TSTP Solution File: FLD067-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : FLD067-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Sat Jul 16 02:17:21 EDT 2022
% Result : Unsatisfiable 6.40s 6.61s
% Output : CNFRefutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 46
% Syntax : Number of formulae : 263 ( 135 unt; 12 typ; 0 def)
% Number of atoms : 1446 ( 379 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2473 ( 353 ~; 437 |; 0 &;1683 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 483 ( 0 ^ 483 !; 0 ?; 483 :)
% 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_defined,type,
defined: $i > $o ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_u,type,
u: $i ).
thf(1,axiom,
~ ( equalish @ additive_identity @ multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
thf(2,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( less_or_equal @ Y @ Z )
| ~ ( less_or_equal @ X @ Z )
| ~ ( equalish @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
thf(3,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( equalish @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
thf(4,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( equalish @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
thf(5,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( equalish @ X @ Z )
| ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( equalish @ X @ Y )
| ~ ( equalish @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
thf(7,axiom,
! [X: $i] :
( ( equalish @ X @ X )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_equality) ).
thf(8,axiom,
! [Y: $i,Z: $i] :
( ( less_or_equal @ additive_identity @ ( multiply @ Y @ Z ) )
| ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( less_or_equal @ additive_identity @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(9,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ ( add @ X @ Z ) @ ( add @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( less_or_equal @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
| ( less_or_equal @ Y @ X )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(11,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ X @ Z )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( equalish @ X @ Y )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(13,axiom,
! [X: $i] :
( ( defined @ ( multiplicative_inverse @ X ) )
| ~ ( defined @ X )
| ( equalish @ X @ additive_identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(14,axiom,
defined @ multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(15,axiom,
! [X: $i,Y: $i] :
( ( defined @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(16,axiom,
! [X: $i] :
( ( defined @ ( additive_inverse @ X ) )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(17,axiom,
defined @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(18,axiom,
! [X: $i,Y: $i] :
( ( defined @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(19,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) @ ( multiply @ ( add @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
thf(20,axiom,
! [X: $i,Y: $i] :
( ( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(21,axiom,
! [X: $i] :
( ( equalish @ ( multiply @ X @ ( multiplicative_inverse @ X ) ) @ multiplicative_identity )
| ~ ( defined @ X )
| ( equalish @ X @ additive_identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(22,axiom,
! [X: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ X ) @ X )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(23,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( equalish @ ( multiply @ X @ ( multiply @ Y @ Z ) ) @ ( multiply @ ( multiply @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication) ).
thf(24,axiom,
! [X: $i,Y: $i] :
( ( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
thf(25,axiom,
! [X: $i] :
( ( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(26,axiom,
! [X: $i] :
( ( equalish @ ( add @ additive_identity @ X ) @ X )
| ~ ( defined @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(27,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition) ).
thf(28,axiom,
defined @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
thf(29,axiom,
defined @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
thf(30,axiom,
defined @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
thf(31,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(32,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,negated_conjecture,
~ ( less_or_equal @ additive_identity @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_6) ).
thf(34,negated_conjecture,
equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_5) ).
thf(35,negated_conjecture,
less_or_equal @ a @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
thf(36,plain,
$false = $false,
inference(unfold_def,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ( equalish @ additive_identity @ multiplicative_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(38,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( less_or_equal @ Y @ Z )
| ~ ( less_or_equal @ X @ Z )
| ~ ( equalish @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(39,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( equalish @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( equalish @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(41,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ X @ Z )
| ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ X @ Y )
