TSTP Solution File: CAT004-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : CAT004-1 : 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 : n019.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 : Fri Jul 15 00:03:45 EDT 2022
% Result : Unsatisfiable 36.63s 36.84s
% Output : CNFRefutation 36.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 37
% Syntax : Number of formulae : 225 ( 122 unt; 12 typ; 0 def)
% Number of atoms : 1226 ( 349 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 2149 ( 308 ~; 393 |; 0 &;1448 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 692 ( 0 ^ 692 !; 0 ?; 692 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_codomain,type,
codomain: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_d,type,
d: $i ).
thf(tp_defined,type,
defined: $i > $i > $o ).
thf(tp_domain,type,
domain: $i > $i ).
thf(tp_g,type,
g: $i ).
thf(tp_h,type,
h: $i ).
thf(tp_identity_map,type,
identity_map: $i > $o ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( Z = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ~ ( identity_map @ Y )
| ( product @ X @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ~ ( identity_map @ X )
| ( product @ X @ Y @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
thf(4,axiom,
! [X: $i] : ( product @ ( codomain @ X ) @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_codomain) ).
thf(5,axiom,
! [X: $i] : ( product @ X @ ( domain @ X ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
thf(6,axiom,
! [X: $i] : ( defined @ ( codomain @ X ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
thf(7,axiom,
! [X: $i] : ( defined @ X @ ( domain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
thf(8,axiom,
! [X: $i] : ( identity_map @ ( codomain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
thf(9,axiom,
! [X: $i] : ( identity_map @ ( domain @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( defined @ X @ Y )
| ~ ( defined @ Y @ Z )
| ~ ( identity_map @ Y )
| ( defined @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom6) ).
thf(11,axiom,
! [Y: $i,Z: $i,Yz: $i,X: $i,Xyz: $i,Xy: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( product @ X @ Yz @ Xyz )
| ~ ( product @ X @ Y @ Xy )
| ( product @ Xy @ Z @ Xyz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom5) ).
thf(12,axiom,
! [Y: $i,Z: $i,Yz: $i,X: $i,Xy: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( product @ X @ Y @ Xy )
| ~ ( defined @ X @ Yz )
| ( defined @ Xy @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom4) ).
thf(13,axiom,
! [Y: $i,Z: $i,Yz: $i,X: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( defined @ X @ Yz )
| ( defined @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom3) ).
thf(14,axiom,
! [X: $i,Y: $i,Xy: $i,Z: $i,Xyz: $i,Yz: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( product @ Xy @ Z @ Xyz )
| ~ ( product @ Y @ Z @ Yz )
| ( product @ X @ Yz @ Xyz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom2) ).
thf(15,axiom,
! [X: $i,Y: $i,Xy: $i,Z: $i,Yz: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( product @ Y @ Z @ Yz )
| ~ ( defined @ Xy @ Z )
| ( defined @ X @ Yz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom1) ).
thf(16,axiom,
! [X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( defined @ Xy @ Z )
| ( defined @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
thf(17,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( defined @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property1) ).
thf(18,axiom,
! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ( product @ X @ Y @ ( compose @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).
thf(19,axiom,
product @ g @ c @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gc_equals_d) ).
thf(20,axiom,
product @ h @ c @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hc_equals_d) ).
thf(21,axiom,
product @ a @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
thf(22,axiom,
! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ b @ W )
| ~ ( product @ Y @ b @ W )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product2) ).
thf(23,axiom,
! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ a @ W )
| ~ ( product @ Y @ a @ W )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product1) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
thf(27,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( product @ X @ Y @ Z )
| ~ ( product @ X @ Y @ W )
| ( Z = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ~ ( identity_map @ Y )
| ( product @ X @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ~ ( identity_map @ X )
| ( product @ X @ Y @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [X: $i] : ( product @ ( codomain @ X ) @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(32,plain,
( ( ! [X: $i] : ( product @ X @ ( domain @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(33,plain,
( ( ! [X: $i] : ( defined @ ( codomain @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(34,plain,
