @ aPb_S_IaPc )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(50,plain,
( ( product @ a @ c @ aPc )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(51,plain,
( ( product @ a @ b @ aPb )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(52,plain,
( ( sum @ b @ ( additive_inverse @ c ) @ bS_Ic )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(53,plain,
( ( ~ ( product @ a @ bS_Ic @ aPb_S_IaPc ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(57,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)],[34]) ).
thf(58,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)],[35]) ).
thf(59,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)],[36]) ).
thf(60,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)],[37]) ).
thf(61,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)],[38]) ).
thf(62,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)],[39]) ).
thf(63,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)],[41]) ).
thf(64,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)],[42]) ).
thf(65,plain,
( ( ~ ( product @ a @ bS_Ic @ aPb_S_IaPc ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(66,plain,
( ( sum @ b @ ( additive_inverse @ c ) @ bS_Ic )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(67,plain,
( ( product @ a @ b @ aPb )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(68,plain,
( ( product @ a @ c @ aPc )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(69,plain,
( ( sum @ aPb @ ( additive_inverse @ aPc ) @ aPb_S_IaPc )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(70,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(71,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(74,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(75,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(76,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)],[64]) ).
thf(77,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)],[63]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(79,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)],[62]) ).
thf(80,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)],[61]) ).
thf(81,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)],[60]) ).
thf(82,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)],[59]) ).
thf(83,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)],[58]) ).
thf(84,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)],[57]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ A @ ( additive_inverse @ B ) @ ( additive_inverse @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ ( additive_inverse @ A ) @ B @ ( additive_inverse @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(89,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( product @ A @ B @ C )
| ( product @ ( additive_inverse @ A ) @ ( additive_inverse @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(90,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(91,plain,
( ( product @ a @ bS_Ic @ aPb_S_IaPc )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(92,plain,
! [SV1: $i] :
( ( sum @ additive_identity @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV2: $i] :
( ( sum @ SV2 @ additive_identity @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV3: $i] :
( ( ! [SY80: $i] : ( product @ SV3 @ SY80 @ ( multiply @ SV3 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(95,plain,
! [SV4: $i] :
( ( ! [SY81: $i] : ( sum @ SV4 @ SY81 @ ( add @ SV4 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(96,plain,
! [SV5: $i] :
( ( sum @ ( additive_inverse @ SV5 ) @ SV5 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(97,plain,
! [SV6: $i] :
( ( sum @ SV6 @ ( additive_inverse @ SV6 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV7: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i] :
( ~ ( sum @ SV7 @ SY82 @ SY83 )
| ! [SY85: $i] :
( ~ ( sum @ SY82 @ SY84 @ SY85 )
| ! [SY86: $i] :
( ~ ( sum @ SY83 @ SY84 @ SY86 )
| ( sum @ SV7 @ SY85 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV8: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i] :
( ~ ( sum @ SV8 @ SY87 @ SY88 )
| ! [SY90: $i] :
( ~ ( sum @ SY87 @ SY89 @ SY90 )
| ! [SY91: $i] :
( ~ ( sum @ SV8 @ SY90 @ SY91 )
| ( sum @ SY88 @ SY89 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
! [SV9: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( sum @ SV9 @ SY92 @ SY93 )
| ( sum @ SY92 @ SV9 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(101,plain,
! [SV10: $i] :
( ( ! [SY94: $i,SY95: $i,SY96: $i] :
( ~ ( product @ SV10 @ SY94 @ SY95 )
| ! [SY97: $i] :
( ~ ( product @ SY94 @ SY96 @ SY97 )
| ! [SY98: $i] :
( ~ ( product @ SY95 @ SY96 @ SY98 )
| ( product @ SV10 @ SY97 @ SY98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(102,plain,
! [SV11: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i] :
( ~ ( product @ SV11 @ SY99 @ SY100 )
| ! [SY102: $i] :
( ~ ( product @ SY99 @ SY101 @ SY102 )
| ! [SY103: $i] :
( ~ ( product @ SV11 @ SY102 @ SY103 )
| ( product @ SY100 @ SY101 @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(103,plain,
! [SV12: $i] :
( ( ! [SY104: $i,SY105: $i,SY106: $i,SY107: $i] :
( ~ ( product @ SV12 @ SY104 @ SY105 )
| ~ ( product @ SV12 @ SY106 @ SY107 )
| ! [SY108: $i] :
( ~ ( sum @ SY104 @ SY106 @ SY108 )
| ! [SY109: $i] :
( ~ ( product @ SV12 @ SY108 @ SY109 )
| ( sum @ SY105 @ SY107 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(104,plain,
! [SV13: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i,SY113: $i] :
( ~ ( product @ SV13 @ SY110 @ SY111 )
| ~ ( product @ SV13 @ SY112 @ SY113 )
| ! [SY114: $i] :
( ~ ( sum @ SY110 @ SY112 @ SY114 )
| ! [SY115: $i] :
( ~ ( sum @ SY111 @ SY113 @ SY115 )
