TSTP Solution File: RNG003-1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG003-1 : 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 : n020.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 20:33:54 EDT 2022
% Result : Unsatisfiable 0.55s 0.72s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 31
% Syntax : Number of formulae : 227 ( 122 unt; 10 typ; 0 def)
% Number of atoms : 1511 ( 400 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3191 ( 415 ~; 552 |; 0 &;2224 @)
% ( 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 : 1072 ( 0 ^1072 !; 0 ?;1072 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_additive_inverse,type,
additive_inverse: $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_d,type,
d: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(2,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(3,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(4,axiom,
! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(5,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(6,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ X @ V3 @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(7,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(8,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(10,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W )
| ( sum @ U @ Z @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(11,axiom,
! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W )
| ( sum @ X @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(12,axiom,
! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(13,axiom,
! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(14,axiom,
! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(15,axiom,
! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(16,axiom,
! [X: $i] : ( sum @ X @ additive_identity @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(17,axiom,
! [X: $i] : ( sum @ additive_identity @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(18,axiom,
sum @ b @ c @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c_is_d) ).
thf(19,axiom,
sum @ a @ c @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_plus_c_is_d) ).
thf(20,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(21,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_b) ).
thf(23,plain,
$false = $false,
inference(unfold_def,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ X @ Y @ V )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ X @ Y @ V )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ V3 @ X @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [Y: $i,X: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ Y @ X @ V1 )
| ~ ( product @ Z @ X @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ V3 @ X @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( sum @ V1 @ V2 @ V4 )
| ( product @ X @ V3 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i] :
( ~ ( product @ X @ Y @ V1 )
| ~ ( product @ X @ Z @ V2 )
| ~ ( sum @ Y @ Z @ V3 )
| ~ ( product @ X @ V3 @ V4 )
| ( sum @ V1 @ V2 @ V4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ X @ V @ W )
| ( product @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( product @ X @ Y @ U )
| ~ ( product @ Y @ Z @ V )
| ~ ( product @ U @ Z @ W )
| ( product @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ X @ V @ W )
| ( sum @ U @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,U: $i,Z: $i,V: $i,W: $i] :
( ~ ( sum @ X @ Y @ U )
| ~ ( sum @ Y @ Z @ V )
| ~ ( sum @ U @ Z @ W )
| ( sum @ X @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( sum @ b @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( sum @ a @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ( a != b ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(44,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(45,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)],[24]) ).
thf(46,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)],[25]) ).
thf(47,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)],[26]) ).
thf(48,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)],[27]) ).
thf(49,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)],[28]) ).
thf(50,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)],[29]) ).
thf(51,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)],[30]) ).
thf(52,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)],[31]) ).
thf(53,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)],[33]) ).
thf(54,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)],[34]) ).
thf(55,plain,
( ( ( a != b ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(56,plain,
( ( ( a != b ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(57,plain,
( ( sum @ a @ c @ d )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(58,plain,
( ( sum @ b @ c @ d )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(59,plain,
( ( ! [X: $i] : ( sum @ additive_identity @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ! [X: $i] : ( sum @ X @ additive_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] : ( sum @ X @ Y @ ( add @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(63,plain,
( ( ! [X: $i] : ( sum @ ( additive_inverse @ X ) @ X @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(64,plain,
( ( ! [X: $i] : ( sum @ X @ ( additive_inverse @ X ) @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(65,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)],[54]) ).