( ( ! [X: $i] : ( defined @ X @ ( domain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(35,plain,
( ( ! [X: $i] : ( identity_map @ ( codomain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(36,plain,
( ( ! [X: $i] : ( identity_map @ ( domain @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( defined @ X @ Y )
| ~ ( defined @ Y @ Z )
| ~ ( identity_map @ Y )
| ( defined @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( ! [Y: $i,Z: $i,Yz: $i,X: $i,Xyz: $i,Xy: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( product @ X @ Yz @ Xyz )
| ~ ( product @ X @ Y @ Xy )
| ( product @ Xy @ Z @ Xyz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( ! [Y: $i,Z: $i,Yz: $i,X: $i,Xy: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( product @ X @ Y @ Xy )
| ~ ( defined @ X @ Yz )
| ( defined @ Xy @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ! [Y: $i,Z: $i,Yz: $i,X: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( defined @ X @ Yz )
| ( defined @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,Xy: $i,Z: $i,Xyz: $i,Yz: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( product @ Xy @ Z @ Xyz )
| ~ ( product @ Y @ Z @ Yz )
| ( product @ X @ Yz @ Xyz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Xy: $i,Z: $i,Yz: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( product @ Y @ Z @ Yz )
| ~ ( defined @ Xy @ Z )
| ( defined @ X @ Yz ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( defined @ Xy @ Z )
| ( defined @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( defined @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ( product @ X @ Y @ ( compose @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
( ( product @ g @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(47,plain,
( ( product @ h @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( product @ a @ b @ c )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ b @ W )
| ~ ( product @ Y @ b @ W )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [X: $i,W: $i,Y: $i] :
( ~ ( product @ X @ a @ W )
| ~ ( product @ Y @ a @ W )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ( h != g ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(52,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ! [Z: $i] :
( ~ ( defined @ Y @ Z )
| ~ ( identity_map @ Y )
| ( defined @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(55,plain,
( ( ! [Y: $i,Z: $i,Yz: $i,X: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ! [Xyz: $i] :
( ~ ( product @ X @ Yz @ Xyz )
| ! [Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ( product @ Xy @ Z @ Xyz ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(56,plain,
( ( ! [Y: $i,Z: $i,Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ! [X: $i,Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( defined @ X @ Yz )
| ( defined @ Xy @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(57,plain,
( ( ! [Y: $i,Z: $i,Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ! [X: $i] :
( ~ ( defined @ X @ Yz )
| ( defined @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ X @ Y @ Xy )
| ! [Xyz: $i] :
( ~ ( product @ Xy @ Z @ Xyz )
| ! [Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ( product @ X @ Yz @ Xyz ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ! [Z: $i,Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( defined @ Xy @ Z )
| ( defined @ X @ Yz ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ! [Z: $i] :
( ~ ( defined @ Xy @ Z )
| ( defined @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( product @ X @ Y @ Z )
| ( defined @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(62,plain,
( ( ! [X: $i,W: $i] :
( ~ ( product @ X @ b @ W )
| ! [Y: $i] :
( ~ ( product @ Y @ b @ W )
| ( X = Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(63,plain,
( ( ! [X: $i,W: $i] :
( ~ ( product @ X @ a @ W )
| ! [Y: $i] :
( ~ ( product @ Y @ a @ W )
| ( X = Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(64,plain,
( ( ( h != g ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(65,plain,
( ( ( h != g ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [X: $i,W: $i] :
( ~ ( product @ X @ a @ W )
| ! [Y: $i] :
( ~ ( product @ Y @ a @ W )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(67,plain,
( ( ! [X: $i,W: $i] :
( ~ ( product @ X @ b @ W )
| ! [Y: $i] :
( ~ ( product @ Y @ b @ W )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(68,plain,
( ( product @ a @ b @ c )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
( ( product @ h @ c @ d )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(70,plain,
( ( product @ g @ c @ d )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ( product @ X @ Y @ ( compose @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( product @ X @ Y @ Z )
| ( defined @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i,Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ! [Z: $i] :
( ~ ( defined @ Xy @ Z )