| ( product @ SV13 @ SY114 @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV14: $i] :
( ( ! [SY116: $i,SY117: $i,SY118: $i,SY119: $i] :
( ~ ( product @ SV14 @ SY116 @ SY117 )
| ~ ( product @ SY118 @ SY116 @ SY119 )
| ! [SY120: $i] :
( ~ ( sum @ SV14 @ SY118 @ SY120 )
| ! [V4: $i] :
( ~ ( product @ SY120 @ SY116 @ V4 )
| ( sum @ SY117 @ SY119 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV15: $i] :
( ( ! [SY122: $i,SY123: $i,SY124: $i,SY125: $i] :
( ~ ( product @ SV15 @ SY122 @ SY123 )
| ~ ( product @ SY124 @ SY122 @ SY125 )
| ! [SY126: $i] :
( ~ ( sum @ SV15 @ SY124 @ SY126 )
| ! [V4: $i] :
( ~ ( sum @ SY123 @ SY125 @ V4 )
| ( product @ SY126 @ SY122 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(107,plain,
! [SV16: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( sum @ SV16 @ SY128 @ SY129 )
| ! [SY130: $i] :
( ~ ( sum @ SV16 @ SY128 @ SY130 )
| ( SY129 = SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV17: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ~ ( product @ SV17 @ SY131 @ SY132 )
| ! [SY133: $i] :
( ~ ( product @ SV17 @ SY131 @ SY133 )
| ( SY132 = SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV18: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( product @ SV18 @ SY134 @ SY135 )
| ( product @ SV18 @ ( additive_inverse @ SY134 ) @ ( additive_inverse @ SY135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(110,plain,
! [SV19: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ~ ( product @ SV19 @ SY136 @ SY137 )
| ( product @ ( additive_inverse @ SV19 ) @ SY136 @ ( additive_inverse @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(111,plain,
! [SV20: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ( product @ SV20 @ SY138 @ SY139 )
| ( product @ ( additive_inverse @ SV20 ) @ ( additive_inverse @ SY138 ) @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(112,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(113,plain,
! [SV21: $i,SV3: $i] :
( ( product @ SV3 @ SV21 @ ( multiply @ SV3 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV22: $i,SV4: $i] :
( ( sum @ SV4 @ SV22 @ ( add @ SV4 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( sum @ SV7 @ SV23 @ SY140 )
| ! [SY142: $i] :
( ~ ( sum @ SV23 @ SY141 @ SY142 )
| ! [SY86: $i] :
( ~ ( sum @ SY140 @ SY141 @ SY86 )
| ( sum @ SV7 @ SY142 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV24: $i,SV8: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ~ ( sum @ SV8 @ SV24 @ SY144 )
| ! [SY146: $i] :
( ~ ( sum @ SV24 @ SY145 @ SY146 )
| ! [SY91: $i] :
( ~ ( sum @ SV8 @ SY146 @ SY91 )
| ( sum @ SY144 @ SY145 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV25: $i,SV9: $i] :
( ( ! [SY148: $i] :
( ~ ( sum @ SV9 @ SV25 @ SY148 )
| ( sum @ SV25 @ SV9 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ( product @ SV10 @ SV26 @ SY149 )
| ! [SY151: $i] :
( ~ ( product @ SV26 @ SY150 @ SY151 )
| ! [SY98: $i] :
( ~ ( product @ SY149 @ SY150 @ SY98 )
| ( product @ SV10 @ SY151 @ SY98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV27: $i,SV11: $i] :
( ( ! [SY153: $i,SY154: $i] :
( ~ ( product @ SV11 @ SV27 @ SY153 )
| ! [SY155: $i] :
( ~ ( product @ SV27 @ SY154 @ SY155 )
| ! [SY103: $i] :
( ~ ( product @ SV11 @ SY155 @ SY103 )
| ( product @ SY153 @ SY154 @ SY103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV28: $i,SV12: $i] :
( ( ! [SY157: $i,SY158: $i,SY159: $i] :
( ~ ( product @ SV12 @ SV28 @ SY157 )
| ~ ( product @ SV12 @ SY158 @ SY159 )
| ! [SY160: $i] :
( ~ ( sum @ SV28 @ SY158 @ SY160 )
| ! [SY109: $i] :
( ~ ( product @ SV12 @ SY160 @ SY109 )
| ( sum @ SY157 @ SY159 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV29: $i,SV13: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i] :
( ~ ( product @ SV13 @ SV29 @ SY162 )
| ~ ( product @ SV13 @ SY163 @ SY164 )
| ! [SY165: $i] :
( ~ ( sum @ SV29 @ SY163 @ SY165 )
| ! [SY115: $i] :
( ~ ( sum @ SY162 @ SY164 @ SY115 )
| ( product @ SV13 @ SY165 @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV30: $i,SV14: $i] :
( ( ! [SY167: $i,SY168: $i,SY169: $i] :
( ~ ( product @ SV14 @ SV30 @ SY167 )
| ~ ( product @ SY168 @ SV30 @ SY169 )
| ! [SY170: $i] :
( ~ ( sum @ SV14 @ SY168 @ SY170 )
| ! [SY171: $i] :
( ~ ( product @ SY170 @ SV30 @ SY171 )
| ( sum @ SY167 @ SY169 @ SY171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV31: $i,SV15: $i] :
( ( ! [SY172: $i,SY173: $i,SY174: $i] :
( ~ ( product @ SV15 @ SV31 @ SY172 )
| ~ ( product @ SY173 @ SV31 @ SY174 )
| ! [SY175: $i] :
( ~ ( sum @ SV15 @ SY173 @ SY175 )
| ! [SY176: $i] :
( ~ ( sum @ SY172 @ SY174 @ SY176 )
| ( product @ SY175 @ SV31 @ SY176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV32: $i,SV16: $i] :
( ( ! [SY177: $i] :
( ~ ( sum @ SV16 @ SV32 @ SY177 )
| ! [SY178: $i] :
( ~ ( sum @ SV16 @ SV32 @ SY178 )
| ( SY177 = SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(125,plain,
! [SV33: $i,SV17: $i] :
( ( ! [SY179: $i] :
( ~ ( product @ SV17 @ SV33 @ SY179 )
| ! [SY180: $i] :
( ~ ( product @ SV17 @ SV33 @ SY180 )
| ( SY179 = SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(126,plain,
! [SV34: $i,SV18: $i] :
( ( ! [SY181: $i] :
( ~ ( product @ SV18 @ SV34 @ SY181 )
| ( product @ SV18 @ ( additive_inverse @ SV34 ) @ ( additive_inverse @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV35: $i,SV19: $i] :
( ( ! [SY182: $i] :
( ~ ( product @ SV19 @ SV35 @ SY182 )
| ( product @ ( additive_inverse @ SV19 ) @ SV35 @ ( additive_inverse @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(128,plain,
! [SV36: $i,SV20: $i] :
( ( ! [SY183: $i] :
( ~ ( product @ SV20 @ SV36 @ SY183 )
| ( product @ ( additive_inverse @ SV20 ) @ ( additive_inverse @ SV36 ) @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(129,plain,