| ~ ( equalish @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( equalish @ X @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(44,plain,
( ( ! [Y: $i,Z: $i] :
( ( less_or_equal @ additive_identity @ ( multiply @ Y @ Z ) )
| ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( less_or_equal @ additive_identity @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(45,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ ( add @ X @ Z ) @ ( add @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( less_or_equal @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
| ( less_or_equal @ Y @ X )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(47,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ X @ Z )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ X @ Y )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(49,plain,
( ( ! [X: $i] :
( ( defined @ ( multiplicative_inverse @ X ) )
| ~ ( defined @ X )
| ( equalish @ X @ additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(50,plain,
( ( defined @ multiplicative_identity )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( defined @ ( additive_inverse @ X ) )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(53,plain,
( ( defined @ additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) @ ( multiply @ ( add @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(57,plain,
( ( ! [X: $i] :
( ( equalish @ ( multiply @ X @ ( multiplicative_inverse @ X ) ) @ multiplicative_identity )
| ~ ( defined @ X )
| ( equalish @ X @ additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ X ) @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( equalish @ ( multiply @ X @ ( multiply @ Y @ Z ) ) @ ( multiply @ ( multiply @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( equalish @ ( add @ additive_identity @ X ) @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(64,plain,
( ( defined @ u )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(65,plain,
( ( defined @ b )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(66,plain,
( ( defined @ a )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(67,plain,
( ( ~ ( less_or_equal @ additive_identity @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(68,plain,
( ( equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(69,plain,
( ( less_or_equal @ a @ b )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(70,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(71,plain,
( ( ! [Y: $i,Z: $i] :
( ( less_or_equal @ Y @ Z )
| ! [X: $i] :
( ~ ( less_or_equal @ X @ Z )
| ~ ( equalish @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(72,plain,
( ( ! [X: $i,Z: $i] :
( ( equalish @ X @ Z )
| ! [Y: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(73,plain,
( ( ! [X: $i,Z: $i] :
( ( less_or_equal @ X @ Z )
| ! [Y: $i] :
( ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(74,plain,
( ( less_or_equal @ a @ b )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(75,plain,
( ( equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ( less_or_equal @ additive_identity @ u ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(77,plain,
( ( defined @ a )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(78,plain,
( ( defined @ b )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(79,plain,
( ( defined @ u )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( equalish @ ( add @ X @ ( add @ Y @ Z ) ) @ ( add @ ( add @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(81,plain,
( ( ! [X: $i] :
( ( equalish @ ( add @ additive_identity @ X ) @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(82,plain,
( ( ! [X: $i] :
( ( equalish @ ( add @ X @ ( additive_inverse @ X ) ) @ additive_identity )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ ( add @ X @ Y ) @ ( add @ Y @ X ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( equalish @ ( multiply @ X @ ( multiply @ Y @ Z ) ) @ ( multiply @ ( multiply @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(85,plain,
( ( ! [X: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ X ) @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(86,plain,
( ( ! [X: $i] :
( ( equalish @ ( multiply @ X @ ( multiplicative_inverse @ X ) ) @ multiplicative_identity )
| ~ ( defined @ X )
| ( equalish @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(87,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ ( multiply @ X @ Y ) @ ( multiply @ Y @ X ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(88,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) @ ( multiply @ ( add @ X @ Y ) @ Z ) )
| ~ ( defined @ X )
| ~ ( defined @ Y )
| ~ ( defined @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( add @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(90,plain,
( ( defined @ additive_identity )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(91,plain,
( ( ! [X: $i] :
( ( defined @ ( additive_inverse @ X ) )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i] :
( ( defined @ ( multiply @ X @ Y ) )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(93,plain,
( ( defined @ multiplicative_identity )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(94,plain,
( ( ! [X: $i] :
( ( defined @ ( multiplicative_inverse @ X ) )
| ~ ( defined @ X )
| ( equalish @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(95,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ X @ Y )
| ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(96,plain,