| ( defined @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ! [Z: $i,Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ~ ( defined @ Xy @ Z )
| ( defined @ X @ Yz ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i,Xy: $i,Z: $i] :
( ~ ( product @ X @ Y @ Xy )
| ! [Xyz: $i] :
( ~ ( product @ Xy @ Z @ Xyz )
| ! [Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ( product @ X @ Yz @ Xyz ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(76,plain,
( ( ! [Y: $i,Z: $i,Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ! [X: $i] :
( ~ ( defined @ X @ Yz )
| ( defined @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(77,plain,
( ( ! [Y: $i,Z: $i,Yz: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ! [X: $i,Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ~ ( defined @ X @ Yz )
| ( defined @ Xy @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(78,plain,
( ( ! [Y: $i,Z: $i,Yz: $i,X: $i] :
( ~ ( product @ Y @ Z @ Yz )
| ! [Xyz: $i] :
( ~ ( product @ X @ Yz @ Xyz )
| ! [Xy: $i] :
( ~ ( product @ X @ Y @ Xy )
| ( product @ Xy @ Z @ Xyz ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ! [Z: $i] :
( ~ ( defined @ Y @ Z )
| ~ ( identity_map @ Y )
| ( defined @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(80,plain,
( ( ! [X: $i] : ( identity_map @ ( domain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(81,plain,
( ( ! [X: $i] : ( identity_map @ ( codomain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(82,plain,
( ( ! [X: $i] : ( defined @ X @ ( domain @ X ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(83,plain,
( ( ! [X: $i] : ( defined @ ( codomain @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(84,plain,
( ( ! [X: $i] : ( product @ X @ ( domain @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(85,plain,
( ( ! [X: $i] : ( product @ ( codomain @ X ) @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ~ ( identity_map @ X )
| ( product @ X @ Y @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(87,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( defined @ X @ Y )
| ~ ( identity_map @ Y )
| ( product @ X @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(88,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( product @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(89,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(90,plain,
( ( h = g )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(91,plain,
! [SV1: $i] :
( ( ! [SY58: $i] :
( ~ ( product @ SV1 @ a @ SY58 )
| ! [SY59: $i] :
( ~ ( product @ SY59 @ a @ SY58 )
| ( SV1 = SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(92,plain,
! [SV2: $i] :
( ( ! [SY60: $i] :
( ~ ( product @ SV2 @ b @ SY60 )
| ! [SY61: $i] :
( ~ ( product @ SY61 @ b @ SY60 )
| ( SV2 = SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV3: $i] :
( ( ! [SY62: $i] :
( ~ ( defined @ SV3 @ SY62 )
| ( product @ SV3 @ SY62 @ ( compose @ SV3 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
! [SV4: $i] :
( ( ! [SY63: $i] :
( ! [SY64: $i] :
~ ( product @ SV4 @ SY63 @ SY64 )
| ( defined @ SV4 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(95,plain,
! [SV5: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ~ ( product @ SV5 @ SY65 @ SY66 )
| ! [Z: $i] :
( ~ ( defined @ SY66 @ Z )
| ( defined @ SY65 @ Z ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ~ ( product @ SV6 @ SY68 @ SY69 )
| ! [SY70: $i,SY71: $i] :
( ~ ( product @ SY68 @ SY70 @ SY71 )
| ~ ( defined @ SY69 @ SY70 )
| ( defined @ SV6 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ( product @ SV7 @ SY72 @ SY73 )
| ! [SY75: $i] :
( ~ ( product @ SY73 @ SY74 @ SY75 )
| ! [SY76: $i] :
( ~ ( product @ SY72 @ SY74 @ SY76 )
| ( product @ SV7 @ SY76 @ SY75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ( product @ SV8 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( defined @ SY79 @ SY78 )
| ( defined @ SY79 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( product @ SV9 @ SY80 @ SY81 )
| ! [SY82: $i,SY83: $i] :
( ~ ( product @ SY82 @ SV9 @ SY83 )
| ~ ( defined @ SY82 @ SY81 )
| ( defined @ SY83 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
! [SV10: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( product @ SV10 @ SY84 @ SY85 )
| ! [SY87: $i] :
( ~ ( product @ SY86 @ SY85 @ SY87 )
| ! [SY88: $i] :
( ~ ( product @ SY86 @ SV10 @ SY88 )
| ( product @ SY88 @ SY84 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(101,plain,
! [SV11: $i] :
( ( ! [SY89: $i] :
( ~ ( defined @ SV11 @ SY89 )
| ! [SY90: $i] :
( ~ ( defined @ SY89 @ SY90 )
| ~ ( identity_map @ SY89 )
| ( defined @ SV11 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(102,plain,
! [SV12: $i] :
( ( identity_map @ ( domain @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(103,plain,
! [SV13: $i] :
( ( identity_map @ ( codomain @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(104,plain,
! [SV14: $i] :
( ( defined @ SV14 @ ( domain @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(105,plain,
! [SV15: $i] :
( ( defined @ ( codomain @ SV15 ) @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(106,plain,