! [SV37: $i,SV23: $i,SV7: $i] :
( ( ! [SY184: $i] :
( ~ ( sum @ SV7 @ SV23 @ SV37 )
| ! [SY185: $i] :
( ~ ( sum @ SV23 @ SY184 @ SY185 )
| ! [SY186: $i] :
( ~ ( sum @ SV37 @ SY184 @ SY186 )
| ( sum @ SV7 @ SY185 @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV38: $i,SV24: $i,SV8: $i] :
( ( ! [SY187: $i] :
( ~ ( sum @ SV8 @ SV24 @ SV38 )
| ! [SY188: $i] :
( ~ ( sum @ SV24 @ SY187 @ SY188 )
| ! [SY189: $i] :
( ~ ( sum @ SV8 @ SY188 @ SY189 )
| ( sum @ SV38 @ SY187 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV39: $i,SV25: $i,SV9: $i] :
( ( ~ ( sum @ SV9 @ SV25 @ SV39 )
| ( sum @ SV25 @ SV9 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV40: $i,SV26: $i,SV10: $i] :
( ( ! [SY190: $i] :
( ~ ( product @ SV10 @ SV26 @ SV40 )
| ! [SY191: $i] :
( ~ ( product @ SV26 @ SY190 @ SY191 )
| ! [SY192: $i] :
( ~ ( product @ SV40 @ SY190 @ SY192 )
| ( product @ SV10 @ SY191 @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV41: $i,SV27: $i,SV11: $i] :
( ( ! [SY193: $i] :
( ~ ( product @ SV11 @ SV27 @ SV41 )
| ! [SY194: $i] :
( ~ ( product @ SV27 @ SY193 @ SY194 )
| ! [SY195: $i] :
( ~ ( product @ SV11 @ SY194 @ SY195 )
| ( product @ SV41 @ SY193 @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV42: $i,SV28: $i,SV12: $i] :
( ( ! [SY196: $i,SY197: $i] :
( ~ ( product @ SV12 @ SV28 @ SV42 )
| ~ ( product @ SV12 @ SY196 @ SY197 )
| ! [SY198: $i] :
( ~ ( sum @ SV28 @ SY196 @ SY198 )
| ! [SY199: $i] :
( ~ ( product @ SV12 @ SY198 @ SY199 )
| ( sum @ SV42 @ SY197 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV43: $i,SV29: $i,SV13: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ~ ( product @ SV13 @ SV29 @ SV43 )
| ~ ( product @ SV13 @ SY200 @ SY201 )
| ! [SY202: $i] :
( ~ ( sum @ SV29 @ SY200 @ SY202 )
| ! [SY203: $i] :
( ~ ( sum @ SV43 @ SY201 @ SY203 )
| ( product @ SV13 @ SY202 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV44: $i,SV30: $i,SV14: $i] :
( ( ! [SY204: $i,SY205: $i] :
( ~ ( product @ SV14 @ SV30 @ SV44 )
| ~ ( product @ SY204 @ SV30 @ SY205 )
| ! [SY206: $i] :
( ~ ( sum @ SV14 @ SY204 @ SY206 )
| ! [SY207: $i] :
( ~ ( product @ SY206 @ SV30 @ SY207 )
| ( sum @ SV44 @ SY205 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV45: $i,SV31: $i,SV15: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ~ ( product @ SV15 @ SV31 @ SV45 )
| ~ ( product @ SY208 @ SV31 @ SY209 )
| ! [SY210: $i] :
( ~ ( sum @ SV15 @ SY208 @ SY210 )
| ! [SY211: $i] :
( ~ ( sum @ SV45 @ SY209 @ SY211 )
| ( product @ SY210 @ SV31 @ SY211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV46: $i,SV32: $i,SV16: $i] :
( ( ~ ( sum @ SV16 @ SV32 @ SV46 )
| ! [SY212: $i] :
( ~ ( sum @ SV16 @ SV32 @ SY212 )
| ( SV46 = SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV47: $i,SV33: $i,SV17: $i] :
( ( ~ ( product @ SV17 @ SV33 @ SV47 )
| ! [SY213: $i] :
( ~ ( product @ SV17 @ SV33 @ SY213 )
| ( SV47 = SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV48: $i,SV34: $i,SV18: $i] :
( ( ~ ( product @ SV18 @ SV34 @ SV48 )
| ( product @ SV18 @ ( additive_inverse @ SV34 ) @ ( additive_inverse @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV49: $i,SV35: $i,SV19: $i] :
( ( ~ ( product @ SV19 @ SV35 @ SV49 )
| ( product @ ( additive_inverse @ SV19 ) @ SV35 @ ( additive_inverse @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV50: $i,SV36: $i,SV20: $i] :
( ( ~ ( product @ SV20 @ SV36 @ SV50 )
| ( product @ ( additive_inverse @ SV20 ) @ ( additive_inverse @ SV36 ) @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV51: $i,SV37: $i,SV23: $i,SV7: $i] :
( ( ~ ( sum @ SV7 @ SV23 @ SV37 )
| ! [SY214: $i] :
( ~ ( sum @ SV23 @ SV51 @ SY214 )
| ! [SY215: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY215 )
| ( sum @ SV7 @ SY214 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV52: $i,SV38: $i,SV24: $i,SV8: $i] :
( ( ~ ( sum @ SV8 @ SV24 @ SV38 )
| ! [SY216: $i] :
( ~ ( sum @ SV24 @ SV52 @ SY216 )
| ! [SY217: $i] :
( ~ ( sum @ SV8 @ SY216 @ SY217 )
| ( sum @ SV38 @ SV52 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV39: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( sum @ SV9 @ SV25 @ SV39 ) )
= $true )
| ( ( sum @ SV25 @ SV9 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV53: $i,SV40: $i,SV26: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV26 @ SV40 )
| ! [SY218: $i] :
( ~ ( product @ SV26 @ SV53 @ SY218 )
| ! [SY219: $i] :
( ~ ( product @ SV40 @ SV53 @ SY219 )
| ( product @ SV10 @ SY218 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV54: $i,SV41: $i,SV27: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV27 @ SV41 )
| ! [SY220: $i] :
( ~ ( product @ SV27 @ SV54 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SV11 @ SY220 @ SY221 )
| ( product @ SV41 @ SV54 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV55: $i,SV42: $i,SV28: $i,SV12: $i] :
( ( ! [SY222: $i] :
( ~ ( product @ SV12 @ SV28 @ SV42 )
| ~ ( product @ SV12 @ SV55 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV28 @ SV55 @ SY223 )
| ! [SY199: $i] :
( ~ ( product @ SV12 @ SY223 @ SY199 )
| ( sum @ SV42 @ SY222 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV56: $i,SV43: $i,SV29: $i,SV13: $i] :
( ( ! [SY225: $i] :
( ~ ( product @ SV13 @ SV29 @ SV43 )
| ~ ( product @ SV13 @ SV56 @ SY225 )
| ! [SY226: $i] :
( ~ ( sum @ SV29 @ SV56 @ SY226 )
| ! [SY203: $i] :
( ~ ( sum @ SV43 @ SY225 @ SY203 )
| ( product @ SV13 @ SY226 @ SY203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV57: $i,SV44: $i,SV30: $i,SV14: $i] :
( ( ! [SY228: $i] :
( ~ ( product @ SV14 @ SV30 @ SV44 )
| ~ ( product @ SV57 @ SV30 @ SY228 )
| ! [SY229: $i] :