( ( ! [X: $i,Z: $i] :
( ( less_or_equal @ X @ Z )
| ! [Y: $i] :
( ~ ( less_or_equal @ X @ Y )
| ~ ( less_or_equal @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i] :
( ( less_or_equal @ X @ Y )
| ( less_or_equal @ Y @ X )
| ~ ( defined @ X )
| ~ ( defined @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(98,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( less_or_equal @ ( add @ X @ Z ) @ ( add @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( less_or_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(99,plain,
( ( ! [Y: $i,Z: $i] :
( ( less_or_equal @ additive_identity @ ( multiply @ Y @ Z ) )
| ~ ( less_or_equal @ additive_identity @ Y )
| ~ ( less_or_equal @ additive_identity @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(100,plain,
( ( ! [X: $i] :
( ( equalish @ X @ X )
| ~ ( defined @ X ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i] :
( ( equalish @ X @ Y )
| ~ ( equalish @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(102,plain,
( ( ! [X: $i,Z: $i] :
( ( equalish @ X @ Z )
| ! [Y: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(103,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( add @ X @ Z ) @ ( add @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( equalish @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(104,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( equalish @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) )
| ~ ( defined @ Z )
| ~ ( equalish @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(105,plain,
( ( ! [Y: $i,Z: $i] :
( ( less_or_equal @ Y @ Z )
| ! [X: $i] :
( ~ ( less_or_equal @ X @ Z )
| ~ ( equalish @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(106,plain,
( ( ~ ( equalish @ additive_identity @ multiplicative_identity ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(107,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(108,plain,
( ( less_or_equal @ additive_identity @ u )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(109,plain,
! [SV1: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( equalish @ ( add @ SV1 @ ( add @ SY50 @ SY51 ) ) @ ( add @ ( add @ SV1 @ SY50 ) @ SY51 ) )
| ~ ( defined @ SV1 )
| ~ ( defined @ SY50 )
| ~ ( defined @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(110,plain,
! [SV2: $i] :
( ( ( equalish @ ( add @ additive_identity @ SV2 ) @ SV2 )
| ~ ( defined @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(111,plain,
! [SV3: $i] :
( ( ( equalish @ ( add @ SV3 @ ( additive_inverse @ SV3 ) ) @ additive_identity )
| ~ ( defined @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(112,plain,
! [SV4: $i] :
( ( ! [SY52: $i] :
( ( equalish @ ( add @ SV4 @ SY52 ) @ ( add @ SY52 @ SV4 ) )
| ~ ( defined @ SV4 )
| ~ ( defined @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(113,plain,
! [SV5: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( equalish @ ( multiply @ SV5 @ ( multiply @ SY53 @ SY54 ) ) @ ( multiply @ ( multiply @ SV5 @ SY53 ) @ SY54 ) )
| ~ ( defined @ SV5 )
| ~ ( defined @ SY53 )
| ~ ( defined @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(114,plain,
! [SV6: $i] :
( ( ( equalish @ ( multiply @ multiplicative_identity @ SV6 ) @ SV6 )
| ~ ( defined @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(115,plain,
! [SV7: $i] :
( ( ( equalish @ ( multiply @ SV7 @ ( multiplicative_inverse @ SV7 ) ) @ multiplicative_identity )
| ~ ( defined @ SV7 )
| ( equalish @ SV7 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(116,plain,
! [SV8: $i] :
( ( ! [SY55: $i] :
( ( equalish @ ( multiply @ SV8 @ SY55 ) @ ( multiply @ SY55 @ SV8 ) )
| ~ ( defined @ SV8 )
| ~ ( defined @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(117,plain,
! [SV9: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ( equalish @ ( add @ ( multiply @ SV9 @ SY56 ) @ ( multiply @ SY57 @ SY56 ) ) @ ( multiply @ ( add @ SV9 @ SY57 ) @ SY56 ) )
| ~ ( defined @ SV9 )
| ~ ( defined @ SY57 )
| ~ ( defined @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(118,plain,
! [SV10: $i] :
( ( ! [SY58: $i] :
( ( defined @ ( add @ SV10 @ SY58 ) )
| ~ ( defined @ SV10 )
| ~ ( defined @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(119,plain,
! [SV11: $i] :
( ( ( defined @ ( additive_inverse @ SV11 ) )
| ~ ( defined @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(120,plain,
! [SV12: $i] :
( ( ! [SY59: $i] :
( ( defined @ ( multiply @ SV12 @ SY59 ) )
| ~ ( defined @ SV12 )
| ~ ( defined @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(121,plain,
! [SV13: $i] :
( ( ( defined @ ( multiplicative_inverse @ SV13 ) )
| ~ ( defined @ SV13 )
| ( equalish @ SV13 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(122,plain,
! [SV14: $i] :
( ( ! [SY60: $i] :
( ( equalish @ SV14 @ SY60 )
| ~ ( less_or_equal @ SV14 @ SY60 )
| ~ ( less_or_equal @ SY60 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(123,plain,
! [SV15: $i] :
( ( ! [SY61: $i] :
( ( less_or_equal @ SV15 @ SY61 )
| ! [SY62: $i] :
( ~ ( less_or_equal @ SV15 @ SY62 )
| ~ ( less_or_equal @ SY62 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(124,plain,
! [SV16: $i] :
( ( ! [SY63: $i] :
( ( less_or_equal @ SV16 @ SY63 )
| ( less_or_equal @ SY63 @ SV16 )
| ~ ( defined @ SV16 )
| ~ ( defined @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(125,plain,
! [SV17: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( less_or_equal @ ( add @ SV17 @ SY64 ) @ ( add @ SY65 @ SY64 ) )
| ~ ( defined @ SY64 )