thf(66,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)],[53]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( sum @ X @ Y @ Z )
| ( sum @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(68,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)],[52]) ).
thf(69,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)],[51]) ).
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(copy,[status(thm)],[50]) ).
thf(71,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)],[49]) ).
thf(72,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)],[48]) ).
thf(73,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)],[47]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( sum @ X @ Y @ U )
| ! [V: $i] :
( ~ ( sum @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( product @ X @ Y @ U )
| ! [V: $i] :
( ~ ( product @ X @ Y @ V )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(76,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(77,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(78,plain,
! [SV1: $i] :
( ( sum @ additive_identity @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(79,plain,
! [SV2: $i] :
( ( sum @ SV2 @ additive_identity @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(80,plain,
! [SV3: $i] :
( ( ! [SY71: $i] : ( product @ SV3 @ SY71 @ ( multiply @ SV3 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(81,plain,
! [SV4: $i] :
( ( ! [SY72: $i] : ( sum @ SV4 @ SY72 @ ( add @ SV4 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(82,plain,
! [SV5: $i] :
( ( sum @ ( additive_inverse @ SV5 ) @ SV5 @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(83,plain,
! [SV6: $i] :
( ( sum @ SV6 @ ( additive_inverse @ SV6 ) @ additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(84,plain,
! [SV7: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ( sum @ SV7 @ SY73 @ SY74 )
| ! [SY76: $i] :
( ~ ( sum @ SY73 @ SY75 @ SY76 )
| ! [SY77: $i] :
( ~ ( sum @ SY74 @ SY75 @ SY77 )
| ( sum @ SV7 @ SY76 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(85,plain,
! [SV8: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i] :
( ~ ( sum @ SV8 @ SY78 @ SY79 )
| ! [SY81: $i] :
( ~ ( sum @ SY78 @ SY80 @ SY81 )
| ! [SY82: $i] :
( ~ ( sum @ SV8 @ SY81 @ SY82 )
| ( sum @ SY79 @ SY80 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(86,plain,
! [SV9: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ( sum @ SV9 @ SY83 @ SY84 )
| ( sum @ SY83 @ SV9 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(87,plain,
! [SV10: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ( product @ SV10 @ SY85 @ SY86 )
| ! [SY88: $i] :
( ~ ( product @ SY85 @ SY87 @ SY88 )
| ! [SY89: $i] :
( ~ ( product @ SY86 @ SY87 @ SY89 )
| ( product @ SV10 @ SY88 @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(88,plain,
! [SV11: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ~ ( product @ SV11 @ SY90 @ SY91 )
| ! [SY93: $i] :
( ~ ( product @ SY90 @ SY92 @ SY93 )
| ! [SY94: $i] :
( ~ ( product @ SV11 @ SY93 @ SY94 )
| ( product @ SY91 @ SY92 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(89,plain,
! [SV12: $i] :
( ( ! [SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ~ ( product @ SV12 @ SY95 @ SY96 )
| ~ ( product @ SV12 @ SY97 @ SY98 )
| ! [SY99: $i] :
( ~ ( sum @ SY95 @ SY97 @ SY99 )
| ! [SY100: $i] :
( ~ ( product @ SV12 @ SY99 @ SY100 )
| ( sum @ SY96 @ SY98 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(90,plain,
! [SV13: $i] :
( ( ! [SY101: $i,SY102: $i,SY103: $i,SY104: $i] :
( ~ ( product @ SV13 @ SY101 @ SY102 )
| ~ ( product @ SV13 @ SY103 @ SY104 )
| ! [SY105: $i] :
( ~ ( sum @ SY101 @ SY103 @ SY105 )
| ! [SY106: $i] :
( ~ ( sum @ SY102 @ SY104 @ SY106 )
| ( product @ SV13 @ SY105 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV14: $i] :
( ( ! [SY107: $i,SY108: $i,SY109: $i,SY110: $i] :
( ~ ( product @ SV14 @ SY107 @ SY108 )
| ~ ( product @ SY109 @ SY107 @ SY110 )
| ! [SY111: $i] :
( ~ ( sum @ SV14 @ SY109 @ SY111 )
| ! [V4: $i] :
( ~ ( product @ SY111 @ SY107 @ V4 )
| ( sum @ SY108 @ SY110 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(92,plain,
! [SV15: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] :
( ~ ( product @ SV15 @ SY113 @ SY114 )
| ~ ( product @ SY115 @ SY113 @ SY116 )
| ! [SY117: $i] :
( ~ ( sum @ SV15 @ SY115 @ SY117 )
| ! [V4: $i] :
( ~ ( sum @ SY114 @ SY116 @ V4 )
| ( product @ SY117 @ SY113 @ V4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(93,plain,
! [SV16: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( sum @ SV16 @ SY119 @ SY120 )
| ! [SY121: $i] :
( ~ ( sum @ SV16 @ SY119 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV17: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ~ ( product @ SV17 @ SY122 @ SY123 )
| ! [SY124: $i] :
( ~ ( product @ SV17 @ SY122 @ SY124 )
| ( SY123 = SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(95,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(96,plain,
! [SV18: $i,SV3: $i] :
( ( product @ SV3 @ SV18 @ ( multiply @ SV3 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV19: $i,SV4: $i] :
( ( sum @ SV4 @ SV19 @ ( add @ SV4 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( sum @ SV7 @ SV20 @ SY125 )
| ! [SY127: $i] :
( ~ ( sum @ SV20 @ SY126 @ SY127 )
| ! [SY77: $i] :
( ~ ( sum @ SY125 @ SY126 @ SY77 )
| ( sum @ SV7 @ SY127 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ( sum @ SV8 @ SV21 @ SY129 )
| ! [SY131: $i] :
( ~ ( sum @ SV21 @ SY130 @ SY131 )