( ~ ( sum @ SV14 @ SV57 @ SY229 )
| ! [SY207: $i] :
( ~ ( product @ SY229 @ SV30 @ SY207 )
| ( sum @ SV44 @ SY228 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV58: $i,SV45: $i,SV31: $i,SV15: $i] :
( ( ! [SY231: $i] :
( ~ ( product @ SV15 @ SV31 @ SV45 )
| ~ ( product @ SV58 @ SV31 @ SY231 )
| ! [SY232: $i] :
( ~ ( sum @ SV15 @ SV58 @ SY232 )
| ! [SY211: $i] :
( ~ ( sum @ SV45 @ SY231 @ SY211 )
| ( product @ SY232 @ SV31 @ SY211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV46: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV32 @ SV46 ) )
= $true )
| ( ( ! [SY212: $i] :
( ~ ( sum @ SV16 @ SV32 @ SY212 )
| ( SV46 = SY212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV47: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV33 @ SV47 ) )
= $true )
| ( ( ! [SY213: $i] :
( ~ ( product @ SV17 @ SV33 @ SY213 )
| ( SV47 = SY213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV48: $i,SV34: $i,SV18: $i] :
( ( ( ~ ( product @ SV18 @ SV34 @ SV48 ) )
= $true )
| ( ( product @ SV18 @ ( additive_inverse @ SV34 ) @ ( additive_inverse @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV49: $i,SV35: $i,SV19: $i] :
( ( ( ~ ( product @ SV19 @ SV35 @ SV49 ) )
= $true )
| ( ( product @ ( additive_inverse @ SV19 ) @ SV35 @ ( additive_inverse @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV50: $i,SV36: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV36 @ SV50 ) )
= $true )
| ( ( product @ ( additive_inverse @ SV20 ) @ ( additive_inverse @ SV36 ) @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV51: $i,SV37: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( sum @ SV7 @ SV23 @ SV37 ) )
= $true )
| ( ( ! [SY214: $i] :
( ~ ( sum @ SV23 @ SV51 @ SY214 )
| ! [SY215: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY215 )
| ( sum @ SV7 @ SY214 @ SY215 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV52: $i,SV38: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV24 @ SV38 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( sum @ SV24 @ SV52 @ SY216 )
| ! [SY217: $i] :
( ~ ( sum @ SV8 @ SY216 @ SY217 )
| ( sum @ SV38 @ SV52 @ SY217 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV39: $i,SV25: $i,SV9: $i] :
( ( ( sum @ SV9 @ SV25 @ SV39 )
= $false )
| ( ( sum @ SV25 @ SV9 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(160,plain,
! [SV53: $i,SV40: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV26 @ SV40 ) )
= $true )
| ( ( ! [SY218: $i] :
( ~ ( product @ SV26 @ SV53 @ SY218 )
| ! [SY219: $i] :
( ~ ( product @ SV40 @ SV53 @ SY219 )
| ( product @ SV10 @ SY218 @ SY219 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV54: $i,SV41: $i,SV27: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV27 @ SV41 ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( product @ SV27 @ SV54 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SV11 @ SY220 @ SY221 )
| ( product @ SV41 @ SV54 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(162,plain,
! [SV59: $i,SV55: $i,SV42: $i,SV28: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV28 @ SV42 )
| ~ ( product @ SV12 @ SV55 @ SV59 )
| ! [SY234: $i] :
( ~ ( sum @ SV28 @ SV55 @ SY234 )
| ! [SY235: $i] :
( ~ ( product @ SV12 @ SY234 @ SY235 )
| ( sum @ SV42 @ SV59 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV60: $i,SV56: $i,SV43: $i,SV29: $i,SV13: $i] :
( ( ~ ( product @ SV13 @ SV29 @ SV43 )
| ~ ( product @ SV13 @ SV56 @ SV60 )
| ! [SY236: $i] :
( ~ ( sum @ SV29 @ SV56 @ SY236 )
| ! [SY237: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY237 )
| ( product @ SV13 @ SY236 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV61: $i,SV57: $i,SV44: $i,SV30: $i,SV14: $i] :
( ( ~ ( product @ SV14 @ SV30 @ SV44 )
| ~ ( product @ SV57 @ SV30 @ SV61 )
| ! [SY238: $i] :
( ~ ( sum @ SV14 @ SV57 @ SY238 )
| ! [SY239: $i] :
( ~ ( product @ SY238 @ SV30 @ SY239 )
| ( sum @ SV44 @ SV61 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV62: $i,SV58: $i,SV45: $i,SV31: $i,SV15: $i] :
( ( ~ ( product @ SV15 @ SV31 @ SV45 )
| ~ ( product @ SV58 @ SV31 @ SV62 )
| ! [SY240: $i] :
( ~ ( sum @ SV15 @ SV58 @ SY240 )
| ! [SY241: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY241 )
| ( product @ SY240 @ SV31 @ SY241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(166,plain,
! [SV46: $i,SV32: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV32 @ SV46 )
= $false )
| ( ( ! [SY212: $i] :
( ~ ( sum @ SV16 @ SV32 @ SY212 )
| ( SV46 = SY212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV47: $i,SV33: $i,SV17: $i] :
( ( ( product @ SV17 @ SV33 @ SV47 )
= $false )
| ( ( ! [SY213: $i] :
( ~ ( product @ SV17 @ SV33 @ SY213 )
| ( SV47 = SY213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(168,plain,
! [SV48: $i,SV34: $i,SV18: $i] :
( ( ( product @ SV18 @ SV34 @ SV48 )
= $false )
| ( ( product @ SV18 @ ( additive_inverse @ SV34 ) @ ( additive_inverse @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV49: $i,SV35: $i,SV19: $i] :
( ( ( product @ SV19 @ SV35 @ SV49 )
= $false )
| ( ( product @ ( additive_inverse @ SV19 ) @ SV35 @ ( additive_inverse @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV50: $i,SV36: $i,SV20: $i] :
( ( ( product @ SV20 @ SV36 @ SV50 )
= $false )
| ( ( product @ ( additive_inverse @ SV20 ) @ ( additive_inverse @ SV36 ) @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(171,plain,
! [SV51: $i,SV37: $i,SV23: $i,SV7: $i] :
( ( ( sum @ SV7 @ SV23 @ SV37 )
= $false )
| ( ( ! [SY214: $i] :
( ~ ( sum @ SV23 @ SV51 @ SY214 )
| ! [SY215: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY215 )
| ( sum @ SV7 @ SY214 @ SY215 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(172,plain,