| ~ ( less_or_equal @ SV17 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(126,plain,
! [SV18: $i] :
( ( ! [SY66: $i] :
( ( less_or_equal @ additive_identity @ ( multiply @ SV18 @ SY66 ) )
| ~ ( less_or_equal @ additive_identity @ SV18 )
| ~ ( less_or_equal @ additive_identity @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(127,plain,
! [SV19: $i] :
( ( ( equalish @ SV19 @ SV19 )
| ~ ( defined @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(128,plain,
! [SV20: $i] :
( ( ! [SY67: $i] :
( ( equalish @ SV20 @ SY67 )
| ~ ( equalish @ SY67 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(129,plain,
! [SV21: $i] :
( ( ! [SY68: $i] :
( ( equalish @ SV21 @ SY68 )
| ! [SY69: $i] :
( ~ ( equalish @ SV21 @ SY69 )
| ~ ( equalish @ SY69 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(130,plain,
! [SV22: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ( equalish @ ( add @ SV22 @ SY70 ) @ ( add @ SY71 @ SY70 ) )
| ~ ( defined @ SY70 )
| ~ ( equalish @ SV22 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(131,plain,
! [SV23: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( equalish @ ( multiply @ SV23 @ SY72 ) @ ( multiply @ SY73 @ SY72 ) )
| ~ ( defined @ SY72 )
| ~ ( equalish @ SV23 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(132,plain,
! [SV24: $i] :
( ( ! [SY74: $i] :
( ( less_or_equal @ SV24 @ SY74 )
| ! [SY75: $i] :
( ~ ( less_or_equal @ SY75 @ SY74 )
| ~ ( equalish @ SY75 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(133,plain,
( ( equalish @ additive_identity @ multiplicative_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(134,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(135,plain,
! [SV25: $i,SV1: $i] :
( ( ! [SY76: $i] :
( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SY76 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SY76 ) )
| ~ ( defined @ SV1 )
| ~ ( defined @ SV25 )
| ~ ( defined @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(136,plain,
! [SV2: $i] :
( ( ( equalish @ ( add @ additive_identity @ SV2 ) @ SV2 )
= $true )
| ( ( ~ ( defined @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(137,plain,
! [SV3: $i] :
( ( ( equalish @ ( add @ SV3 @ ( additive_inverse @ SV3 ) ) @ additive_identity )
= $true )
| ( ( ~ ( defined @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(138,plain,
! [SV26: $i,SV4: $i] :
( ( ( equalish @ ( add @ SV4 @ SV26 ) @ ( add @ SV26 @ SV4 ) )
| ~ ( defined @ SV4 )
| ~ ( defined @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(139,plain,
! [SV27: $i,SV5: $i] :
( ( ! [SY77: $i] :
( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SY77 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SY77 ) )
| ~ ( defined @ SV5 )
| ~ ( defined @ SV27 )
| ~ ( defined @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(140,plain,
! [SV6: $i] :
( ( ( equalish @ ( multiply @ multiplicative_identity @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( defined @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(141,plain,
! [SV7: $i] :
( ( ( equalish @ ( multiply @ SV7 @ ( multiplicative_inverse @ SV7 ) ) @ multiplicative_identity )
= $true )
| ( ( ~ ( defined @ SV7 )
| ( equalish @ SV7 @ additive_identity ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(142,plain,
! [SV28: $i,SV8: $i] :
( ( ( equalish @ ( multiply @ SV8 @ SV28 ) @ ( multiply @ SV28 @ SV8 ) )
| ~ ( defined @ SV8 )
| ~ ( defined @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV29: $i,SV9: $i] :
( ( ! [SY78: $i] :
( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SY78 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SY78 ) @ SV29 ) )
| ~ ( defined @ SV9 )
| ~ ( defined @ SY78 )
| ~ ( defined @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
! [SV30: $i,SV10: $i] :
( ( ( defined @ ( add @ SV10 @ SV30 ) )
| ~ ( defined @ SV10 )
| ~ ( defined @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(145,plain,
! [SV11: $i] :
( ( ( defined @ ( additive_inverse @ SV11 ) )
= $true )
| ( ( ~ ( defined @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(146,plain,
! [SV31: $i,SV12: $i] :
( ( ( defined @ ( multiply @ SV12 @ SV31 ) )
| ~ ( defined @ SV12 )
| ~ ( defined @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(147,plain,
! [SV13: $i] :
( ( ( defined @ ( multiplicative_inverse @ SV13 ) )
= $true )
| ( ( ~ ( defined @ SV13 )
| ( equalish @ SV13 @ additive_identity ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(148,plain,
! [SV32: $i,SV14: $i] :
( ( ( equalish @ SV14 @ SV32 )
| ~ ( less_or_equal @ SV14 @ SV32 )
| ~ ( less_or_equal @ SV32 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(149,plain,
! [SV33: $i,SV15: $i] :
( ( ( less_or_equal @ SV15 @ SV33 )
| ! [SY79: $i] :
( ~ ( less_or_equal @ SV15 @ SY79 )
| ~ ( less_or_equal @ SY79 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(150,plain,
! [SV34: $i,SV16: $i] :
( ( ( less_or_equal @ SV16 @ SV34 )
| ( less_or_equal @ SV34 @ SV16 )
| ~ ( defined @ SV16 )
| ~ ( defined @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(151,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY80: $i] :
( ( less_or_equal @ ( add @ SV17 @ SV35 ) @ ( add @ SY80 @ SV35 ) )
| ~ ( defined @ SV35 )
| ~ ( less_or_equal @ SV17 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV36: $i,SV18: $i] :
( ( ( less_or_equal @ additive_identity @ ( multiply @ SV18 @ SV36 ) )
| ~ ( less_or_equal @ additive_identity @ SV18 )
| ~ ( less_or_equal @ additive_identity @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(153,plain,