| ! [SY82: $i] :
( ~ ( sum @ SV8 @ SY131 @ SY82 )
| ( sum @ SY129 @ SY130 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV22: $i,SV9: $i] :
( ( ! [SY133: $i] :
( ~ ( sum @ SV9 @ SV22 @ SY133 )
| ( sum @ SV22 @ SV9 @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV23: $i,SV10: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( product @ SV10 @ SV23 @ SY134 )
| ! [SY136: $i] :
( ~ ( product @ SV23 @ SY135 @ SY136 )
| ! [SY89: $i] :
( ~ ( product @ SY134 @ SY135 @ SY89 )
| ( product @ SV10 @ SY136 @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ( product @ SV11 @ SV24 @ SY138 )
| ! [SY140: $i] :
( ~ ( product @ SV24 @ SY139 @ SY140 )
| ! [SY94: $i] :
( ~ ( product @ SV11 @ SY140 @ SY94 )
| ( product @ SY138 @ SY139 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i] :
( ~ ( product @ SV12 @ SV25 @ SY142 )
| ~ ( product @ SV12 @ SY143 @ SY144 )
| ! [SY145: $i] :
( ~ ( sum @ SV25 @ SY143 @ SY145 )
| ! [SY100: $i] :
( ~ ( product @ SV12 @ SY145 @ SY100 )
| ( sum @ SY142 @ SY144 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY147: $i,SY148: $i,SY149: $i] :
( ~ ( product @ SV13 @ SV26 @ SY147 )
| ~ ( product @ SV13 @ SY148 @ SY149 )
| ! [SY150: $i] :
( ~ ( sum @ SV26 @ SY148 @ SY150 )
| ! [SY106: $i] :
( ~ ( sum @ SY147 @ SY149 @ SY106 )
| ( product @ SV13 @ SY150 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY152: $i,SY153: $i,SY154: $i] :
( ~ ( product @ SV14 @ SV27 @ SY152 )
| ~ ( product @ SY153 @ SV27 @ SY154 )
| ! [SY155: $i] :
( ~ ( sum @ SV14 @ SY153 @ SY155 )
| ! [SY156: $i] :
( ~ ( product @ SY155 @ SV27 @ SY156 )
| ( sum @ SY152 @ SY154 @ SY156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV28: $i,SV15: $i] :
( ( ! [SY157: $i,SY158: $i,SY159: $i] :
( ~ ( product @ SV15 @ SV28 @ SY157 )
| ~ ( product @ SY158 @ SV28 @ SY159 )
| ! [SY160: $i] :
( ~ ( sum @ SV15 @ SY158 @ SY160 )
| ! [SY161: $i] :
( ~ ( sum @ SY157 @ SY159 @ SY161 )
| ( product @ SY160 @ SV28 @ SY161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV29: $i,SV16: $i] :
( ( ! [SY162: $i] :
( ~ ( sum @ SV16 @ SV29 @ SY162 )
| ! [SY163: $i] :
( ~ ( sum @ SV16 @ SV29 @ SY163 )
| ( SY162 = SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV30: $i,SV17: $i] :
( ( ! [SY164: $i] :
( ~ ( product @ SV17 @ SV30 @ SY164 )
| ! [SY165: $i] :
( ~ ( product @ SV17 @ SV30 @ SY165 )
| ( SY164 = SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV31: $i,SV20: $i,SV7: $i] :
( ( ! [SY166: $i] :
( ~ ( sum @ SV7 @ SV20 @ SV31 )
| ! [SY167: $i] :
( ~ ( sum @ SV20 @ SY166 @ SY167 )
| ! [SY168: $i] :
( ~ ( sum @ SV31 @ SY166 @ SY168 )
| ( sum @ SV7 @ SY167 @ SY168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV32: $i,SV21: $i,SV8: $i] :
( ( ! [SY169: $i] :
( ~ ( sum @ SV8 @ SV21 @ SV32 )
| ! [SY170: $i] :
( ~ ( sum @ SV21 @ SY169 @ SY170 )
| ! [SY171: $i] :
( ~ ( sum @ SV8 @ SY170 @ SY171 )
| ( sum @ SV32 @ SY169 @ SY171 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV33: $i,SV22: $i,SV9: $i] :
( ( ~ ( sum @ SV9 @ SV22 @ SV33 )
| ( sum @ SV22 @ SV9 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV34: $i,SV23: $i,SV10: $i] :
( ( ! [SY172: $i] :
( ~ ( product @ SV10 @ SV23 @ SV34 )
| ! [SY173: $i] :
( ~ ( product @ SV23 @ SY172 @ SY173 )
| ! [SY174: $i] :
( ~ ( product @ SV34 @ SY172 @ SY174 )
| ( product @ SV10 @ SY173 @ SY174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV35: $i,SV24: $i,SV11: $i] :
( ( ! [SY175: $i] :
( ~ ( product @ SV11 @ SV24 @ SV35 )
| ! [SY176: $i] :
( ~ ( product @ SV24 @ SY175 @ SY176 )
| ! [SY177: $i] :
( ~ ( product @ SV11 @ SY176 @ SY177 )
| ( product @ SV35 @ SY175 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV36: $i,SV25: $i,SV12: $i] :
( ( ! [SY178: $i,SY179: $i] :
( ~ ( product @ SV12 @ SV25 @ SV36 )
| ~ ( product @ SV12 @ SY178 @ SY179 )
| ! [SY180: $i] :
( ~ ( sum @ SV25 @ SY178 @ SY180 )
| ! [SY181: $i] :
( ~ ( product @ SV12 @ SY180 @ SY181 )
| ( sum @ SV36 @ SY179 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV37: $i,SV26: $i,SV13: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ~ ( product @ SV13 @ SV26 @ SV37 )
| ~ ( product @ SV13 @ SY182 @ SY183 )
| ! [SY184: $i] :
( ~ ( sum @ SV26 @ SY182 @ SY184 )
| ! [SY185: $i] :
( ~ ( sum @ SV37 @ SY183 @ SY185 )
| ( product @ SV13 @ SY184 @ SY185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV38: $i,SV27: $i,SV14: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ~ ( product @ SV14 @ SV27 @ SV38 )
| ~ ( product @ SY186 @ SV27 @ SY187 )
| ! [SY188: $i] :
( ~ ( sum @ SV14 @ SY186 @ SY188 )
| ! [SY189: $i] :
( ~ ( product @ SY188 @ SV27 @ SY189 )
| ( sum @ SV38 @ SY187 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV39: $i,SV28: $i,SV15: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ~ ( product @ SV15 @ SV28 @ SV39 )
| ~ ( product @ SY190 @ SV28 @ SY191 )
| ! [SY192: $i] :
( ~ ( sum @ SV15 @ SY190 @ SY192 )
| ! [SY193: $i] :
( ~ ( sum @ SV39 @ SY191 @ SY193 )
| ( product @ SY192 @ SV28 @ SY193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ( sum @ SV16 @ SV29 @ SV40 )
| ! [SY194: $i] :
( ~ ( sum @ SV16 @ SV29 @ SY194 )
| ( SV40 = SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV41: $i,SV30: $i,SV17: $i] :
( ( ~ ( product @ SV17 @ SV30 @ SV41 )
| ! [SY195: $i] :
( ~ ( product @ SV17 @ SV30 @ SY195 )
| ( SV41 = SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV42: $i,SV31: $i,SV20: $i,SV7: $i] :
( ( ~ ( sum @ SV7 @ SV20 @ SV31 )
| ! [SY196: $i] :
( ~ ( sum @ SV20 @ SV42 @ SY196 )