! [SV52: $i,SV38: $i,SV24: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV24 @ SV38 )
= $false )
| ( ( ! [SY216: $i] :
( ~ ( sum @ SV24 @ SV52 @ SY216 )
| ! [SY217: $i] :
( ~ ( sum @ SV8 @ SY216 @ SY217 )
| ( sum @ SV38 @ SV52 @ SY217 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV53: $i,SV40: $i,SV26: $i,SV10: $i] :
( ( ( product @ SV10 @ SV26 @ SV40 )
= $false )
| ( ( ! [SY218: $i] :
( ~ ( product @ SV26 @ SV53 @ SY218 )
| ! [SY219: $i] :
( ~ ( product @ SV40 @ SV53 @ SY219 )
| ( product @ SV10 @ SY218 @ SY219 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(174,plain,
! [SV54: $i,SV41: $i,SV27: $i,SV11: $i] :
( ( ( product @ SV11 @ SV27 @ SV41 )
= $false )
| ( ( ! [SY220: $i] :
( ~ ( product @ SV27 @ SV54 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SV11 @ SY220 @ SY221 )
| ( product @ SV41 @ SV54 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(175,plain,
! [SV59: $i,SV55: $i,SV42: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV28 @ SV42 ) )
= $true )
| ( ( ~ ( product @ SV12 @ SV55 @ SV59 )
| ! [SY234: $i] :
( ~ ( sum @ SV28 @ SV55 @ SY234 )
| ! [SY235: $i] :
( ~ ( product @ SV12 @ SY234 @ SY235 )
| ( sum @ SV42 @ SV59 @ SY235 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(176,plain,
! [SV60: $i,SV56: $i,SV43: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV29 @ SV43 ) )
= $true )
| ( ( ~ ( product @ SV13 @ SV56 @ SV60 )
| ! [SY236: $i] :
( ~ ( sum @ SV29 @ SV56 @ SY236 )
| ! [SY237: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY237 )
| ( product @ SV13 @ SY236 @ SY237 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(177,plain,
! [SV61: $i,SV57: $i,SV44: $i,SV30: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV30 @ SV44 ) )
= $true )
| ( ( ~ ( product @ SV57 @ SV30 @ SV61 )
| ! [SY238: $i] :
( ~ ( sum @ SV14 @ SV57 @ SY238 )
| ! [SY239: $i] :
( ~ ( product @ SY238 @ SV30 @ SY239 )
| ( sum @ SV44 @ SV61 @ SY239 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(178,plain,
! [SV62: $i,SV58: $i,SV45: $i,SV31: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV31 @ SV45 ) )
= $true )
| ( ( ~ ( product @ SV58 @ SV31 @ SV62 )
| ! [SY240: $i] :
( ~ ( sum @ SV15 @ SV58 @ SY240 )
| ! [SY241: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY241 )
| ( product @ SY240 @ SV31 @ SY241 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(179,plain,
! [SV46: $i,SV63: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV32 @ SV63 )
| ( SV46 = SV63 ) )
= $true )
| ( ( sum @ SV16 @ SV32 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV47: $i,SV64: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV33 @ SV64 )
| ( SV47 = SV64 ) )
= $true )
| ( ( product @ SV17 @ SV33 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV7: $i,SV37: $i,SV65: $i,SV51: $i,SV23: $i] :
( ( ( ~ ( sum @ SV23 @ SV51 @ SV65 )
| ! [SY242: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY242 )
| ( sum @ SV7 @ SV65 @ SY242 ) ) )
= $true )
| ( ( sum @ SV7 @ SV23 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV38: $i,SV8: $i,SV66: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV52 @ SV66 )
| ! [SY243: $i] :
( ~ ( sum @ SV8 @ SV66 @ SY243 )
| ( sum @ SV38 @ SV52 @ SY243 ) ) )
= $true )
| ( ( sum @ SV8 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV10: $i,SV40: $i,SV67: $i,SV53: $i,SV26: $i] :
( ( ( ~ ( product @ SV26 @ SV53 @ SV67 )
| ! [SY244: $i] :
( ~ ( product @ SV40 @ SV53 @ SY244 )
| ( product @ SV10 @ SV67 @ SY244 ) ) )
= $true )
| ( ( product @ SV10 @ SV26 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV41: $i,SV11: $i,SV68: $i,SV54: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV54 @ SV68 )
| ! [SY245: $i] :
( ~ ( product @ SV11 @ SV68 @ SY245 )
| ( product @ SV41 @ SV54 @ SY245 ) ) )
= $true )
| ( ( product @ SV11 @ SV27 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV59: $i,SV55: $i,SV42: $i,SV28: $i,SV12: $i] :
( ( ( product @ SV12 @ SV28 @ SV42 )
= $false )
| ( ( ~ ( product @ SV12 @ SV55 @ SV59 )
| ! [SY234: $i] :
( ~ ( sum @ SV28 @ SV55 @ SY234 )
| ! [SY235: $i] :
( ~ ( product @ SV12 @ SY234 @ SY235 )
| ( sum @ SV42 @ SV59 @ SY235 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV60: $i,SV56: $i,SV43: $i,SV29: $i,SV13: $i] :
( ( ( product @ SV13 @ SV29 @ SV43 )
= $false )
| ( ( ~ ( product @ SV13 @ SV56 @ SV60 )
| ! [SY236: $i] :
( ~ ( sum @ SV29 @ SV56 @ SY236 )
| ! [SY237: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY237 )
| ( product @ SV13 @ SY236 @ SY237 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV61: $i,SV57: $i,SV44: $i,SV30: $i,SV14: $i] :
( ( ( product @ SV14 @ SV30 @ SV44 )
= $false )
| ( ( ~ ( product @ SV57 @ SV30 @ SV61 )
| ! [SY238: $i] :
( ~ ( sum @ SV14 @ SV57 @ SY238 )
| ! [SY239: $i] :
( ~ ( product @ SY238 @ SV30 @ SY239 )
| ( sum @ SV44 @ SV61 @ SY239 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV62: $i,SV58: $i,SV45: $i,SV31: $i,SV15: $i] :
( ( ( product @ SV15 @ SV31 @ SV45 )
= $false )
| ( ( ~ ( product @ SV58 @ SV31 @ SV62 )
| ! [SY240: $i] :
( ~ ( sum @ SV15 @ SV58 @ SY240 )
| ! [SY241: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY241 )
| ( product @ SY240 @ SV31 @ SY241 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV46: $i,SV63: $i,SV32: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV32 @ SV63 ) )
= $true )
| ( ( SV46 = SV63 )
= $true )
| ( ( sum @ SV16 @ SV32 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(190,plain,
! [SV47: $i,SV64: $i,SV33: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV33 @ SV64 ) )
= $true )
| ( ( SV47 = SV64 )
= $true )
| ( ( product @ SV17 @ SV33 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(191,plain,
! [SV7: $i,SV37: $i,SV65: $i,SV51: $i,SV23: $i] :