! [SV16: $i] :
( ( product @ SV16 @ ( domain @ SV16 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(107,plain,
! [SV17: $i] :
( ( product @ ( codomain @ SV17 ) @ SV17 @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(108,plain,
! [SV18: $i] :
( ( ! [SY91: $i] :
( ~ ( defined @ SV18 @ SY91 )
| ~ ( identity_map @ SV18 )
| ( product @ SV18 @ SY91 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
! [SV19: $i] :
( ( ! [SY92: $i] :
( ~ ( defined @ SV19 @ SY92 )
| ~ ( identity_map @ SY92 )
| ( product @ SV19 @ SY92 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(110,plain,
! [SV20: $i] :
( ( ! [SY93: $i,SY94: $i] :
( ~ ( product @ SV20 @ SY93 @ SY94 )
| ! [SY95: $i] :
( ~ ( product @ SV20 @ SY93 @ SY95 )
| ( SY94 = SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(111,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(112,plain,
! [SV21: $i,SV1: $i] :
( ( ~ ( product @ SV1 @ a @ SV21 )
| ! [SY96: $i] :
( ~ ( product @ SY96 @ a @ SV21 )
| ( SV1 = SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(113,plain,
! [SV22: $i,SV2: $i] :
( ( ~ ( product @ SV2 @ b @ SV22 )
| ! [SY97: $i] :
( ~ ( product @ SY97 @ b @ SV22 )
| ( SV2 = SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(114,plain,
! [SV23: $i,SV3: $i] :
( ( ~ ( defined @ SV3 @ SV23 )
| ( product @ SV3 @ SV23 @ ( compose @ SV3 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(115,plain,
! [SV24: $i,SV4: $i] :
( ( ! [SY98: $i] :
~ ( product @ SV4 @ SV24 @ SY98 )
| ( defined @ SV4 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(116,plain,
! [SV25: $i,SV5: $i] :
( ( ! [SY99: $i] :
( ~ ( product @ SV5 @ SV25 @ SY99 )
| ! [SY100: $i] :
( ~ ( defined @ SY99 @ SY100 )
| ( defined @ SV25 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(117,plain,
! [SV26: $i,SV6: $i] :
( ( ! [SY101: $i] :
( ~ ( product @ SV6 @ SV26 @ SY101 )
| ! [SY102: $i,SY103: $i] :
( ~ ( product @ SV26 @ SY102 @ SY103 )
| ~ ( defined @ SY101 @ SY102 )
| ( defined @ SV6 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(118,plain,
! [SV27: $i,SV7: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( product @ SV7 @ SV27 @ SY104 )
| ! [SY106: $i] :
( ~ ( product @ SY104 @ SY105 @ SY106 )
| ! [SY107: $i] :
( ~ ( product @ SV27 @ SY105 @ SY107 )
| ( product @ SV7 @ SY107 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(119,plain,
! [SV28: $i,SV8: $i] :
( ( ! [SY108: $i] :
( ~ ( product @ SV8 @ SV28 @ SY108 )
| ! [SY79: $i] :
( ~ ( defined @ SY79 @ SY108 )
| ( defined @ SY79 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(120,plain,
! [SV29: $i,SV9: $i] :
( ( ! [SY110: $i] :
( ~ ( product @ SV9 @ SV29 @ SY110 )
| ! [SY111: $i,SY112: $i] :
( ~ ( product @ SY111 @ SV9 @ SY112 )
| ~ ( defined @ SY111 @ SY110 )
| ( defined @ SY112 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(121,plain,
! [SV30: $i,SV10: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( product @ SV10 @ SV30 @ SY113 )
| ! [SY115: $i] :
( ~ ( product @ SY114 @ SY113 @ SY115 )
| ! [SY116: $i] :
( ~ ( product @ SY114 @ SV10 @ SY116 )
| ( product @ SY116 @ SV30 @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(122,plain,
! [SV31: $i,SV11: $i] :
( ( ~ ( defined @ SV11 @ SV31 )
| ! [SY117: $i] :
( ~ ( defined @ SV31 @ SY117 )
| ~ ( identity_map @ SV31 )
| ( defined @ SV11 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(123,plain,
! [SV32: $i,SV18: $i] :
( ( ~ ( defined @ SV18 @ SV32 )
| ~ ( identity_map @ SV18 )
| ( product @ SV18 @ SV32 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV33: $i,SV19: $i] :
( ( ~ ( defined @ SV19 @ SV33 )
| ~ ( identity_map @ SV33 )
| ( product @ SV19 @ SV33 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV34: $i,SV20: $i] :
( ( ! [SY118: $i] :
( ~ ( product @ SV20 @ SV34 @ SY118 )
| ! [SY119: $i] :
( ~ ( product @ SV20 @ SV34 @ SY119 )
| ( SY118 = SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV21: $i,SV1: $i] :
( ( ( ~ ( product @ SV1 @ a @ SV21 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( product @ SY96 @ a @ SV21 )
| ( SV1 = SY96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV22: $i,SV2: $i] :
( ( ( ~ ( product @ SV2 @ b @ SV22 ) )
= $true )
| ( ( ! [SY97: $i] :
( ~ ( product @ SY97 @ b @ SV22 )
| ( SV2 = SY97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV23: $i,SV3: $i] :
( ( ( ~ ( defined @ SV3 @ SV23 ) )
= $true )
| ( ( product @ SV3 @ SV23 @ ( compose @ SV3 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(129,plain,
! [SV24: $i,SV4: $i] :
( ( ( ! [SY98: $i] :
~ ( product @ SV4 @ SV24 @ SY98 ) )
= $true )
| ( ( defined @ SV4 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(130,plain,
! [SV35: $i,SV25: $i,SV5: $i] :
( ( ~ ( product @ SV5 @ SV25 @ SV35 )
| ! [SY120: $i] :
( ~ ( defined @ SV35 @ SY120 )
| ( defined @ SV25 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(131,plain,
! [SV36: $i,SV26: $i,SV6: $i] :
( ( ~ ( product @ SV6 @ SV26 @ SV36 )
| ! [SY121: $i,SY122: $i] :
( ~ ( product @ SV26 @ SY121 @ SY122 )