| ! [SY197: $i] :
( ~ ( sum @ SV31 @ SV42 @ SY197 )
| ( sum @ SV7 @ SY196 @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV43: $i,SV32: $i,SV21: $i,SV8: $i] :
( ( ~ ( sum @ SV8 @ SV21 @ SV32 )
| ! [SY198: $i] :
( ~ ( sum @ SV21 @ SV43 @ SY198 )
| ! [SY199: $i] :
( ~ ( sum @ SV8 @ SY198 @ SY199 )
| ( sum @ SV32 @ SV43 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV33: $i,SV22: $i,SV9: $i] :
( ( ( ~ ( sum @ SV9 @ SV22 @ SV33 ) )
= $true )
| ( ( sum @ SV22 @ SV9 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV44: $i,SV34: $i,SV23: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV23 @ SV34 )
| ! [SY200: $i] :
( ~ ( product @ SV23 @ SV44 @ SY200 )
| ! [SY201: $i] :
( ~ ( product @ SV34 @ SV44 @ SY201 )
| ( product @ SV10 @ SY200 @ SY201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV45: $i,SV35: $i,SV24: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV24 @ SV35 )
| ! [SY202: $i] :
( ~ ( product @ SV24 @ SV45 @ SY202 )
| ! [SY203: $i] :
( ~ ( product @ SV11 @ SY202 @ SY203 )
| ( product @ SV35 @ SV45 @ SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ! [SY204: $i] :
( ~ ( product @ SV12 @ SV25 @ SV36 )
| ~ ( product @ SV12 @ SV46 @ SY204 )
| ! [SY205: $i] :
( ~ ( sum @ SV25 @ SV46 @ SY205 )
| ! [SY181: $i] :
( ~ ( product @ SV12 @ SY205 @ SY181 )
| ( sum @ SV36 @ SY204 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ! [SY207: $i] :
( ~ ( product @ SV13 @ SV26 @ SV37 )
| ~ ( product @ SV13 @ SV47 @ SY207 )
| ! [SY208: $i] :
( ~ ( sum @ SV26 @ SV47 @ SY208 )
| ! [SY185: $i] :
( ~ ( sum @ SV37 @ SY207 @ SY185 )
| ( product @ SV13 @ SY208 @ SY185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ! [SY210: $i] :
( ~ ( product @ SV14 @ SV27 @ SV38 )
| ~ ( product @ SV48 @ SV27 @ SY210 )
| ! [SY211: $i] :
( ~ ( sum @ SV14 @ SV48 @ SY211 )
| ! [SY189: $i] :
( ~ ( product @ SY211 @ SV27 @ SY189 )
| ( sum @ SV38 @ SY210 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ! [SY213: $i] :
( ~ ( product @ SV15 @ SV28 @ SV39 )
| ~ ( product @ SV49 @ SV28 @ SY213 )
| ! [SY214: $i] :
( ~ ( sum @ SV15 @ SV49 @ SY214 )
| ! [SY193: $i] :
( ~ ( sum @ SV39 @ SY213 @ SY193 )
| ( product @ SY214 @ SV28 @ SY193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV29 @ SV40 ) )
= $true )
| ( ( ! [SY194: $i] :
( ~ ( sum @ SV16 @ SV29 @ SY194 )
| ( SV40 = SY194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV41: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV30 @ SV41 ) )
= $true )
| ( ( ! [SY195: $i] :
( ~ ( product @ SV17 @ SV30 @ SY195 )
| ( SV41 = SY195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV42: $i,SV31: $i,SV20: $i,SV7: $i] :
( ( ( ~ ( sum @ SV7 @ SV20 @ SV31 ) )
= $true )
| ( ( ! [SY196: $i] :
( ~ ( sum @ SV20 @ SV42 @ SY196 )
| ! [SY197: $i] :
( ~ ( sum @ SV31 @ SV42 @ SY197 )
| ( sum @ SV7 @ SY196 @ SY197 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV43: $i,SV32: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV21 @ SV32 ) )
= $true )
| ( ( ! [SY198: $i] :
( ~ ( sum @ SV21 @ SV43 @ SY198 )
| ! [SY199: $i] :
( ~ ( sum @ SV8 @ SY198 @ SY199 )
| ( sum @ SV32 @ SV43 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV33: $i,SV22: $i,SV9: $i] :
( ( ( sum @ SV9 @ SV22 @ SV33 )
= $false )
| ( ( sum @ SV22 @ SV9 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV44: $i,SV34: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV23 @ SV34 ) )
= $true )
| ( ( ! [SY200: $i] :
( ~ ( product @ SV23 @ SV44 @ SY200 )
| ! [SY201: $i] :
( ~ ( product @ SV34 @ SV44 @ SY201 )
| ( product @ SV10 @ SY200 @ SY201 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV45: $i,SV35: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV24 @ SV35 ) )
= $true )
| ( ( ! [SY202: $i] :
( ~ ( product @ SV24 @ SV45 @ SY202 )
| ! [SY203: $i] :
( ~ ( product @ SV11 @ SY202 @ SY203 )
| ( product @ SV35 @ SV45 @ SY203 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(136,plain,
! [SV50: $i,SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ~ ( product @ SV12 @ SV25 @ SV36 )
| ~ ( product @ SV12 @ SV46 @ SV50 )
| ! [SY216: $i] :
( ~ ( sum @ SV25 @ SV46 @ SY216 )
| ! [SY217: $i] :
( ~ ( product @ SV12 @ SY216 @ SY217 )
| ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV51: $i,SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ~ ( product @ SV13 @ SV26 @ SV37 )
| ~ ( product @ SV13 @ SV47 @ SV51 )
| ! [SY218: $i] :
( ~ ( sum @ SV26 @ SV47 @ SY218 )
| ! [SY219: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY219 )
| ( product @ SV13 @ SY218 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(138,plain,
! [SV52: $i,SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ~ ( product @ SV14 @ SV27 @ SV38 )
| ~ ( product @ SV48 @ SV27 @ SV52 )
| ! [SY220: $i] :
( ~ ( sum @ SV14 @ SV48 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SY220 @ SV27 @ SY221 )
| ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(139,plain,
! [SV53: $i,SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ~ ( product @ SV15 @ SV28 @ SV39 )
| ~ ( product @ SV49 @ SV28 @ SV53 )
| ! [SY222: $i] :
( ~ ( sum @ SV15 @ SV49 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY223 )
| ( product @ SY222 @ SV28 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV29 @ SV40 )
= $false )
| ( ( ! [SY194: $i] :
( ~ ( sum @ SV16 @ SV29 @ SY194 )
| ( SV40 = SY194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV41: $i,SV30: $i,SV17: $i] :
( ( ( product @ SV17 @ SV30 @ SV41 )
= $false )
| ( ( ! [SY195: $i] :