( ( ( ~ ( sum @ SV23 @ SV51 @ SV65 ) )
= $true )
| ( ( ! [SY242: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY242 )
| ( sum @ SV7 @ SV65 @ SY242 ) ) )
= $true )
| ( ( sum @ SV7 @ SV23 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV38: $i,SV8: $i,SV66: $i,SV52: $i,SV24: $i] :
( ( ( ~ ( sum @ SV24 @ SV52 @ SV66 ) )
= $true )
| ( ( ! [SY243: $i] :
( ~ ( sum @ SV8 @ SV66 @ SY243 )
| ( sum @ SV38 @ SV52 @ SY243 ) ) )
= $true )
| ( ( sum @ SV8 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(193,plain,
! [SV10: $i,SV40: $i,SV67: $i,SV53: $i,SV26: $i] :
( ( ( ~ ( product @ SV26 @ SV53 @ SV67 ) )
= $true )
| ( ( ! [SY244: $i] :
( ~ ( product @ SV40 @ SV53 @ SY244 )
| ( product @ SV10 @ SV67 @ SY244 ) ) )
= $true )
| ( ( product @ SV10 @ SV26 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV41: $i,SV11: $i,SV68: $i,SV54: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV54 @ SV68 ) )
= $true )
| ( ( ! [SY245: $i] :
( ~ ( product @ SV11 @ SV68 @ SY245 )
| ( product @ SV41 @ SV54 @ SY245 ) ) )
= $true )
| ( ( product @ SV11 @ SV27 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(195,plain,
! [SV42: $i,SV28: $i,SV59: $i,SV55: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV55 @ SV59 ) )
= $true )
| ( ( ! [SY234: $i] :
( ~ ( sum @ SV28 @ SV55 @ SY234 )
| ! [SY235: $i] :
( ~ ( product @ SV12 @ SY234 @ SY235 )
| ( sum @ SV42 @ SV59 @ SY235 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(196,plain,
! [SV43: $i,SV29: $i,SV60: $i,SV56: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV56 @ SV60 ) )
= $true )
| ( ( ! [SY236: $i] :
( ~ ( sum @ SV29 @ SV56 @ SY236 )
| ! [SY237: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY237 )
| ( product @ SV13 @ SY236 @ SY237 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(197,plain,
! [SV44: $i,SV14: $i,SV61: $i,SV30: $i,SV57: $i] :
( ( ( ~ ( product @ SV57 @ SV30 @ SV61 ) )
= $true )
| ( ( ! [SY238: $i] :
( ~ ( sum @ SV14 @ SV57 @ SY238 )
| ! [SY239: $i] :
( ~ ( product @ SY238 @ SV30 @ SY239 )
| ( sum @ SV44 @ SV61 @ SY239 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(198,plain,
! [SV45: $i,SV15: $i,SV62: $i,SV31: $i,SV58: $i] :
( ( ( ~ ( product @ SV58 @ SV31 @ SV62 ) )
= $true )
| ( ( ! [SY240: $i] :
( ~ ( sum @ SV15 @ SV58 @ SY240 )
| ! [SY241: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY241 )
| ( product @ SY240 @ SV31 @ SY241 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(199,plain,
! [SV46: $i,SV63: $i,SV32: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV32 @ SV63 )
= $false )
| ( ( SV46 = SV63 )
= $true )
| ( ( sum @ SV16 @ SV32 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(200,plain,
! [SV47: $i,SV64: $i,SV33: $i,SV17: $i] :
( ( ( product @ SV17 @ SV33 @ SV64 )
= $false )
| ( ( SV47 = SV64 )
= $true )
| ( ( product @ SV17 @ SV33 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(201,plain,
! [SV7: $i,SV37: $i,SV65: $i,SV51: $i,SV23: $i] :
( ( ( sum @ SV23 @ SV51 @ SV65 )
= $false )
| ( ( ! [SY242: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY242 )
| ( sum @ SV7 @ SV65 @ SY242 ) ) )
= $true )
| ( ( sum @ SV7 @ SV23 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(202,plain,
! [SV38: $i,SV8: $i,SV66: $i,SV52: $i,SV24: $i] :
( ( ( sum @ SV24 @ SV52 @ SV66 )
= $false )
| ( ( ! [SY243: $i] :
( ~ ( sum @ SV8 @ SV66 @ SY243 )
| ( sum @ SV38 @ SV52 @ SY243 ) ) )
= $true )
| ( ( sum @ SV8 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(203,plain,
! [SV10: $i,SV40: $i,SV67: $i,SV53: $i,SV26: $i] :
( ( ( product @ SV26 @ SV53 @ SV67 )
= $false )
| ( ( ! [SY244: $i] :
( ~ ( product @ SV40 @ SV53 @ SY244 )
| ( product @ SV10 @ SV67 @ SY244 ) ) )
= $true )
| ( ( product @ SV10 @ SV26 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(204,plain,
! [SV41: $i,SV11: $i,SV68: $i,SV54: $i,SV27: $i] :
( ( ( product @ SV27 @ SV54 @ SV68 )
= $false )
| ( ( ! [SY245: $i] :
( ~ ( product @ SV11 @ SV68 @ SY245 )
| ( product @ SV41 @ SV54 @ SY245 ) ) )
= $true )
| ( ( product @ SV11 @ SV27 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(205,plain,
! [SV42: $i,SV28: $i,SV59: $i,SV55: $i,SV12: $i] :
( ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( ! [SY234: $i] :
( ~ ( sum @ SV28 @ SV55 @ SY234 )
| ! [SY235: $i] :
( ~ ( product @ SV12 @ SY234 @ SY235 )
| ( sum @ SV42 @ SV59 @ SY235 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(206,plain,
! [SV43: $i,SV29: $i,SV60: $i,SV56: $i,SV13: $i] :
( ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( ! [SY236: $i] :
( ~ ( sum @ SV29 @ SV56 @ SY236 )
| ! [SY237: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY237 )
| ( product @ SV13 @ SY236 @ SY237 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(207,plain,
! [SV44: $i,SV14: $i,SV61: $i,SV30: $i,SV57: $i] :
( ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( ! [SY238: $i] :
( ~ ( sum @ SV14 @ SV57 @ SY238 )
| ! [SY239: $i] :
( ~ ( product @ SY238 @ SV30 @ SY239 )
| ( sum @ SV44 @ SV61 @ SY239 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(208,plain,
! [SV45: $i,SV15: $i,SV62: $i,SV31: $i,SV58: $i] :
( ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( ! [SY240: $i] :
( ~ ( sum @ SV15 @ SV58 @ SY240 )
| ! [SY241: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY241 )
| ( product @ SY240 @ SV31 @ SY241 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(209,plain,
! [SV23: $i,SV65: $i,SV7: $i,SV69: $i,SV51: $i,SV37: $i] :
( ( ( ~ ( sum @ SV37 @ SV51 @ SV69 )
| ( sum @ SV7 @ SV65 @ SV69 ) )
= $true )
| ( ( sum @ SV23 @ SV51 @ SV65 )
= $false )
| ( ( sum @ SV7 @ SV23 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV24: $i,SV52: $i,SV38: $i,SV70: $i,SV66: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV66 @ SV70 )