! [SV19: $i] :
( ( ( equalish @ SV19 @ SV19 )
= $true )
| ( ( ~ ( defined @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV37: $i,SV20: $i] :
( ( ( equalish @ SV20 @ SV37 )
| ~ ( equalish @ SV37 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
! [SV38: $i,SV21: $i] :
( ( ( equalish @ SV21 @ SV38 )
| ! [SY81: $i] :
( ~ ( equalish @ SV21 @ SY81 )
| ~ ( equalish @ SY81 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV39: $i,SV22: $i] :
( ( ! [SY82: $i] :
( ( equalish @ ( add @ SV22 @ SV39 ) @ ( add @ SY82 @ SV39 ) )
| ~ ( defined @ SV39 )
| ~ ( equalish @ SV22 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(157,plain,
! [SV40: $i,SV23: $i] :
( ( ! [SY83: $i] :
( ( equalish @ ( multiply @ SV23 @ SV40 ) @ ( multiply @ SY83 @ SV40 ) )
| ~ ( defined @ SV40 )
| ~ ( equalish @ SV23 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(158,plain,
! [SV41: $i,SV24: $i] :
( ( ( less_or_equal @ SV24 @ SV41 )
| ! [SY84: $i] :
( ~ ( less_or_equal @ SY84 @ SV41 )
| ~ ( equalish @ SY84 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(159,plain,
! [SV42: $i,SV25: $i,SV1: $i] :
( ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
| ~ ( defined @ SV1 )
| ~ ( defined @ SV25 )
| ~ ( defined @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(160,plain,
! [SV2: $i] :
( ( ( defined @ SV2 )
= $false )
| ( ( equalish @ ( add @ additive_identity @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(161,plain,
! [SV3: $i] :
( ( ( defined @ SV3 )
= $false )
| ( ( equalish @ ( add @ SV3 @ ( additive_inverse @ SV3 ) ) @ additive_identity )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(162,plain,
! [SV26: $i,SV4: $i] :
( ( ( equalish @ ( add @ SV4 @ SV26 ) @ ( add @ SV26 @ SV4 ) )
= $true )
| ( ( ~ ( defined @ SV4 )
| ~ ( defined @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(163,plain,
! [SV43: $i,SV27: $i,SV5: $i] :
( ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
| ~ ( defined @ SV5 )
| ~ ( defined @ SV27 )
| ~ ( defined @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(164,plain,
! [SV6: $i] :
( ( ( defined @ SV6 )
= $false )
| ( ( equalish @ ( multiply @ multiplicative_identity @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(165,plain,
! [SV7: $i] :
( ( ( ~ ( defined @ SV7 ) )
= $true )
| ( ( equalish @ SV7 @ additive_identity )
= $true )
| ( ( equalish @ ( multiply @ SV7 @ ( multiplicative_inverse @ SV7 ) ) @ multiplicative_identity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(166,plain,
! [SV28: $i,SV8: $i] :
( ( ( equalish @ ( multiply @ SV8 @ SV28 ) @ ( multiply @ SV28 @ SV8 ) )
= $true )
| ( ( ~ ( defined @ SV8 )
| ~ ( defined @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(167,plain,
! [SV44: $i,SV29: $i,SV9: $i] :
( ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
| ~ ( defined @ SV9 )
| ~ ( defined @ SV44 )
| ~ ( defined @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(168,plain,
! [SV30: $i,SV10: $i] :
( ( ( defined @ ( add @ SV10 @ SV30 ) )
= $true )
| ( ( ~ ( defined @ SV10 )
| ~ ( defined @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(169,plain,
! [SV11: $i] :
( ( ( defined @ SV11 )
= $false )
| ( ( defined @ ( additive_inverse @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV31: $i,SV12: $i] :
( ( ( defined @ ( multiply @ SV12 @ SV31 ) )
= $true )
| ( ( ~ ( defined @ SV12 )
| ~ ( defined @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV13: $i] :
( ( ( ~ ( defined @ SV13 ) )
= $true )
| ( ( equalish @ SV13 @ additive_identity )
= $true )
| ( ( defined @ ( multiplicative_inverse @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV32: $i,SV14: $i] :
( ( ( equalish @ SV14 @ SV32 )
= $true )
| ( ( ~ ( less_or_equal @ SV14 @ SV32 )
| ~ ( less_or_equal @ SV32 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV33: $i,SV15: $i] :
( ( ( less_or_equal @ SV15 @ SV33 )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( less_or_equal @ SV15 @ SY79 )
| ~ ( less_or_equal @ SY79 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(174,plain,
! [SV34: $i,SV16: $i] :
( ( ( less_or_equal @ SV16 @ SV34 )
= $true )
| ( ( ( less_or_equal @ SV34 @ SV16 )
| ~ ( defined @ SV16 )
| ~ ( defined @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(175,plain,
! [SV45: $i,SV35: $i,SV17: $i] :
( ( ( less_or_equal @ ( add @ SV17 @ SV35 ) @ ( add @ SV45 @ SV35 ) )
| ~ ( defined @ SV35 )
| ~ ( less_or_equal @ SV17 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(176,plain,
! [SV36: $i,SV18: $i] :
( ( ( less_or_equal @ additive_identity @ ( multiply @ SV18 @ SV36 ) )
= $true )
| ( ( ~ ( less_or_equal @ additive_identity @ SV18 )
| ~ ( less_or_equal @ additive_identity @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(177,plain,
! [SV19: $i] :
( ( ( defined @ SV19 )
= $false )
| ( ( equalish @ SV19 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(178,plain,
! [SV37: $i,SV20: $i] :
( ( ( equalish @ SV20 @ SV37 )
= $true )
| ( ( ~ ( equalish @ SV37 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(179,plain,
! [SV38: $i,SV21: $i] :
( ( ( equalish @ SV21 @ SV38 )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( equalish @ SV21 @ SY81 )
| ~ ( equalish @ SY81 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(180,plain,
! [SV46: $i,SV39: $i,SV22: $i] :
( ( ( equalish @ ( add @ SV22 @ SV39 ) @ ( add @ SV46 @ SV39 ) )
| ~ ( defined @ SV39 )
| ~ ( equalish @ SV22 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(181,plain,