( ~ ( product @ SV17 @ SV30 @ SY195 )
| ( SV41 = SY195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(142,plain,
! [SV42: $i,SV31: $i,SV20: $i,SV7: $i] :
( ( ( sum @ SV7 @ SV20 @ SV31 )
= $false )
| ( ( ! [SY196: $i] :
( ~ ( sum @ SV20 @ SV42 @ SY196 )
| ! [SY197: $i] :
( ~ ( sum @ SV31 @ SV42 @ SY197 )
| ( sum @ SV7 @ SY196 @ SY197 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV43: $i,SV32: $i,SV21: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV21 @ SV32 )
= $false )
| ( ( ! [SY198: $i] :
( ~ ( sum @ SV21 @ SV43 @ SY198 )
| ! [SY199: $i] :
( ~ ( sum @ SV8 @ SY198 @ SY199 )
| ( sum @ SV32 @ SV43 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV44: $i,SV34: $i,SV23: $i,SV10: $i] :
( ( ( product @ SV10 @ SV23 @ SV34 )
= $false )
| ( ( ! [SY200: $i] :
( ~ ( product @ SV23 @ SV44 @ SY200 )
| ! [SY201: $i] :
( ~ ( product @ SV34 @ SV44 @ SY201 )
| ( product @ SV10 @ SY200 @ SY201 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV45: $i,SV35: $i,SV24: $i,SV11: $i] :
( ( ( product @ SV11 @ SV24 @ SV35 )
= $false )
| ( ( ! [SY202: $i] :
( ~ ( product @ SV24 @ SV45 @ SY202 )
| ! [SY203: $i] :
( ~ ( product @ SV11 @ SY202 @ SY203 )
| ( product @ SV35 @ SV45 @ SY203 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV50: $i,SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV25 @ SV36 ) )
= $true )
| ( ( ~ ( product @ SV12 @ SV46 @ SV50 )
| ! [SY216: $i] :
( ~ ( sum @ SV25 @ SV46 @ SY216 )
| ! [SY217: $i] :
( ~ ( product @ SV12 @ SY216 @ SY217 )
| ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV51: $i,SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV26 @ SV37 ) )
= $true )
| ( ( ~ ( product @ SV13 @ SV47 @ SV51 )
| ! [SY218: $i] :
( ~ ( sum @ SV26 @ SV47 @ SY218 )
| ! [SY219: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY219 )
| ( product @ SV13 @ SY218 @ SY219 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV52: $i,SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ( ~ ( product @ SV14 @ SV27 @ SV38 ) )
= $true )
| ( ( ~ ( product @ SV48 @ SV27 @ SV52 )
| ! [SY220: $i] :
( ~ ( sum @ SV14 @ SV48 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SY220 @ SV27 @ SY221 )
| ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV53: $i,SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ( ~ ( product @ SV15 @ SV28 @ SV39 ) )
= $true )
| ( ( ~ ( product @ SV49 @ SV28 @ SV53 )
| ! [SY222: $i] :
( ~ ( sum @ SV15 @ SV49 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY223 )
| ( product @ SY222 @ SV28 @ SY223 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(150,plain,
! [SV40: $i,SV54: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV29 @ SV54 )
| ( SV40 = SV54 ) )
= $true )
| ( ( sum @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV41: $i,SV55: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV30 @ SV55 )
| ( SV41 = SV55 ) )
= $true )
| ( ( product @ SV17 @ SV30 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV7: $i,SV31: $i,SV56: $i,SV42: $i,SV20: $i] :
( ( ( ~ ( sum @ SV20 @ SV42 @ SV56 )
| ! [SY224: $i] :
( ~ ( sum @ SV31 @ SV42 @ SY224 )
| ( sum @ SV7 @ SV56 @ SY224 ) ) )
= $true )
| ( ( sum @ SV7 @ SV20 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV32: $i,SV8: $i,SV57: $i,SV43: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV43 @ SV57 )
| ! [SY225: $i] :
( ~ ( sum @ SV8 @ SV57 @ SY225 )
| ( sum @ SV32 @ SV43 @ SY225 ) ) )
= $true )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV10: $i,SV34: $i,SV58: $i,SV44: $i,SV23: $i] :
( ( ( ~ ( product @ SV23 @ SV44 @ SV58 )
| ! [SY226: $i] :
( ~ ( product @ SV34 @ SV44 @ SY226 )
| ( product @ SV10 @ SV58 @ SY226 ) ) )
= $true )
| ( ( product @ SV10 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV35: $i,SV11: $i,SV59: $i,SV45: $i,SV24: $i] :
( ( ( ~ ( product @ SV24 @ SV45 @ SV59 )
| ! [SY227: $i] :
( ~ ( product @ SV11 @ SV59 @ SY227 )
| ( product @ SV35 @ SV45 @ SY227 ) ) )
= $true )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV50: $i,SV46: $i,SV36: $i,SV25: $i,SV12: $i] :
( ( ( product @ SV12 @ SV25 @ SV36 )
= $false )
| ( ( ~ ( product @ SV12 @ SV46 @ SV50 )
| ! [SY216: $i] :
( ~ ( sum @ SV25 @ SV46 @ SY216 )
| ! [SY217: $i] :
( ~ ( product @ SV12 @ SY216 @ SY217 )
| ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV51: $i,SV47: $i,SV37: $i,SV26: $i,SV13: $i] :
( ( ( product @ SV13 @ SV26 @ SV37 )
= $false )
| ( ( ~ ( product @ SV13 @ SV47 @ SV51 )
| ! [SY218: $i] :
( ~ ( sum @ SV26 @ SV47 @ SY218 )
| ! [SY219: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY219 )
| ( product @ SV13 @ SY218 @ SY219 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV52: $i,SV48: $i,SV38: $i,SV27: $i,SV14: $i] :
( ( ( product @ SV14 @ SV27 @ SV38 )
= $false )
| ( ( ~ ( product @ SV48 @ SV27 @ SV52 )
| ! [SY220: $i] :
( ~ ( sum @ SV14 @ SV48 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SY220 @ SV27 @ SY221 )
| ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV53: $i,SV49: $i,SV39: $i,SV28: $i,SV15: $i] :
( ( ( product @ SV15 @ SV28 @ SV39 )
= $false )
| ( ( ~ ( product @ SV49 @ SV28 @ SV53 )
| ! [SY222: $i] :
( ~ ( sum @ SV15 @ SV49 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY223 )
| ( product @ SY222 @ SV28 @ SY223 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV40: $i,SV54: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( sum @ SV16 @ SV29 @ SV54 ) )
= $true )
| ( ( SV40 = SV54 )
= $true )