| ( sum @ SV38 @ SV52 @ SV70 ) )
= $true )
| ( ( sum @ SV24 @ SV52 @ SV66 )
= $false )
| ( ( sum @ SV8 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV26: $i,SV67: $i,SV10: $i,SV71: $i,SV53: $i,SV40: $i] :
( ( ( ~ ( product @ SV40 @ SV53 @ SV71 )
| ( product @ SV10 @ SV67 @ SV71 ) )
= $true )
| ( ( product @ SV26 @ SV53 @ SV67 )
= $false )
| ( ( product @ SV10 @ SV26 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV27: $i,SV54: $i,SV41: $i,SV72: $i,SV68: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV68 @ SV72 )
| ( product @ SV41 @ SV54 @ SV72 ) )
= $true )
| ( ( product @ SV27 @ SV54 @ SV68 )
= $false )
| ( ( product @ SV11 @ SV27 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(213,plain,
! [SV59: $i,SV42: $i,SV12: $i,SV73: $i,SV55: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV55 @ SV73 )
| ! [SY246: $i] :
( ~ ( product @ SV12 @ SV73 @ SY246 )
| ( sum @ SV42 @ SV59 @ SY246 ) ) )
= $true )
| ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(214,plain,
! [SV13: $i,SV60: $i,SV43: $i,SV74: $i,SV56: $i,SV29: $i] :
( ( ( ~ ( sum @ SV29 @ SV56 @ SV74 )
| ! [SY247: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY247 )
| ( product @ SV13 @ SV74 @ SY247 ) ) )
= $true )
| ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(215,plain,
! [SV61: $i,SV44: $i,SV30: $i,SV75: $i,SV57: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV57 @ SV75 )
| ! [SY248: $i] :
( ~ ( product @ SV75 @ SV30 @ SY248 )
| ( sum @ SV44 @ SV61 @ SY248 ) ) )
= $true )
| ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(216,plain,
! [SV31: $i,SV62: $i,SV45: $i,SV76: $i,SV58: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV58 @ SV76 )
| ! [SY249: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY249 )
| ( product @ SV76 @ SV31 @ SY249 ) ) )
= $true )
| ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(217,plain,
! [SV23: $i,SV65: $i,SV7: $i,SV69: $i,SV51: $i,SV37: $i] :
( ( ( ~ ( sum @ SV37 @ SV51 @ SV69 ) )
= $true )
| ( ( sum @ SV7 @ SV65 @ SV69 )
= $true )
| ( ( sum @ SV23 @ SV51 @ SV65 )
= $false )
| ( ( sum @ SV7 @ SV23 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(218,plain,
! [SV24: $i,SV52: $i,SV38: $i,SV70: $i,SV66: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV66 @ SV70 ) )
= $true )
| ( ( sum @ SV38 @ SV52 @ SV70 )
= $true )
| ( ( sum @ SV24 @ SV52 @ SV66 )
= $false )
| ( ( sum @ SV8 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(219,plain,
! [SV26: $i,SV67: $i,SV10: $i,SV71: $i,SV53: $i,SV40: $i] :
( ( ( ~ ( product @ SV40 @ SV53 @ SV71 ) )
= $true )
| ( ( product @ SV10 @ SV67 @ SV71 )
= $true )
| ( ( product @ SV26 @ SV53 @ SV67 )
= $false )
| ( ( product @ SV10 @ SV26 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV27: $i,SV54: $i,SV41: $i,SV72: $i,SV68: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV68 @ SV72 ) )
= $true )
| ( ( product @ SV41 @ SV54 @ SV72 )
= $true )
| ( ( product @ SV27 @ SV54 @ SV68 )
= $false )
| ( ( product @ SV11 @ SV27 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV59: $i,SV42: $i,SV12: $i,SV73: $i,SV55: $i,SV28: $i] :
( ( ( ~ ( sum @ SV28 @ SV55 @ SV73 ) )
= $true )
| ( ( ! [SY246: $i] :
( ~ ( product @ SV12 @ SV73 @ SY246 )
| ( sum @ SV42 @ SV59 @ SY246 ) ) )
= $true )
| ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(222,plain,
! [SV13: $i,SV60: $i,SV43: $i,SV74: $i,SV56: $i,SV29: $i] :
( ( ( ~ ( sum @ SV29 @ SV56 @ SV74 ) )
= $true )
| ( ( ! [SY247: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY247 )
| ( product @ SV13 @ SV74 @ SY247 ) ) )
= $true )
| ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(223,plain,
! [SV61: $i,SV44: $i,SV30: $i,SV75: $i,SV57: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV57 @ SV75 ) )
= $true )
| ( ( ! [SY248: $i] :
( ~ ( product @ SV75 @ SV30 @ SY248 )
| ( sum @ SV44 @ SV61 @ SY248 ) ) )
= $true )
| ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV31: $i,SV62: $i,SV45: $i,SV76: $i,SV58: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV58 @ SV76 ) )
= $true )
| ( ( ! [SY249: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY249 )
| ( product @ SV76 @ SV31 @ SY249 ) ) )
= $true )
| ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV23: $i,SV65: $i,SV7: $i,SV69: $i,SV51: $i,SV37: $i] :
( ( ( sum @ SV37 @ SV51 @ SV69 )
= $false )
| ( ( sum @ SV7 @ SV65 @ SV69 )
= $true )
| ( ( sum @ SV23 @ SV51 @ SV65 )
= $false )
| ( ( sum @ SV7 @ SV23 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV24: $i,SV52: $i,SV38: $i,SV70: $i,SV66: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV66 @ SV70 )
= $false )
| ( ( sum @ SV38 @ SV52 @ SV70 )
= $true )
| ( ( sum @ SV24 @ SV52 @ SV66 )
= $false )
| ( ( sum @ SV8 @ SV24 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV26: $i,SV67: $i,SV10: $i,SV71: $i,SV53: $i,SV40: $i] :
( ( ( product @ SV40 @ SV53 @ SV71 )
= $false )
| ( ( product @ SV10 @ SV67 @ SV71 )
= $true )
| ( ( product @ SV26 @ SV53 @ SV67 )
= $false )
| ( ( product @ SV10 @ SV26 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV27: $i,SV54: $i,SV41: $i,SV72: $i,SV68: $i,SV11: $i] :
( ( ( product @ SV11 @ SV68 @ SV72 )
= $false )
| ( ( product @ SV41 @ SV54 @ SV72 )
= $true )
| ( ( product @ SV27 @ SV54 @ SV68 )
= $false )
| ( ( product @ SV11 @ SV27 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV59: $i,SV42: $i,SV12: $i,SV73: $i,SV55: $i,SV28: $i] :
( ( ( sum @ SV28 @ SV55 @ SV73 )
= $false )
| ( ( ! [SY246: $i] :
( ~ ( product @ SV12 @ SV73 @ SY246 )
| ( sum @ SV42 @ SV59 @ SY246 ) ) )
= $true )
| ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(230,plain,
