%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KRS163+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:26:33 AM UTC 2026
% Result : Theorem 1.11s 0.43s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 607 ( 380 unt; 0 typ; 0 def)
% Number of atoms : 3331 (1254 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 2821 ( 833 ~; 782 |; 51 &;1134 @)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 887 ( 0 ^; 887 !; 0 ?; 887 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cA,type,
cA: $i > $o ).
thf(tp_cB,type,
cB: $i > $o ).
thf(tp_cowlNothing,type,
cowlNothing: $i > $o ).
thf(tp_cowlThing,type,
cowlThing: $i > $o ).
thf(tp_ia,type,
ia: $i ).
thf(tp_ib,type,
ib: $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK3_X,type,
sK3_X: $i ).
thf(tp_sK4_X,type,
sK4_X: $i ).
thf(tp_xsd_integer,type,
xsd_integer: $i > $o ).
thf(tp_xsd_string,type,
xsd_string: $i > $o ).
thf(1,axiom,
! [X: $i] :
~ ( ( cB @ X )
& ( cA @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(2,axiom,
cowlThing @ ib,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(3,axiom,
cB @ ib,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(4,axiom,
cowlThing @ ia,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(5,axiom,
cA @ ia,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(6,axiom,
! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(7,axiom,
! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cB @ A ) )
=> ( cB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cB_substitution_1) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cA @ A ) )
=> ( cA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cA_substitution_1) ).
thf(14,conjecture,
( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ( cowlThing @ ia )
& ( cowlThing @ ib )
& ( ia != ib ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
thf(15,negated_conjecture,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ( cowlThing @ ia )
& ( cowlThing @ ib )
& ( ia != ib ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ( cowlThing @ ia )
& ( cowlThing @ ib )
& ( ia != ib ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X: $i] :
~ ( ( cB @ X )
& ( cA @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( cowlThing @ ib )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( cB @ ib )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( cowlThing @ ia )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( cA @ ia )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( cB @ A ) )
=> ( cB @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( cA @ A ) )
=> ( cA @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [X: $i] : ( cowlThing @ X ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(31,plain,
( ( ! [X: $i] :
~ ( cowlNothing @ X ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
=> ~ ( xsd_integer @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(33,plain,
( ( ! [X: $i] :
( ~ ( xsd_integer @ X )
=> ( xsd_string @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(34,plain,
( ( cowlThing @ ia )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(35,plain,
( ( cowlThing @ ib )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(36,plain,
( ( ia != ib )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[16]) ).
thf(37,plain,
( ( ~ ! [X: $i] : ( cowlThing @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(38,plain,
( ( ~ ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(39,plain,
( ( ~ ! [X: $i] :
( ( xsd_string @ X )
=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(40,plain,
( ( ~ ! [X: $i] :
( ~ ( xsd_integer @ X )
=> ( xsd_string @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(41,plain,
( ( ~ ( cowlThing @ ia ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(42,plain,
( ( ~ ( cowlThing @ ib ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(43,plain,
( ( ~ ( ( ia != ib ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(44,plain,
( ( ~ ( cowlThing @ sK1_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(45,plain,
( ( cowlNothing @ sK2_X )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(46,plain,
( ( ( xsd_string @ sK3_X )
& ( xsd_integer @ sK3_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(47,plain,
( ( ~ ( xsd_integer @ sK4_X )
& ~ ( xsd_string @ sK4_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(48,plain,
( ( ia = ib )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(49,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(50,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(51,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(64,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(65,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(66,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(67,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(68,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(69,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(70,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(71,plain,
( ( ~ ( cowlThing @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(72,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(73,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(74,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ( SV1 != SY17 )
| ~ ( cA @ SV1 )
| ( cA @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV2: $i] :
( ( ! [SY18: $i] :
( ( SV2 != SY18 )
| ~ ( cB @ SV2 )
| ( cB @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(76,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ( SV3 != SY19 )
| ~ ( cowlNothing @ SV3 )
| ( cowlNothing @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV4: $i] :
( ( ! [SY20: $i] :
( ( SV4 != SY20 )
| ~ ( cowlThing @ SV4 )
| ( cowlThing @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV5: $i] :
( ( ! [SY21: $i] :
( ( SV5 != SY21 )
| ~ ( xsd_integer @ SV5 )
| ( xsd_integer @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV6: $i] :
( ( ! [SY22: $i] :
( ( SV6 != SY22 )
| ~ ( xsd_string @ SV6 )
| ( xsd_string @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV7: $i] :
( ( ~ ( cA @ SV7 )
| ~ ( cB @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