| ( ( sum @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV41: $i,SV55: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( product @ SV17 @ SV30 @ SV55 ) )
= $true )
| ( ( SV41 = SV55 )
= $true )
| ( ( product @ SV17 @ SV30 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV7: $i,SV31: $i,SV56: $i,SV42: $i,SV20: $i] :
( ( ( ~ ( sum @ SV20 @ SV42 @ SV56 ) )
= $true )
| ( ( ! [SY224: $i] :
( ~ ( sum @ SV31 @ SV42 @ SY224 )
| ( sum @ SV7 @ SV56 @ SY224 ) ) )
= $true )
| ( ( sum @ SV7 @ SV20 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV32: $i,SV8: $i,SV57: $i,SV43: $i,SV21: $i] :
( ( ( ~ ( sum @ SV21 @ SV43 @ SV57 ) )
= $true )
| ( ( ! [SY225: $i] :
( ~ ( sum @ SV8 @ SV57 @ SY225 )
| ( sum @ SV32 @ SV43 @ SY225 ) ) )
= $true )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV10: $i,SV34: $i,SV58: $i,SV44: $i,SV23: $i] :
( ( ( ~ ( product @ SV23 @ SV44 @ SV58 ) )
= $true )
| ( ( ! [SY226: $i] :
( ~ ( product @ SV34 @ SV44 @ SY226 )
| ( product @ SV10 @ SV58 @ SY226 ) ) )
= $true )
| ( ( product @ SV10 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV35: $i,SV11: $i,SV59: $i,SV45: $i,SV24: $i] :
( ( ( ~ ( product @ SV24 @ SV45 @ SV59 ) )
= $true )
| ( ( ! [SY227: $i] :
( ~ ( product @ SV11 @ SV59 @ SY227 )
| ( product @ SV35 @ SV45 @ SY227 ) ) )
= $true )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV36: $i,SV25: $i,SV50: $i,SV46: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV46 @ SV50 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( sum @ SV25 @ SV46 @ SY216 )
| ! [SY217: $i] :
( ~ ( product @ SV12 @ SY216 @ SY217 )
| ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV37: $i,SV26: $i,SV51: $i,SV47: $i,SV13: $i] :
( ( ( ~ ( product @ SV13 @ SV47 @ SV51 ) )
= $true )
| ( ( ! [SY218: $i] :
( ~ ( sum @ SV26 @ SV47 @ SY218 )
| ! [SY219: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY219 )
| ( product @ SV13 @ SY218 @ SY219 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV38: $i,SV14: $i,SV52: $i,SV27: $i,SV48: $i] :
( ( ( ~ ( product @ SV48 @ SV27 @ SV52 ) )
= $true )
| ( ( ! [SY220: $i] :
( ~ ( sum @ SV14 @ SV48 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SY220 @ SV27 @ SY221 )
| ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV39: $i,SV15: $i,SV53: $i,SV28: $i,SV49: $i] :
( ( ( ~ ( product @ SV49 @ SV28 @ SV53 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( sum @ SV15 @ SV49 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY223 )
| ( product @ SY222 @ SV28 @ SY223 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV40: $i,SV54: $i,SV29: $i,SV16: $i] :
( ( ( sum @ SV16 @ SV29 @ SV54 )
= $false )
| ( ( SV40 = SV54 )
= $true )
| ( ( sum @ SV16 @ SV29 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV41: $i,SV55: $i,SV30: $i,SV17: $i] :
( ( ( product @ SV17 @ SV30 @ SV55 )
= $false )
| ( ( SV41 = SV55 )
= $true )
| ( ( product @ SV17 @ SV30 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV7: $i,SV31: $i,SV56: $i,SV42: $i,SV20: $i] :
( ( ( sum @ SV20 @ SV42 @ SV56 )
= $false )
| ( ( ! [SY224: $i] :
( ~ ( sum @ SV31 @ SV42 @ SY224 )
| ( sum @ SV7 @ SV56 @ SY224 ) ) )
= $true )
| ( ( sum @ SV7 @ SV20 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV32: $i,SV8: $i,SV57: $i,SV43: $i,SV21: $i] :
( ( ( sum @ SV21 @ SV43 @ SV57 )
= $false )
| ( ( ! [SY225: $i] :
( ~ ( sum @ SV8 @ SV57 @ SY225 )
| ( sum @ SV32 @ SV43 @ SY225 ) ) )
= $true )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV10: $i,SV34: $i,SV58: $i,SV44: $i,SV23: $i] :
( ( ( product @ SV23 @ SV44 @ SV58 )
= $false )
| ( ( ! [SY226: $i] :
( ~ ( product @ SV34 @ SV44 @ SY226 )
| ( product @ SV10 @ SV58 @ SY226 ) ) )
= $true )
| ( ( product @ SV10 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV35: $i,SV11: $i,SV59: $i,SV45: $i,SV24: $i] :
( ( ( product @ SV24 @ SV45 @ SV59 )
= $false )
| ( ( ! [SY227: $i] :
( ~ ( product @ SV11 @ SV59 @ SY227 )
| ( product @ SV35 @ SV45 @ SY227 ) ) )
= $true )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV36: $i,SV25: $i,SV50: $i,SV46: $i,SV12: $i] :
( ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( ! [SY216: $i] :
( ~ ( sum @ SV25 @ SV46 @ SY216 )
| ! [SY217: $i] :
( ~ ( product @ SV12 @ SY216 @ SY217 )
| ( sum @ SV36 @ SV50 @ SY217 ) ) ) )
= $true )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV37: $i,SV26: $i,SV51: $i,SV47: $i,SV13: $i] :
( ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( ! [SY218: $i] :
( ~ ( sum @ SV26 @ SV47 @ SY218 )
| ! [SY219: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY219 )
| ( product @ SV13 @ SY218 @ SY219 ) ) ) )
= $true )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV38: $i,SV14: $i,SV52: $i,SV27: $i,SV48: $i] :
( ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( ! [SY220: $i] :
( ~ ( sum @ SV14 @ SV48 @ SY220 )
| ! [SY221: $i] :
( ~ ( product @ SY220 @ SV27 @ SY221 )
| ( sum @ SV38 @ SV52 @ SY221 ) ) ) )
= $true )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV39: $i,SV15: $i,SV53: $i,SV28: $i,SV49: $i] :
( ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( sum @ SV15 @ SV49 @ SY222 )
| ! [SY223: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY223 )
| ( product @ SY222 @ SV28 @ SY223 ) ) ) )
= $true )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV20: $i,SV56: $i,SV7: $i,SV60: $i,SV42: $i,SV31: $i] :
( ( ( ~ ( sum @ SV31 @ SV42 @ SV60 )
| ( sum @ SV7 @ SV56 @ SV60 ) )
= $true )
| ( ( sum @ SV20 @ SV42 @ SV56 )
= $false )
| ( ( sum @ SV7 @ SV20 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV21: $i,SV43: $i,SV32: $i,SV61: $i,SV57: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV57 @ SV61 )