! [SV13: $i,SV60: $i,SV43: $i,SV74: $i,SV56: $i,SV29: $i] :
( ( ( sum @ SV29 @ SV56 @ SV74 )
= $false )
| ( ( ! [SY247: $i] :
( ~ ( sum @ SV43 @ SV60 @ SY247 )
| ( product @ SV13 @ SV74 @ SY247 ) ) )
= $true )
| ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(231,plain,
! [SV61: $i,SV44: $i,SV30: $i,SV75: $i,SV57: $i,SV14: $i] :
( ( ( sum @ SV14 @ SV57 @ SV75 )
= $false )
| ( ( ! [SY248: $i] :
( ~ ( product @ SV75 @ SV30 @ SY248 )
| ( sum @ SV44 @ SV61 @ SY248 ) ) )
= $true )
| ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(232,plain,
! [SV31: $i,SV62: $i,SV45: $i,SV76: $i,SV58: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV58 @ SV76 )
= $false )
| ( ( ! [SY249: $i] :
( ~ ( sum @ SV45 @ SV62 @ SY249 )
| ( product @ SV76 @ SV31 @ SY249 ) ) )
= $true )
| ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(233,plain,
! [SV55: $i,SV28: $i,SV59: $i,SV42: $i,SV77: $i,SV73: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV73 @ SV77 )
| ( sum @ SV42 @ SV59 @ SV77 ) )
= $true )
| ( ( sum @ SV28 @ SV55 @ SV73 )
= $false )
| ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV56: $i,SV29: $i,SV74: $i,SV13: $i,SV78: $i,SV60: $i,SV43: $i] :
( ( ( ~ ( sum @ SV43 @ SV60 @ SV78 )
| ( product @ SV13 @ SV74 @ SV78 ) )
= $true )
| ( ( sum @ SV29 @ SV56 @ SV74 )
= $false )
| ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(235,plain,
! [SV57: $i,SV14: $i,SV61: $i,SV44: $i,SV79: $i,SV30: $i,SV75: $i] :
( ( ( ~ ( product @ SV75 @ SV30 @ SV79 )
| ( sum @ SV44 @ SV61 @ SV79 ) )
= $true )
| ( ( sum @ SV14 @ SV57 @ SV75 )
= $false )
| ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV58: $i,SV15: $i,SV31: $i,SV76: $i,SV80: $i,SV62: $i,SV45: $i] :
( ( ( ~ ( sum @ SV45 @ SV62 @ SV80 )
| ( product @ SV76 @ SV31 @ SV80 ) )
= $true )
| ( ( sum @ SV15 @ SV58 @ SV76 )
= $false )
| ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV55: $i,SV28: $i,SV59: $i,SV42: $i,SV77: $i,SV73: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV73 @ SV77 ) )
= $true )
| ( ( sum @ SV42 @ SV59 @ SV77 )
= $true )
| ( ( sum @ SV28 @ SV55 @ SV73 )
= $false )
| ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV56: $i,SV29: $i,SV74: $i,SV13: $i,SV78: $i,SV60: $i,SV43: $i] :
( ( ( ~ ( sum @ SV43 @ SV60 @ SV78 ) )
= $true )
| ( ( product @ SV13 @ SV74 @ SV78 )
= $true )
| ( ( sum @ SV29 @ SV56 @ SV74 )
= $false )
| ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV57: $i,SV14: $i,SV61: $i,SV44: $i,SV79: $i,SV30: $i,SV75: $i] :
( ( ( ~ ( product @ SV75 @ SV30 @ SV79 ) )
= $true )
| ( ( sum @ SV44 @ SV61 @ SV79 )
= $true )
| ( ( sum @ SV14 @ SV57 @ SV75 )
= $false )
| ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(240,plain,
! [SV58: $i,SV15: $i,SV31: $i,SV76: $i,SV80: $i,SV62: $i,SV45: $i] :
( ( ( ~ ( sum @ SV45 @ SV62 @ SV80 ) )
= $true )
| ( ( product @ SV76 @ SV31 @ SV80 )
= $true )
| ( ( sum @ SV15 @ SV58 @ SV76 )
= $false )
| ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(241,plain,
! [SV55: $i,SV28: $i,SV59: $i,SV42: $i,SV77: $i,SV73: $i,SV12: $i] :
( ( ( product @ SV12 @ SV73 @ SV77 )
= $false )
| ( ( sum @ SV42 @ SV59 @ SV77 )
= $true )
| ( ( sum @ SV28 @ SV55 @ SV73 )
= $false )
| ( ( product @ SV12 @ SV55 @ SV59 )
= $false )
| ( ( product @ SV12 @ SV28 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(242,plain,
! [SV56: $i,SV29: $i,SV74: $i,SV13: $i,SV78: $i,SV60: $i,SV43: $i] :
( ( ( sum @ SV43 @ SV60 @ SV78 )
= $false )
| ( ( product @ SV13 @ SV74 @ SV78 )
= $true )
| ( ( sum @ SV29 @ SV56 @ SV74 )
= $false )
| ( ( product @ SV13 @ SV56 @ SV60 )
= $false )
| ( ( product @ SV13 @ SV29 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(243,plain,
! [SV57: $i,SV14: $i,SV61: $i,SV44: $i,SV79: $i,SV30: $i,SV75: $i] :
( ( ( product @ SV75 @ SV30 @ SV79 )
= $false )
| ( ( sum @ SV44 @ SV61 @ SV79 )
= $true )
| ( ( sum @ SV14 @ SV57 @ SV75 )
= $false )
| ( ( product @ SV57 @ SV30 @ SV61 )
= $false )
| ( ( product @ SV14 @ SV30 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(244,plain,
! [SV58: $i,SV15: $i,SV31: $i,SV76: $i,SV80: $i,SV62: $i,SV45: $i] :
( ( ( sum @ SV45 @ SV62 @ SV80 )
= $false )
| ( ( product @ SV76 @ SV31 @ SV80 )
= $true )
| ( ( sum @ SV15 @ SV58 @ SV76 )
= $false )
| ( ( product @ SV58 @ SV31 @ SV62 )
= $false )
| ( ( product @ SV15 @ SV31 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(245,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,244,243,242,241,228,227,226,225,200,199,170,169,168,159,114,113,112,97,96,93,92,91,69,68,67]) ).
thf(246,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % 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 : Mon May 30 06:05:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.38
% 0.19/0.38 No.of.Axioms: 25
% 0.19/0.38
% 0.19/0.38 Length.of.Defs: 0
% 0.19/0.38
% 0.19/0.38 Contains.Choice.Funs: false
% 0.19/0.42 .
% 0.19/0.42 (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:27,loop_count:0,foatp_calls:0,translation:fof_full).................
% 23.26/23.49
% 23.26/23.49 ********************************
% 23.26/23.49 * All subproblems solved! *
% 23.26/23.49 ********************************
% 23.26/23.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:245,loop_count:0,foatp_calls:1,translation:fof_full)
% 23.26/23.50
% 23.26/23.50 %**** Beginning of derivation protocol ****
% 23.26/23.50 % SZS output start CNFRefutation
% See solution above
% 23.26/23.51
% 23.26/23.51 %**** End of derivation protocol ****
% 23.26/23.51 %**** no. of clauses in derivation: 246 ****
% 23.26/23.51 %**** clause counter: 245 ****
% 23.26/23.51
% 23.26/23.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:245,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------