! [SV47: $i,SV40: $i,SV23: $i] :
( ( ( equalish @ ( multiply @ SV23 @ SV40 ) @ ( multiply @ SV47 @ SV40 ) )
| ~ ( defined @ SV40 )
| ~ ( equalish @ SV23 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(182,plain,
! [SV41: $i,SV24: $i] :
( ( ( less_or_equal @ SV24 @ SV41 )
= $true )
| ( ( ! [SY84: $i] :
( ~ ( less_or_equal @ SY84 @ SV41 )
| ~ ( equalish @ SY84 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(183,plain,
! [SV42: $i,SV25: $i,SV1: $i] :
( ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
= $true )
| ( ( ~ ( defined @ SV1 )
| ~ ( defined @ SV25 )
| ~ ( defined @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(184,plain,
! [SV26: $i,SV4: $i] :
( ( ( ~ ( defined @ SV4 ) )
= $true )
| ( ( ~ ( defined @ SV26 ) )
= $true )
| ( ( equalish @ ( add @ SV4 @ SV26 ) @ ( add @ SV26 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(185,plain,
! [SV43: $i,SV27: $i,SV5: $i] :
( ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
= $true )
| ( ( ~ ( defined @ SV5 )
| ~ ( defined @ SV27 )
| ~ ( defined @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(186,plain,
! [SV7: $i] :
( ( ( defined @ SV7 )
= $false )
| ( ( equalish @ SV7 @ additive_identity )
= $true )
| ( ( equalish @ ( multiply @ SV7 @ ( multiplicative_inverse @ SV7 ) ) @ multiplicative_identity )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(187,plain,
! [SV28: $i,SV8: $i] :
( ( ( ~ ( defined @ SV8 ) )
= $true )
| ( ( ~ ( defined @ SV28 ) )
= $true )
| ( ( equalish @ ( multiply @ SV8 @ SV28 ) @ ( multiply @ SV28 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(188,plain,
! [SV44: $i,SV29: $i,SV9: $i] :
( ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
= $true )
| ( ( ~ ( defined @ SV9 )
| ~ ( defined @ SV44 )
| ~ ( defined @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(189,plain,
! [SV30: $i,SV10: $i] :
( ( ( ~ ( defined @ SV10 ) )
= $true )
| ( ( ~ ( defined @ SV30 ) )
= $true )
| ( ( defined @ ( add @ SV10 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(190,plain,
! [SV31: $i,SV12: $i] :
( ( ( ~ ( defined @ SV12 ) )
= $true )
| ( ( ~ ( defined @ SV31 ) )
= $true )
| ( ( defined @ ( multiply @ SV12 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(191,plain,
! [SV13: $i] :
( ( ( defined @ SV13 )
= $false )
| ( ( equalish @ SV13 @ additive_identity )
= $true )
| ( ( defined @ ( multiplicative_inverse @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(192,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ( less_or_equal @ SV14 @ SV32 ) )
= $true )
| ( ( ~ ( less_or_equal @ SV32 @ SV14 ) )
= $true )
| ( ( equalish @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(193,plain,
! [SV33: $i,SV48: $i,SV15: $i] :
( ( ( ~ ( less_or_equal @ SV15 @ SV48 )
| ~ ( less_or_equal @ SV48 @ SV33 ) )
= $true )
| ( ( less_or_equal @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(194,plain,
! [SV16: $i,SV34: $i] :
( ( ( less_or_equal @ SV34 @ SV16 )
= $true )
| ( ( ~ ( defined @ SV16 )
| ~ ( defined @ SV34 ) )
= $true )
| ( ( less_or_equal @ SV16 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(195,plain,
! [SV45: $i,SV35: $i,SV17: $i] :
( ( ( less_or_equal @ ( add @ SV17 @ SV35 ) @ ( add @ SV45 @ SV35 ) )
= $true )
| ( ( ~ ( defined @ SV35 )
| ~ ( less_or_equal @ SV17 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(196,plain,
! [SV36: $i,SV18: $i] :
( ( ( ~ ( less_or_equal @ additive_identity @ SV18 ) )
= $true )
| ( ( ~ ( less_or_equal @ additive_identity @ SV36 ) )
= $true )
| ( ( less_or_equal @ additive_identity @ ( multiply @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(197,plain,
! [SV20: $i,SV37: $i] :
( ( ( equalish @ SV37 @ SV20 )
= $false )
| ( ( equalish @ SV20 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV38: $i,SV49: $i,SV21: $i] :
( ( ( ~ ( equalish @ SV21 @ SV49 )
| ~ ( equalish @ SV49 @ SV38 ) )
= $true )
| ( ( equalish @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(199,plain,
! [SV46: $i,SV39: $i,SV22: $i] :
( ( ( equalish @ ( add @ SV22 @ SV39 ) @ ( add @ SV46 @ SV39 ) )
= $true )
| ( ( ~ ( defined @ SV39 )
| ~ ( equalish @ SV22 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV47: $i,SV40: $i,SV23: $i] :
( ( ( equalish @ ( multiply @ SV23 @ SV40 ) @ ( multiply @ SV47 @ SV40 ) )
= $true )
| ( ( ~ ( defined @ SV40 )
| ~ ( equalish @ SV23 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(201,plain,
! [SV24: $i,SV41: $i,SV50: $i] :
( ( ( ~ ( less_or_equal @ SV50 @ SV41 )
| ~ ( equalish @ SV50 @ SV24 ) )
= $true )
| ( ( less_or_equal @ SV24 @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV42: $i,SV25: $i,SV1: $i] :
( ( ( ~ ( defined @ SV1 ) )
= $true )
| ( ( ~ ( defined @ SV25 )
| ~ ( defined @ SV42 ) )
= $true )
| ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(203,plain,
! [SV26: $i,SV4: $i] :
( ( ( defined @ SV4 )
= $false )
| ( ( ~ ( defined @ SV26 ) )
= $true )
| ( ( equalish @ ( add @ SV4 @ SV26 ) @ ( add @ SV26 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(204,plain,
! [SV43: $i,SV27: $i,SV5: $i] :
( ( ( ~ ( defined @ SV5 ) )
= $true )
| ( ( ~ ( defined @ SV27 )
| ~ ( defined @ SV43 ) )
= $true )
| ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(205,plain,
! [SV28: $i,SV8: $i] :
( ( ( defined @ SV8 )
= $false )
| ( ( ~ ( defined @ SV28 ) )
= $true )
| ( ( equalish @ ( multiply @ SV8 @ SV28 ) @ ( multiply @ SV28 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(206,plain,
! [SV29: $i,SV44: $i,SV9: $i] :
( ( ( ~ ( defined @ SV9 ) )