| ~ ( defined @ SV36 @ SY121 )
| ( defined @ SV6 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV37: $i,SV27: $i,SV7: $i] :
( ( ! [SY123: $i] :
( ~ ( product @ SV7 @ SV27 @ SV37 )
| ! [SY124: $i] :
( ~ ( product @ SV37 @ SY123 @ SY124 )
| ! [SY107: $i] :
( ~ ( product @ SV27 @ SY123 @ SY107 )
| ( product @ SV7 @ SY107 @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV38: $i,SV28: $i,SV8: $i] :
( ( ~ ( product @ SV8 @ SV28 @ SV38 )
| ! [SY126: $i] :
( ~ ( defined @ SY126 @ SV38 )
| ( defined @ SY126 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV39: $i,SV29: $i,SV9: $i] :
( ( ~ ( product @ SV9 @ SV29 @ SV39 )
| ! [SY127: $i,SY128: $i] :
( ~ ( product @ SY127 @ SV9 @ SY128 )
| ~ ( defined @ SY127 @ SV39 )
| ( defined @ SY128 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV40: $i,SV30: $i,SV10: $i] :
( ( ! [SY129: $i] :
( ~ ( product @ SV10 @ SV30 @ SV40 )
| ! [SY130: $i] :
( ~ ( product @ SY129 @ SV40 @ SY130 )
| ! [SY116: $i] :
( ~ ( product @ SY129 @ SV10 @ SY116 )
| ( product @ SY116 @ SV30 @ SY130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV31: $i,SV11: $i] :
( ( ( ~ ( defined @ SV11 @ SV31 ) )
= $true )
| ( ( ! [SY117: $i] :
( ~ ( defined @ SV31 @ SY117 )
| ~ ( identity_map @ SV31 )
| ( defined @ SV11 @ SY117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV32: $i,SV18: $i] :
( ( ( ~ ( defined @ SV18 @ SV32 ) )
= $true )
| ( ( ~ ( identity_map @ SV18 )
| ( product @ SV18 @ SV32 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV33: $i,SV19: $i] :
( ( ( ~ ( defined @ SV19 @ SV33 ) )
= $true )
| ( ( ~ ( identity_map @ SV33 )
| ( product @ SV19 @ SV33 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV41: $i,SV34: $i,SV20: $i] :
( ( ~ ( product @ SV20 @ SV34 @ SV41 )
| ! [SY132: $i] :
( ~ ( product @ SV20 @ SV34 @ SY132 )
| ( SV41 = SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV21: $i,SV1: $i] :
( ( ( product @ SV1 @ a @ SV21 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( product @ SY96 @ a @ SV21 )
| ( SV1 = SY96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV22: $i,SV2: $i] :
( ( ( product @ SV2 @ b @ SV22 )
= $false )
| ( ( ! [SY97: $i] :
( ~ ( product @ SY97 @ b @ SV22 )
| ( SV2 = SY97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV23: $i,SV3: $i] :
( ( ( defined @ SV3 @ SV23 )
= $false )
| ( ( product @ SV3 @ SV23 @ ( compose @ SV3 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV42: $i,SV24: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV24 @ SV42 ) )
= $true )
| ( ( defined @ SV4 @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV35: $i,SV25: $i,SV5: $i] :
( ( ( ~ ( product @ SV5 @ SV25 @ SV35 ) )
= $true )
| ( ( ! [SY120: $i] :
( ~ ( defined @ SV35 @ SY120 )
| ( defined @ SV25 @ SY120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV36: $i,SV26: $i,SV6: $i] :
( ( ( ~ ( product @ SV6 @ SV26 @ SV36 ) )
= $true )
| ( ( ! [SY121: $i,SY122: $i] :
( ~ ( product @ SV26 @ SY121 @ SY122 )
| ~ ( defined @ SV36 @ SY121 )
| ( defined @ SV6 @ SY122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV43: $i,SV37: $i,SV27: $i,SV7: $i] :
( ( ~ ( product @ SV7 @ SV27 @ SV37 )
| ! [SY133: $i] :
( ~ ( product @ SV37 @ SV43 @ SY133 )
| ! [SY134: $i] :
( ~ ( product @ SV27 @ SV43 @ SY134 )
| ( product @ SV7 @ SY134 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV38: $i,SV28: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV28 @ SV38 ) )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( defined @ SY126 @ SV38 )
| ( defined @ SY126 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV39: $i,SV29: $i,SV9: $i] :
( ( ( ~ ( product @ SV9 @ SV29 @ SV39 ) )
= $true )
| ( ( ! [SY127: $i,SY128: $i] :
( ~ ( product @ SY127 @ SV9 @ SY128 )
| ~ ( defined @ SY127 @ SV39 )
| ( defined @ SY128 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV44: $i,SV40: $i,SV30: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV30 @ SV40 )
| ! [SY135: $i] :
( ~ ( product @ SV44 @ SV40 @ SY135 )
| ! [SY136: $i] :
( ~ ( product @ SV44 @ SV10 @ SY136 )
| ( product @ SY136 @ SV30 @ SY135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV31: $i,SV11: $i] :
( ( ( defined @ SV11 @ SV31 )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( defined @ SV31 @ SY117 )
| ~ ( identity_map @ SV31 )
| ( defined @ SV11 @ SY117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(151,plain,
! [SV32: $i,SV18: $i] :
( ( ( defined @ SV18 @ SV32 )
= $false )
| ( ( ~ ( identity_map @ SV18 )
| ( product @ SV18 @ SV32 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(152,plain,
! [SV33: $i,SV19: $i] :
( ( ( defined @ SV19 @ SV33 )
= $false )
| ( ( ~ ( identity_map @ SV33 )
| ( product @ SV19 @ SV33 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(153,plain,
! [SV41: $i,SV34: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV34 @ SV41 ) )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( product @ SV20 @ SV34 @ SY132 )
| ( SV41 = SY132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV1: $i,SV21: $i,SV45: $i] :