| ( sum @ SV32 @ SV43 @ SV61 ) )
= $true )
| ( ( sum @ SV21 @ SV43 @ SV57 )
= $false )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV23: $i,SV58: $i,SV10: $i,SV62: $i,SV44: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV44 @ SV62 )
| ( product @ SV10 @ SV58 @ SV62 ) )
= $true )
| ( ( product @ SV23 @ SV44 @ SV58 )
= $false )
| ( ( product @ SV10 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV24: $i,SV45: $i,SV35: $i,SV63: $i,SV59: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV59 @ SV63 )
| ( product @ SV35 @ SV45 @ SV63 ) )
= $true )
| ( ( product @ SV24 @ SV45 @ SV59 )
= $false )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV50: $i,SV36: $i,SV12: $i,SV64: $i,SV46: $i,SV25: $i] :
( ( ( ~ ( sum @ SV25 @ SV46 @ SV64 )
| ! [SY228: $i] :
( ~ ( product @ SV12 @ SV64 @ SY228 )
| ( sum @ SV36 @ SV50 @ SY228 ) ) )
= $true )
| ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV13: $i,SV51: $i,SV37: $i,SV65: $i,SV47: $i,SV26: $i] :
( ( ( ~ ( sum @ SV26 @ SV47 @ SV65 )
| ! [SY229: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY229 )
| ( product @ SV13 @ SV65 @ SY229 ) ) )
= $true )
| ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV52: $i,SV38: $i,SV27: $i,SV66: $i,SV48: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV48 @ SV66 )
| ! [SY230: $i] :
( ~ ( product @ SV66 @ SV27 @ SY230 )
| ( sum @ SV38 @ SV52 @ SY230 ) ) )
= $true )
| ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(187,plain,
! [SV28: $i,SV53: $i,SV39: $i,SV67: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV49 @ SV67 )
| ! [SY231: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY231 )
| ( product @ SV67 @ SV28 @ SY231 ) ) )
= $true )
| ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV20: $i,SV56: $i,SV7: $i,SV60: $i,SV42: $i,SV31: $i] :
( ( ( ~ ( sum @ SV31 @ SV42 @ SV60 ) )
= $true )
| ( ( sum @ SV7 @ SV56 @ SV60 )
= $true )
| ( ( sum @ SV20 @ SV42 @ SV56 )
= $false )
| ( ( sum @ SV7 @ SV20 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV21: $i,SV43: $i,SV32: $i,SV61: $i,SV57: $i,SV8: $i] :
( ( ( ~ ( sum @ SV8 @ SV57 @ SV61 ) )
= $true )
| ( ( sum @ SV32 @ SV43 @ SV61 )
= $true )
| ( ( sum @ SV21 @ SV43 @ SV57 )
= $false )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV23: $i,SV58: $i,SV10: $i,SV62: $i,SV44: $i,SV34: $i] :
( ( ( ~ ( product @ SV34 @ SV44 @ SV62 ) )
= $true )
| ( ( product @ SV10 @ SV58 @ SV62 )
= $true )
| ( ( product @ SV23 @ SV44 @ SV58 )
= $false )
| ( ( product @ SV10 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV24: $i,SV45: $i,SV35: $i,SV63: $i,SV59: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV59 @ SV63 ) )
= $true )
| ( ( product @ SV35 @ SV45 @ SV63 )
= $true )
| ( ( product @ SV24 @ SV45 @ SV59 )
= $false )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV50: $i,SV36: $i,SV12: $i,SV64: $i,SV46: $i,SV25: $i] :
( ( ( ~ ( sum @ SV25 @ SV46 @ SV64 ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( product @ SV12 @ SV64 @ SY228 )
| ( sum @ SV36 @ SV50 @ SY228 ) ) )
= $true )
| ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV13: $i,SV51: $i,SV37: $i,SV65: $i,SV47: $i,SV26: $i] :
( ( ( ~ ( sum @ SV26 @ SV47 @ SV65 ) )
= $true )
| ( ( ! [SY229: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY229 )
| ( product @ SV13 @ SV65 @ SY229 ) ) )
= $true )
| ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV52: $i,SV38: $i,SV27: $i,SV66: $i,SV48: $i,SV14: $i] :
( ( ( ~ ( sum @ SV14 @ SV48 @ SV66 ) )
= $true )
| ( ( ! [SY230: $i] :
( ~ ( product @ SV66 @ SV27 @ SY230 )
| ( sum @ SV38 @ SV52 @ SY230 ) ) )
= $true )
| ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV28: $i,SV53: $i,SV39: $i,SV67: $i,SV49: $i,SV15: $i] :
( ( ( ~ ( sum @ SV15 @ SV49 @ SV67 ) )
= $true )
| ( ( ! [SY231: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY231 )
| ( product @ SV67 @ SV28 @ SY231 ) ) )
= $true )
| ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV20: $i,SV56: $i,SV7: $i,SV60: $i,SV42: $i,SV31: $i] :
( ( ( sum @ SV31 @ SV42 @ SV60 )
= $false )
| ( ( sum @ SV7 @ SV56 @ SV60 )
= $true )
| ( ( sum @ SV20 @ SV42 @ SV56 )
= $false )
| ( ( sum @ SV7 @ SV20 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV21: $i,SV43: $i,SV32: $i,SV61: $i,SV57: $i,SV8: $i] :
( ( ( sum @ SV8 @ SV57 @ SV61 )
= $false )
| ( ( sum @ SV32 @ SV43 @ SV61 )
= $true )
| ( ( sum @ SV21 @ SV43 @ SV57 )
= $false )
| ( ( sum @ SV8 @ SV21 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(198,plain,
! [SV23: $i,SV58: $i,SV10: $i,SV62: $i,SV44: $i,SV34: $i] :
( ( ( product @ SV34 @ SV44 @ SV62 )
= $false )
| ( ( product @ SV10 @ SV58 @ SV62 )
= $true )
| ( ( product @ SV23 @ SV44 @ SV58 )
= $false )
| ( ( product @ SV10 @ SV23 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(199,plain,
! [SV24: $i,SV45: $i,SV35: $i,SV63: $i,SV59: $i,SV11: $i] :
( ( ( product @ SV11 @ SV59 @ SV63 )
= $false )
| ( ( product @ SV35 @ SV45 @ SV63 )
= $true )
| ( ( product @ SV24 @ SV45 @ SV59 )
= $false )
| ( ( product @ SV11 @ SV24 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV50: $i,SV36: $i,SV12: $i,SV64: $i,SV46: $i,SV25: $i] :
( ( ( sum @ SV25 @ SV46 @ SV64 )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( product @ SV12 @ SV64 @ SY228 )
| ( sum @ SV36 @ SV50 @ SY228 ) ) )
= $true )
| ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV13: $i,SV51: $i,SV37: $i,SV65: $i,SV47: $i,SV26: $i] :