= $true )
| ( ( ~ ( defined @ SV44 )
| ~ ( defined @ SV29 ) )
= $true )
| ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(207,plain,
! [SV30: $i,SV10: $i] :
( ( ( defined @ SV10 )
= $false )
| ( ( ~ ( defined @ SV30 ) )
= $true )
| ( ( defined @ ( add @ SV10 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(208,plain,
! [SV31: $i,SV12: $i] :
( ( ( defined @ SV12 )
= $false )
| ( ( ~ ( defined @ SV31 ) )
= $true )
| ( ( defined @ ( multiply @ SV12 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(209,plain,
! [SV32: $i,SV14: $i] :
( ( ( less_or_equal @ SV14 @ SV32 )
= $false )
| ( ( ~ ( less_or_equal @ SV32 @ SV14 ) )
= $true )
| ( ( equalish @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(210,plain,
! [SV33: $i,SV48: $i,SV15: $i] :
( ( ( ~ ( less_or_equal @ SV15 @ SV48 ) )
= $true )
| ( ( ~ ( less_or_equal @ SV48 @ SV33 ) )
= $true )
| ( ( less_or_equal @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV34: $i,SV16: $i] :
( ( ( ~ ( defined @ SV16 ) )
= $true )
| ( ( ~ ( defined @ SV34 ) )
= $true )
| ( ( less_or_equal @ SV34 @ SV16 )
= $true )
| ( ( less_or_equal @ SV16 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(212,plain,
! [SV45: $i,SV17: $i,SV35: $i] :
( ( ( ~ ( defined @ SV35 ) )
= $true )
| ( ( ~ ( less_or_equal @ SV17 @ SV45 ) )
= $true )
| ( ( less_or_equal @ ( add @ SV17 @ SV35 ) @ ( add @ SV45 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV36: $i,SV18: $i] :
( ( ( less_or_equal @ additive_identity @ SV18 )
= $false )
| ( ( ~ ( less_or_equal @ additive_identity @ SV36 ) )
= $true )
| ( ( less_or_equal @ additive_identity @ ( multiply @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV38: $i,SV49: $i,SV21: $i] :
( ( ( ~ ( equalish @ SV21 @ SV49 ) )
= $true )
| ( ( ~ ( equalish @ SV49 @ SV38 ) )
= $true )
| ( ( equalish @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(215,plain,
! [SV46: $i,SV22: $i,SV39: $i] :
( ( ( ~ ( defined @ SV39 ) )
= $true )
| ( ( ~ ( equalish @ SV22 @ SV46 ) )
= $true )
| ( ( equalish @ ( add @ SV22 @ SV39 ) @ ( add @ SV46 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(216,plain,
! [SV47: $i,SV23: $i,SV40: $i] :
( ( ( ~ ( defined @ SV40 ) )
= $true )
| ( ( ~ ( equalish @ SV23 @ SV47 ) )
= $true )
| ( ( equalish @ ( multiply @ SV23 @ SV40 ) @ ( multiply @ SV47 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(217,plain,
! [SV24: $i,SV41: $i,SV50: $i] :
( ( ( ~ ( less_or_equal @ SV50 @ SV41 ) )
= $true )
| ( ( ~ ( equalish @ SV50 @ SV24 ) )
= $true )
| ( ( less_or_equal @ SV24 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(218,plain,
! [SV42: $i,SV25: $i,SV1: $i] :
( ( ( defined @ SV1 )
= $false )
| ( ( ~ ( defined @ SV25 )
| ~ ( defined @ SV42 ) )
= $true )
| ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(219,plain,
! [SV4: $i,SV26: $i] :
( ( ( defined @ SV26 )
= $false )
| ( ( defined @ SV4 )
= $false )
| ( ( equalish @ ( add @ SV4 @ SV26 ) @ ( add @ SV26 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV43: $i,SV27: $i,SV5: $i] :
( ( ( defined @ SV5 )
= $false )
| ( ( ~ ( defined @ SV27 )
| ~ ( defined @ SV43 ) )
= $true )
| ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV8: $i,SV28: $i] :
( ( ( defined @ SV28 )
= $false )
| ( ( defined @ SV8 )
= $false )
| ( ( equalish @ ( multiply @ SV8 @ SV28 ) @ ( multiply @ SV28 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(222,plain,
! [SV29: $i,SV44: $i,SV9: $i] :
( ( ( defined @ SV9 )
= $false )
| ( ( ~ ( defined @ SV44 )
| ~ ( defined @ SV29 ) )
= $true )
| ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(223,plain,
! [SV10: $i,SV30: $i] :
( ( ( defined @ SV30 )
= $false )
| ( ( defined @ SV10 )
= $false )
| ( ( defined @ ( add @ SV10 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(224,plain,
! [SV12: $i,SV31: $i] :
( ( ( defined @ SV31 )
= $false )
| ( ( defined @ SV12 )
= $false )
| ( ( defined @ ( multiply @ SV12 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(225,plain,
! [SV14: $i,SV32: $i] :
( ( ( less_or_equal @ SV32 @ SV14 )
= $false )
| ( ( less_or_equal @ SV14 @ SV32 )
= $false )
| ( ( equalish @ SV14 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(226,plain,
! [SV33: $i,SV48: $i,SV15: $i] :
( ( ( less_or_equal @ SV15 @ SV48 )
= $false )
| ( ( ~ ( less_or_equal @ SV48 @ SV33 ) )
= $true )
| ( ( less_or_equal @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(227,plain,
! [SV34: $i,SV16: $i] :
( ( ( defined @ SV16 )
= $false )
| ( ( ~ ( defined @ SV34 ) )
= $true )
| ( ( less_or_equal @ SV34 @ SV16 )
= $true )
| ( ( less_or_equal @ SV16 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(228,plain,
! [SV45: $i,SV17: $i,SV35: $i] :
( ( ( defined @ SV35 )
= $false )
| ( ( ~ ( less_or_equal @ SV17 @ SV45 ) )
= $true )
| ( ( less_or_equal @ ( add @ SV17 @ SV35 ) @ ( add @ SV45 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(229,plain,
! [SV18: $i,SV36: $i] :
( ( ( less_or_equal @ additive_identity @ SV36 )
= $false )
| ( ( less_or_equal @ additive_identity @ SV18 )
= $false )
| ( ( less_or_equal @ additive_identity @ ( multiply @ SV18 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(230,plain,
! [SV38: $i,SV49: $i,SV21: $i] :
( ( ( equalish @ SV21 @ SV49 )
= $false )
| ( ( ~ ( equalish @ SV49 @ SV38 ) )
= $true )
| ( ( equalish @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(231,plain,
! [SV46: $i,SV22: $i,SV39: $i] :
( ( ( defined @ SV39 )
= $false )
| ( ( ~ ( equalish @ SV22 @ SV46 ) )
= $true )