( ( ( ~ ( product @ SV45 @ a @ SV21 )
| ( SV1 = SV45 ) )
= $true )
| ( ( product @ SV1 @ a @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV2: $i,SV22: $i,SV46: $i] :
( ( ( ~ ( product @ SV46 @ b @ SV22 )
| ( SV2 = SV46 ) )
= $true )
| ( ( product @ SV2 @ b @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV42: $i,SV24: $i,SV4: $i] :
( ( ( product @ SV4 @ SV24 @ SV42 )
= $false )
| ( ( defined @ SV4 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV35: $i,SV25: $i,SV5: $i] :
( ( ( product @ SV5 @ SV25 @ SV35 )
= $false )
| ( ( ! [SY120: $i] :
( ~ ( defined @ SV35 @ SY120 )
| ( defined @ SV25 @ SY120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV36: $i,SV26: $i,SV6: $i] :
( ( ( product @ SV6 @ SV26 @ SV36 )
= $false )
| ( ( ! [SY121: $i,SY122: $i] :
( ~ ( product @ SV26 @ SY121 @ SY122 )
| ~ ( defined @ SV36 @ SY121 )
| ( defined @ SV6 @ SY122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV43: $i,SV37: $i,SV27: $i,SV7: $i] :
( ( ( ~ ( product @ SV7 @ SV27 @ SV37 ) )
= $true )
| ( ( ! [SY133: $i] :
( ~ ( product @ SV37 @ SV43 @ SY133 )
| ! [SY134: $i] :
( ~ ( product @ SV27 @ SV43 @ SY134 )
| ( product @ SV7 @ SY134 @ SY133 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV38: $i,SV28: $i,SV8: $i] :
( ( ( product @ SV8 @ SV28 @ SV38 )
= $false )
| ( ( ! [SY126: $i] :
( ~ ( defined @ SY126 @ SV38 )
| ( defined @ SY126 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV39: $i,SV29: $i,SV9: $i] :
( ( ( product @ SV9 @ SV29 @ SV39 )
= $false )
| ( ( ! [SY127: $i,SY128: $i] :
( ~ ( product @ SY127 @ SV9 @ SY128 )
| ~ ( defined @ SY127 @ SV39 )
| ( defined @ SY128 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV44: $i,SV40: $i,SV30: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV30 @ SV40 ) )
= $true )
| ( ( ! [SY135: $i] :
( ~ ( product @ SV44 @ SV40 @ SY135 )
| ! [SY136: $i] :
( ~ ( product @ SV44 @ SV10 @ SY136 )
| ( product @ SY136 @ SV30 @ SY135 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV11: $i,SV47: $i,SV31: $i] :
( ( ( ~ ( defined @ SV31 @ SV47 )
| ~ ( identity_map @ SV31 )
| ( defined @ SV11 @ SV47 ) )
= $true )
| ( ( defined @ SV11 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV32: $i,SV18: $i] :
( ( ( ~ ( identity_map @ SV18 ) )
= $true )
| ( ( product @ SV18 @ SV32 @ SV32 )
= $true )
| ( ( defined @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV19: $i,SV33: $i] :
( ( ( ~ ( identity_map @ SV33 ) )
= $true )
| ( ( product @ SV19 @ SV33 @ SV19 )
= $true )
| ( ( defined @ SV19 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV41: $i,SV34: $i,SV20: $i] :
( ( ( product @ SV20 @ SV34 @ SV41 )
= $false )
| ( ( ! [SY132: $i] :
( ~ ( product @ SV20 @ SV34 @ SY132 )
| ( SV41 = SY132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV1: $i,SV21: $i,SV45: $i] :
( ( ( ~ ( product @ SV45 @ a @ SV21 ) )
= $true )
| ( ( SV1 = SV45 )
= $true )
| ( ( product @ SV1 @ a @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV2: $i,SV22: $i,SV46: $i] :
( ( ( ~ ( product @ SV46 @ b @ SV22 ) )
= $true )
| ( ( SV2 = SV46 )
= $true )
| ( ( product @ SV2 @ b @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV5: $i,SV25: $i,SV48: $i,SV35: $i] :
( ( ( ~ ( defined @ SV35 @ SV48 )
| ( defined @ SV25 @ SV48 ) )
= $true )
| ( ( product @ SV5 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV6: $i,SV36: $i,SV49: $i,SV26: $i] :
( ( ( ! [SY137: $i] :
( ~ ( product @ SV26 @ SV49 @ SY137 )
| ~ ( defined @ SV36 @ SV49 )
| ( defined @ SV6 @ SY137 ) ) )
= $true )
| ( ( product @ SV6 @ SV26 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV43: $i,SV37: $i,SV27: $i,SV7: $i] :
( ( ( product @ SV7 @ SV27 @ SV37 )
= $false )
| ( ( ! [SY133: $i] :
( ~ ( product @ SV37 @ SV43 @ SY133 )
| ! [SY134: $i] :
( ~ ( product @ SV27 @ SV43 @ SY134 )
| ( product @ SV7 @ SY134 @ SY133 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV28: $i,SV8: $i,SV38: $i,SV50: $i] :
( ( ( ~ ( defined @ SV50 @ SV38 )
| ( defined @ SV50 @ SV8 ) )
= $true )
| ( ( product @ SV8 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV29: $i,SV39: $i,SV9: $i,SV51: $i] :
( ( ( ! [SY138: $i] :
( ~ ( product @ SV51 @ SV9 @ SY138 )
| ~ ( defined @ SV51 @ SV39 )
| ( defined @ SY138 @ SV29 ) ) )
= $true )
| ( ( product @ SV9 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV44: $i,SV40: $i,SV30: $i,SV10: $i] :
( ( ( product @ SV10 @ SV30 @ SV40 )
= $false )
| ( ( ! [SY135: $i] :
( ~ ( product @ SV44 @ SV40 @ SY135 )
| ! [SY136: $i] :
( ~ ( product @ SV44 @ SV10 @ SY136 )
| ( product @ SY136 @ SV30 @ SY135 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV11: $i,SV47: $i,SV31: $i] :
( ( ( ~ ( defined @ SV31 @ SV47 ) )
= $true )
| ( ( ~ ( identity_map @ SV31 )
| ( defined @ SV11 @ SV47 ) )
= $true )
| ( ( defined @ SV11 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV32: $i,SV18: $i] :
( ( ( identity_map @ SV18 )
= $false )
| ( ( product @ SV18 @ SV32 @ SV32 )
= $true )
| ( ( defined @ SV18 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV19: $i,SV33: $i] :