( ( ( sum @ SV26 @ SV47 @ SV65 )
= $false )
| ( ( ! [SY229: $i] :
( ~ ( sum @ SV37 @ SV51 @ SY229 )
| ( product @ SV13 @ SV65 @ SY229 ) ) )
= $true )
| ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV52: $i,SV38: $i,SV27: $i,SV66: $i,SV48: $i,SV14: $i] :
( ( ( sum @ SV14 @ SV48 @ SV66 )
= $false )
| ( ( ! [SY230: $i] :
( ~ ( product @ SV66 @ SV27 @ SY230 )
| ( sum @ SV38 @ SV52 @ SY230 ) ) )
= $true )
| ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV28: $i,SV53: $i,SV39: $i,SV67: $i,SV49: $i,SV15: $i] :
( ( ( sum @ SV15 @ SV49 @ SV67 )
= $false )
| ( ( ! [SY231: $i] :
( ~ ( sum @ SV39 @ SV53 @ SY231 )
| ( product @ SV67 @ SV28 @ SY231 ) ) )
= $true )
| ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV46: $i,SV25: $i,SV50: $i,SV36: $i,SV68: $i,SV64: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV64 @ SV68 )
| ( sum @ SV36 @ SV50 @ SV68 ) )
= $true )
| ( ( sum @ SV25 @ SV46 @ SV64 )
= $false )
| ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV47: $i,SV26: $i,SV65: $i,SV13: $i,SV69: $i,SV51: $i,SV37: $i] :
( ( ( ~ ( sum @ SV37 @ SV51 @ SV69 )
| ( product @ SV13 @ SV65 @ SV69 ) )
= $true )
| ( ( sum @ SV26 @ SV47 @ SV65 )
= $false )
| ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(206,plain,
! [SV48: $i,SV14: $i,SV52: $i,SV38: $i,SV70: $i,SV27: $i,SV66: $i] :
( ( ( ~ ( product @ SV66 @ SV27 @ SV70 )
| ( sum @ SV38 @ SV52 @ SV70 ) )
= $true )
| ( ( sum @ SV14 @ SV48 @ SV66 )
= $false )
| ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV49: $i,SV15: $i,SV28: $i,SV67: $i,SV71: $i,SV53: $i,SV39: $i] :
( ( ( ~ ( sum @ SV39 @ SV53 @ SV71 )
| ( product @ SV67 @ SV28 @ SV71 ) )
= $true )
| ( ( sum @ SV15 @ SV49 @ SV67 )
= $false )
| ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV46: $i,SV25: $i,SV50: $i,SV36: $i,SV68: $i,SV64: $i,SV12: $i] :
( ( ( ~ ( product @ SV12 @ SV64 @ SV68 ) )
= $true )
| ( ( sum @ SV36 @ SV50 @ SV68 )
= $true )
| ( ( sum @ SV25 @ SV46 @ SV64 )
= $false )
| ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV47: $i,SV26: $i,SV65: $i,SV13: $i,SV69: $i,SV51: $i,SV37: $i] :
( ( ( ~ ( sum @ SV37 @ SV51 @ SV69 ) )
= $true )
| ( ( product @ SV13 @ SV65 @ SV69 )
= $true )
| ( ( sum @ SV26 @ SV47 @ SV65 )
= $false )
| ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV48: $i,SV14: $i,SV52: $i,SV38: $i,SV70: $i,SV27: $i,SV66: $i] :
( ( ( ~ ( product @ SV66 @ SV27 @ SV70 ) )
= $true )
| ( ( sum @ SV38 @ SV52 @ SV70 )
= $true )
| ( ( sum @ SV14 @ SV48 @ SV66 )
= $false )
| ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(211,plain,
! [SV49: $i,SV15: $i,SV28: $i,SV67: $i,SV71: $i,SV53: $i,SV39: $i] :
( ( ( ~ ( sum @ SV39 @ SV53 @ SV71 ) )
= $true )
| ( ( product @ SV67 @ SV28 @ SV71 )
= $true )
| ( ( sum @ SV15 @ SV49 @ SV67 )
= $false )
| ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV46: $i,SV25: $i,SV50: $i,SV36: $i,SV68: $i,SV64: $i,SV12: $i] :
( ( ( product @ SV12 @ SV64 @ SV68 )
= $false )
| ( ( sum @ SV36 @ SV50 @ SV68 )
= $true )
| ( ( sum @ SV25 @ SV46 @ SV64 )
= $false )
| ( ( product @ SV12 @ SV46 @ SV50 )
= $false )
| ( ( product @ SV12 @ SV25 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(213,plain,
! [SV47: $i,SV26: $i,SV65: $i,SV13: $i,SV69: $i,SV51: $i,SV37: $i] :
( ( ( sum @ SV37 @ SV51 @ SV69 )
= $false )
| ( ( product @ SV13 @ SV65 @ SV69 )
= $true )
| ( ( sum @ SV26 @ SV47 @ SV65 )
= $false )
| ( ( product @ SV13 @ SV47 @ SV51 )
= $false )
| ( ( product @ SV13 @ SV26 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(214,plain,
! [SV48: $i,SV14: $i,SV52: $i,SV38: $i,SV70: $i,SV27: $i,SV66: $i] :
( ( ( product @ SV66 @ SV27 @ SV70 )
= $false )
| ( ( sum @ SV38 @ SV52 @ SV70 )
= $true )
| ( ( sum @ SV14 @ SV48 @ SV66 )
= $false )
| ( ( product @ SV48 @ SV27 @ SV52 )
= $false )
| ( ( product @ SV14 @ SV27 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV49: $i,SV15: $i,SV28: $i,SV67: $i,SV71: $i,SV53: $i,SV39: $i] :
( ( ( sum @ SV39 @ SV53 @ SV71 )
= $false )
| ( ( product @ SV67 @ SV28 @ SV71 )
= $true )
| ( ( sum @ SV15 @ SV49 @ SV67 )
= $false )
| ( ( product @ SV49 @ SV28 @ SV53 )
= $false )
| ( ( product @ SV15 @ SV28 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(216,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,215,214,213,212,199,198,197,196,171,170,133,97,96,95,83,82,79,78,77,58]) ).
thf(217,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : RNG003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 08:03:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.37
% 0.12/0.37 No.of.Axioms: 20
% 0.12/0.37
% 0.12/0.37 Length.of.Defs: 0
% 0.12/0.37
% 0.12/0.37 Contains.Choice.Funs: false
% 0.12/0.40 (rf:0,axioms:20,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:22,loop_count:0,foatp_calls:0,translation:fof_full)................
% 0.55/0.72
% 0.55/0.72 ********************************
% 0.55/0.72 * All subproblems solved! *
% 0.55/0.72 ********************************
% 0.55/0.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:216,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.73
% 0.55/0.73 %**** Beginning of derivation protocol ****
% 0.55/0.73 % SZS output start CNFRefutation
% See solution above
% 0.55/0.74
% 0.55/0.74 %**** End of derivation protocol ****
% 0.55/0.74 %**** no. of clauses in derivation: 217 ****
% 0.55/0.74 %**** clause counter: 216 ****
% 0.55/0.74
% 0.55/0.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:216,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------