| ( ( equalish @ ( add @ SV22 @ SV39 ) @ ( add @ SV46 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV47: $i,SV23: $i,SV40: $i] :
( ( ( defined @ SV40 )
= $false )
| ( ( ~ ( equalish @ SV23 @ SV47 ) )
= $true )
| ( ( equalish @ ( multiply @ SV23 @ SV40 ) @ ( multiply @ SV47 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV24: $i,SV41: $i,SV50: $i] :
( ( ( less_or_equal @ SV50 @ SV41 )
= $false )
| ( ( ~ ( equalish @ SV50 @ SV24 ) )
= $true )
| ( ( less_or_equal @ SV24 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(234,plain,
! [SV1: $i,SV42: $i,SV25: $i] :
( ( ( ~ ( defined @ SV25 ) )
= $true )
| ( ( ~ ( defined @ SV42 ) )
= $true )
| ( ( defined @ SV1 )
= $false )
| ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV5: $i,SV43: $i,SV27: $i] :
( ( ( ~ ( defined @ SV27 ) )
= $true )
| ( ( ~ ( defined @ SV43 ) )
= $true )
| ( ( defined @ SV5 )
= $false )
| ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV9: $i,SV29: $i,SV44: $i] :
( ( ( ~ ( defined @ SV44 ) )
= $true )
| ( ( ~ ( defined @ SV29 ) )
= $true )
| ( ( defined @ SV9 )
= $false )
| ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(237,plain,
! [SV15: $i,SV33: $i,SV48: $i] :
( ( ( less_or_equal @ SV48 @ SV33 )
= $false )
| ( ( less_or_equal @ SV15 @ SV48 )
= $false )
| ( ( less_or_equal @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV16: $i,SV34: $i] :
( ( ( defined @ SV34 )
= $false )
| ( ( defined @ SV16 )
= $false )
| ( ( less_or_equal @ SV34 @ SV16 )
= $true )
| ( ( less_or_equal @ SV16 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV35: $i,SV45: $i,SV17: $i] :
( ( ( less_or_equal @ SV17 @ SV45 )
= $false )
| ( ( defined @ SV35 )
= $false )
| ( ( less_or_equal @ ( add @ SV17 @ SV35 ) @ ( add @ SV45 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV21: $i,SV38: $i,SV49: $i] :
( ( ( equalish @ SV49 @ SV38 )
= $false )
| ( ( equalish @ SV21 @ SV49 )
= $false )
| ( ( equalish @ SV21 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV39: $i,SV46: $i,SV22: $i] :
( ( ( equalish @ SV22 @ SV46 )
= $false )
| ( ( defined @ SV39 )
= $false )
| ( ( equalish @ ( add @ SV22 @ SV39 ) @ ( add @ SV46 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV40: $i,SV47: $i,SV23: $i] :
( ( ( equalish @ SV23 @ SV47 )
= $false )
| ( ( defined @ SV40 )
= $false )
| ( ( equalish @ ( multiply @ SV23 @ SV40 ) @ ( multiply @ SV47 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV41: $i,SV24: $i,SV50: $i] :
( ( ( equalish @ SV50 @ SV24 )
= $false )
| ( ( less_or_equal @ SV50 @ SV41 )
= $false )
| ( ( less_or_equal @ SV24 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV1: $i,SV42: $i,SV25: $i] :
( ( ( defined @ SV25 )
= $false )
| ( ( ~ ( defined @ SV42 ) )
= $true )
| ( ( defined @ SV1 )
= $false )
| ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV5: $i,SV43: $i,SV27: $i] :
( ( ( defined @ SV27 )
= $false )
| ( ( ~ ( defined @ SV43 ) )
= $true )
| ( ( defined @ SV5 )
= $false )
| ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(246,plain,
! [SV9: $i,SV29: $i,SV44: $i] :
( ( ( defined @ SV44 )
= $false )
| ( ( ~ ( defined @ SV29 ) )
= $true )
| ( ( defined @ SV9 )
= $false )
| ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV1: $i,SV25: $i,SV42: $i] :
( ( ( defined @ SV42 )
= $false )
| ( ( defined @ SV25 )
= $false )
| ( ( defined @ SV1 )
= $false )
| ( ( equalish @ ( add @ SV1 @ ( add @ SV25 @ SV42 ) ) @ ( add @ ( add @ SV1 @ SV25 ) @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(248,plain,
! [SV5: $i,SV27: $i,SV43: $i] :
( ( ( defined @ SV43 )
= $false )
| ( ( defined @ SV27 )
= $false )
| ( ( defined @ SV5 )
= $false )
| ( ( equalish @ ( multiply @ SV5 @ ( multiply @ SV27 @ SV43 ) ) @ ( multiply @ ( multiply @ SV5 @ SV27 ) @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(249,plain,
! [SV9: $i,SV44: $i,SV29: $i] :
( ( ( defined @ SV29 )
= $false )
| ( ( defined @ SV44 )
= $false )
| ( ( defined @ SV9 )
= $false )
| ( ( equalish @ ( add @ ( multiply @ SV9 @ SV29 ) @ ( multiply @ SV44 @ SV29 ) ) @ ( multiply @ ( add @ SV9 @ SV44 ) @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(250,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,249,248,247,243,242,241,240,239,238,237,229,225,224,223,221,219,197,191,186,177,169,164,161,160,134,133,108,93,90,79,78,77,75]) ).
thf(251,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD067-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 6 21:17:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 33
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.38 .
% 0.13/0.38 (rf:0,axioms:33,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:35,loop_count:0,foatp_calls:0,translation:fof_full).........
% 6.40/6.61
% 6.40/6.61 ********************************
% 6.40/6.61 * All subproblems solved! *
% 6.40/6.61 ********************************
% 6.40/6.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:33,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:250,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.40/6.63
% 6.40/6.63 %**** Beginning of derivation protocol ****
% 6.40/6.63 % SZS output start CNFRefutation
% See solution above
% 6.40/6.63
% 6.40/6.63 %**** End of derivation protocol ****
% 6.40/6.63 %**** no. of clauses in derivation: 251 ****
% 6.40/6.63 %**** clause counter: 250 ****
% 6.40/6.63
% 6.40/6.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:33,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:250,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------