( ( ( identity_map @ SV33 )
= $false )
| ( ( product @ SV19 @ SV33 @ SV19 )
= $true )
| ( ( defined @ SV19 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV41: $i,SV52: $i,SV34: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV34 @ SV52 )
| ( SV41 = SV52 ) )
= $true )
| ( ( product @ SV20 @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV1: $i,SV21: $i,SV45: $i] :
( ( ( product @ SV45 @ a @ SV21 )
= $false )
| ( ( SV1 = SV45 )
= $true )
| ( ( product @ SV1 @ a @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV2: $i,SV22: $i,SV46: $i] :
( ( ( product @ SV46 @ b @ SV22 )
= $false )
| ( ( SV2 = SV46 )
= $true )
| ( ( product @ SV2 @ b @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV5: $i,SV25: $i,SV48: $i,SV35: $i] :
( ( ( ~ ( defined @ SV35 @ SV48 ) )
= $true )
| ( ( defined @ SV25 @ SV48 )
= $true )
| ( ( product @ SV5 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV6: $i,SV36: $i,SV53: $i,SV49: $i,SV26: $i] :
( ( ( ~ ( product @ SV26 @ SV49 @ SV53 )
| ~ ( defined @ SV36 @ SV49 )
| ( defined @ SV6 @ SV53 ) )
= $true )
| ( ( product @ SV6 @ SV26 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV7: $i,SV27: $i,SV54: $i,SV43: $i,SV37: $i] :
( ( ( ~ ( product @ SV37 @ SV43 @ SV54 )
| ! [SY139: $i] :
( ~ ( product @ SV27 @ SV43 @ SY139 )
| ( product @ SV7 @ SY139 @ SV54 ) ) )
= $true )
| ( ( product @ SV7 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV28: $i,SV8: $i,SV38: $i,SV50: $i] :
( ( ( ~ ( defined @ SV50 @ SV38 ) )
= $true )
| ( ( defined @ SV50 @ SV8 )
= $true )
| ( ( product @ SV8 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV29: $i,SV39: $i,SV55: $i,SV9: $i,SV51: $i] :
( ( ( ~ ( product @ SV51 @ SV9 @ SV55 )
| ~ ( defined @ SV51 @ SV39 )
| ( defined @ SV55 @ SV29 ) )
= $true )
| ( ( product @ SV9 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV30: $i,SV10: $i,SV56: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( product @ SV44 @ SV40 @ SV56 )
| ! [SY140: $i] :
( ~ ( product @ SV44 @ SV10 @ SY140 )
| ( product @ SY140 @ SV30 @ SV56 ) ) )
= $true )
| ( ( product @ SV10 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV11: $i,SV47: $i,SV31: $i] :
( ( ( defined @ SV31 @ SV47 )
= $false )
| ( ( ~ ( identity_map @ SV31 )
| ( defined @ SV11 @ SV47 ) )
= $true )
| ( ( defined @ SV11 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV41: $i,SV52: $i,SV34: $i,SV20: $i] :
( ( ( ~ ( product @ SV20 @ SV34 @ SV52 ) )
= $true )
| ( ( SV41 = SV52 )
= $true )
| ( ( product @ SV20 @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV5: $i,SV25: $i,SV48: $i,SV35: $i] :
( ( ( defined @ SV35 @ SV48 )
= $false )
| ( ( defined @ SV25 @ SV48 )
= $true )
| ( ( product @ SV5 @ SV25 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV6: $i,SV36: $i,SV53: $i,SV49: $i,SV26: $i] :
( ( ( ~ ( product @ SV26 @ SV49 @ SV53 ) )
= $true )
| ( ( ~ ( defined @ SV36 @ SV49 )
| ( defined @ SV6 @ SV53 ) )
= $true )
| ( ( product @ SV6 @ SV26 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(191,plain,
! [SV7: $i,SV27: $i,SV54: $i,SV43: $i,SV37: $i] :
( ( ( ~ ( product @ SV37 @ SV43 @ SV54 ) )
= $true )
| ( ( ! [SY139: $i] :
( ~ ( product @ SV27 @ SV43 @ SY139 )
| ( product @ SV7 @ SY139 @ SV54 ) ) )
= $true )
| ( ( product @ SV7 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(192,plain,
! [SV28: $i,SV8: $i,SV38: $i,SV50: $i] :
( ( ( defined @ SV50 @ SV38 )
= $false )
| ( ( defined @ SV50 @ SV8 )
= $true )
| ( ( product @ SV8 @ SV28 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(193,plain,
! [SV29: $i,SV39: $i,SV55: $i,SV9: $i,SV51: $i] :
( ( ( ~ ( product @ SV51 @ SV9 @ SV55 ) )
= $true )
| ( ( ~ ( defined @ SV51 @ SV39 )
| ( defined @ SV55 @ SV29 ) )
= $true )
| ( ( product @ SV9 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV30: $i,SV10: $i,SV56: $i,SV40: $i,SV44: $i] :
( ( ( ~ ( product @ SV44 @ SV40 @ SV56 ) )
= $true )
| ( ( ! [SY140: $i] :
( ~ ( product @ SV44 @ SV10 @ SY140 )
| ( product @ SY140 @ SV30 @ SV56 ) ) )
= $true )
| ( ( product @ SV10 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(195,plain,
! [SV47: $i,SV11: $i,SV31: $i] :
( ( ( ~ ( identity_map @ SV31 ) )
= $true )
| ( ( defined @ SV11 @ SV47 )
= $true )
| ( ( defined @ SV31 @ SV47 )
= $false )
| ( ( defined @ SV11 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
! [SV41: $i,SV52: $i,SV34: $i,SV20: $i] :
( ( ( product @ SV20 @ SV34 @ SV52 )
= $false )
| ( ( SV41 = SV52 )
= $true )
| ( ( product @ SV20 @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(197,plain,
! [SV6: $i,SV36: $i,SV53: $i,SV49: $i,SV26: $i] :
( ( ( product @ SV26 @ SV49 @ SV53 )
= $false )
| ( ( ~ ( defined @ SV36 @ SV49 )
| ( defined @ SV6 @ SV53 ) )
= $true )
| ( ( product @ SV6 @ SV26 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV7: $i,SV27: $i,SV54: $i,SV43: $i,SV37: $i] :
( ( ( product @ SV37 @ SV43 @ SV54 )
= $false )
| ( ( ! [SY139: $i] :
( ~ ( product @ SV27 @ SV43 @ SY139 )
| ( product @ SV7 @ SY139 @ SV54 ) ) )
= $true )
| ( ( product @ SV7 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(199,plain,
! [SV29: $i,SV39: $i,SV55: $i,SV9: $i,SV51: $i] :
( ( ( product @ SV51 @ SV9 @ SV55 )
= $false )
| ( ( ~ ( defined @ SV51 @ SV39 )
| ( defined @ SV55 @ SV29 ) )
= $true )
| ( ( product @ SV9 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(200,plain,
! [SV30: $i,SV10: $i,SV56: $i,SV40: $i,SV44: $i] :
( ( ( product @ SV44 @ SV40 @ SV56 )
= $false )
| ( ( ! [SY140: $i] :
( ~ ( product @ SV44 @ SV10 @ SY140 )
| ( product @ SY140 @ SV30 @ SV56 ) ) )
= $true )
| ( ( product @ SV10 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(201,plain,
! [SV47: $i,SV11: $i,SV31: $i] :
( ( ( identity_map @ SV31 )
= $false )
| ( ( defined @ SV11 @ SV47 )
= $true )
| ( ( defined @ SV31 @ SV47 )
= $false )
| ( ( defined @ SV11 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(202,plain,
! [SV26: $i,SV53: $i,SV6: $i,SV49: $i,SV36: $i] :
( ( ( ~ ( defined @ SV36 @ SV49 ) )
= $true )
| ( ( defined @ SV6 @ SV53 )
= $true )
| ( ( product @ SV26 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV6 @ SV26 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(203,plain,
! [SV37: $i,SV54: $i,SV7: $i,SV57: $i,SV43: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV43 @ SV57 )
| ( product @ SV7 @ SV57 @ SV54 ) )
= $true )
| ( ( product @ SV37 @ SV43 @ SV54 )
= $false )
| ( ( product @ SV7 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(204,plain,
! [SV9: $i,SV29: $i,SV55: $i,SV39: $i,SV51: $i] :
( ( ( ~ ( defined @ SV51 @ SV39 ) )
= $true )
| ( ( defined @ SV55 @ SV29 )
= $true )
| ( ( product @ SV51 @ SV9 @ SV55 )
= $false )
| ( ( product @ SV9 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(205,plain,
! [SV40: $i,SV56: $i,SV30: $i,SV58: $i,SV10: $i,SV44: $i] :
( ( ( ~ ( product @ SV44 @ SV10 @ SV58 )
| ( product @ SV58 @ SV30 @ SV56 ) )
= $true )
| ( ( product @ SV44 @ SV40 @ SV56 )
= $false )
| ( ( product @ SV10 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(206,plain,
! [SV26: $i,SV53: $i,SV6: $i,SV49: $i,SV36: $i] :
( ( ( defined @ SV36 @ SV49 )
= $false )
| ( ( defined @ SV6 @ SV53 )
= $true )
| ( ( product @ SV26 @ SV49 @ SV53 )
= $false )
| ( ( product @ SV6 @ SV26 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV37: $i,SV54: $i,SV7: $i,SV57: $i,SV43: $i,SV27: $i] :
( ( ( ~ ( product @ SV27 @ SV43 @ SV57 ) )
= $true )
| ( ( product @ SV7 @ SV57 @ SV54 )
= $true )
| ( ( product @ SV37 @ SV43 @ SV54 )
= $false )
| ( ( product @ SV7 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV9: $i,SV29: $i,SV55: $i,SV39: $i,SV51: $i] :
( ( ( defined @ SV51 @ SV39 )
= $false )
| ( ( defined @ SV55 @ SV29 )
= $true )
| ( ( product @ SV51 @ SV9 @ SV55 )
= $false )
| ( ( product @ SV9 @ SV29 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV40: $i,SV56: $i,SV30: $i,SV58: $i,SV10: $i,SV44: $i] :
( ( ( ~ ( product @ SV44 @ SV10 @ SV58 ) )
= $true )
| ( ( product @ SV58 @ SV30 @ SV56 )
= $true )
| ( ( product @ SV44 @ SV40 @ SV56 )
= $false )
| ( ( product @ SV10 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV37: $i,SV54: $i,SV7: $i,SV57: $i,SV43: $i,SV27: $i] :
( ( ( product @ SV27 @ SV43 @ SV57 )
= $false )
| ( ( product @ SV7 @ SV57 @ SV54 )
= $true )
| ( ( product @ SV37 @ SV43 @ SV54 )
= $false )
| ( ( product @ SV7 @ SV27 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(211,plain,
! [SV40: $i,SV56: $i,SV30: $i,SV58: $i,SV10: $i,SV44: $i] :
( ( ( product @ SV44 @ SV10 @ SV58 )
= $false )
| ( ( product @ SV58 @ SV30 @ SV56 )
= $true )
| ( ( product @ SV44 @ SV40 @ SV56 )
= $false )
| ( ( product @ SV10 @ SV30 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(212,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[68,211,210,208,206,201,196,192,189,180,179,177,176,156,142,111,107,106,105,104,103,102,90,70,69]) ).
thf(213,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : CAT004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 16:48:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.38
% 0.13/0.38 No.of.Axioms: 24
% 0.13/0.38
% 0.13/0.38 Length.of.Defs: 0
% 0.13/0.38
% 0.13/0.38 Contains.Choice.Funs: false
% 0.13/0.40 .
% 0.13/0.40 (rf:0,axioms:24,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:26,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 36.63/36.84
% 36.63/36.84 ********************************
% 36.63/36.84 * All subproblems solved! *
% 36.63/36.84 ********************************
% 36.63/36.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:212,loop_count:0,foatp_calls:1,translation:fof_full)
% 36.63/36.85
% 36.63/36.85 %**** Beginning of derivation protocol ****
% 36.63/36.85 % SZS output start CNFRefutation
% See solution above
% 36.63/36.85
% 36.63/36.85 %**** End of derivation protocol ****
% 36.63/36.85 %**** no. of clauses in derivation: 213 ****
% 36.63/36.85 %**** clause counter: 212 ****
% 36.63/36.85
% 36.63/36.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:212,loop_count:0,foatp_calls:1,translation:fof_full)
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