( ( cowlThing @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV8: $i,SV1: $i] :
( ( ( SV1 != SV8 )
| ~ ( cA @ SV1 )
| ( cA @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV9: $i,SV2: $i] :
( ( ( SV2 != SV9 )
| ~ ( cB @ SV2 )
| ( cB @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV10: $i,SV3: $i] :
( ( ( SV3 != SV10 )
| ~ ( cowlNothing @ SV3 )
| ( cowlNothing @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV11: $i,SV4: $i] :
( ( ( SV4 != SV11 )
| ~ ( cowlThing @ SV4 )
| ( cowlThing @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV12: $i,SV5: $i] :
( ( ( SV5 != SV12 )
| ~ ( xsd_integer @ SV5 )
| ( xsd_integer @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV13: $i,SV6: $i] :
( ( ( SV6 != SV13 )
| ~ ( xsd_string @ SV6 )
| ( xsd_string @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV7: $i] :
( ( ( ~ ( cA @ SV7 ) )
= $true )
| ( ( ~ ( cB @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(91,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(92,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(93,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(94,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(95,plain,
! [SV8: $i,SV1: $i] :
( ( ( ( SV1 != SV8 )
| ~ ( cA @ SV1 ) )
= $true )
| ( ( cA @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV9: $i,SV2: $i] :
( ( ( ( SV2 != SV9 )
| ~ ( cB @ SV2 ) )
= $true )
| ( ( cB @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV10: $i,SV3: $i] :
( ( ( ( SV3 != SV10 )
| ~ ( cowlNothing @ SV3 ) )
= $true )
| ( ( cowlNothing @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV11: $i,SV4: $i] :
( ( ( ( SV4 != SV11 )
| ~ ( cowlThing @ SV4 ) )
= $true )
| ( ( cowlThing @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV12: $i,SV5: $i] :
( ( ( ( SV5 != SV12 )
| ~ ( xsd_integer @ SV5 ) )
= $true )
| ( ( xsd_integer @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV13: $i,SV6: $i] :
( ( ( ( SV6 != SV13 )
| ~ ( xsd_string @ SV6 ) )
= $true )
| ( ( xsd_string @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV7: $i] :
( ( ( cA @ SV7 )
= $false )
| ( ( ~ ( cB @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(102,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(103,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(105,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(106,plain,
! [SV8: $i,SV1: $i] :
( ( ( SV1 != SV8 )
= $true )
| ( ( ~ ( cA @ SV1 ) )
= $true )
| ( ( cA @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV9: $i,SV2: $i] :
( ( ( SV2 != SV9 )
= $true )
| ( ( ~ ( cB @ SV2 ) )
= $true )
| ( ( cB @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV10: $i,SV3: $i] :
( ( ( SV3 != SV10 )
= $true )
| ( ( ~ ( cowlNothing @ SV3 ) )
= $true )
| ( ( cowlNothing @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV11: $i,SV4: $i] :
( ( ( SV4 != SV11 )
= $true )
| ( ( ~ ( cowlThing @ SV4 ) )
= $true )
| ( ( cowlThing @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV12: $i,SV5: $i] :
( ( ( SV5 != SV12 )
= $true )
| ( ( ~ ( xsd_integer @ SV5 ) )
= $true )
| ( ( xsd_integer @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV13: $i,SV6: $i] :
( ( ( SV6 != SV13 )
= $true )
| ( ( ~ ( xsd_string @ SV6 ) )
= $true )
| ( ( xsd_string @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV7: $i] :
( ( ( cB @ SV7 )
= $false )
| ( ( cA @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV14: $i] :
( ( cowlThing @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV15: $i] :
( ( ~ ( cowlNothing @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV16: $i] :
( ( ~ ( xsd_string @ SV16 )
| ~ ( xsd_integer @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV17: $i] :
( ( ( xsd_integer @ SV17 )
| ( xsd_string @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV8: $i,SV1: $i] :
( ( ( SV1 = SV8 )
= $false )
| ( ( ~ ( cA @ SV1 ) )
= $true )
| ( ( cA @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV9: $i,SV2: $i] :
( ( ( SV2 = SV9 )
= $false )
| ( ( ~ ( cB @ SV2 ) )
= $true )
| ( ( cB @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV10: $i,SV3: $i] :
( ( ( SV3 = SV10 )
= $false )
| ( ( ~ ( cowlNothing @ SV3 ) )
= $true )
| ( ( cowlNothing @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV11: $i,SV4: $i] :
( ( ( SV4 = SV11 )
= $false )
| ( ( ~ ( cowlThing @ SV4 ) )
= $true )
| ( ( cowlThing @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV12: $i,SV5: $i] :
( ( ( SV5 = SV12 )
= $false )
| ( ( ~ ( xsd_integer @ SV5 ) )
= $true )
| ( ( xsd_integer @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV13: $i,SV6: $i] :
( ( ( SV6 = SV13 )
= $false )
| ( ( ~ ( xsd_string @ SV6 ) )
= $true )
| ( ( xsd_string @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV15: $i] :
( ( cowlNothing @ SV15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV16: $i] :
( ( ( ~ ( xsd_string @ SV16 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV17: $i] :
( ( ( xsd_integer @ SV17 )
= $true )
| ( ( xsd_string @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV8: $i,SV1: $i] :
( ( ( cA @ SV1 )
= $false )
| ( ( SV1 = SV8 )
= $false )
| ( ( cA @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(127,plain,
! [SV9: $i,SV2: $i] :
( ( ( cB @ SV2 )
= $false )
| ( ( SV2 = SV9 )
= $false )
| ( ( cB @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(128,plain,
! [SV10: $i,SV3: $i] :
( ( ( cowlNothing @ SV3 )
= $false )
| ( ( SV3 = SV10 )
= $false )
| ( ( cowlNothing @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV11: $i,SV4: $i] :
( ( ( cowlThing @ SV4 )
= $false )
| ( ( SV4 = SV11 )
= $false )
| ( ( cowlThing @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV12: $i,SV5: $i] :
( ( ( xsd_integer @ SV5 )
= $false )
| ( ( SV5 = SV12 )
= $false )
| ( ( xsd_integer @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(131,plain,
! [SV13: $i,SV6: $i] :
( ( ( xsd_string @ SV6 )
= $false )
| ( ( SV6 = SV13 )
= $false )
| ( ( xsd_string @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(132,plain,
! [SV16: $i] :
( ( ( xsd_string @ SV16 )
= $false )
| ( ( ~ ( xsd_integer @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV16: $i] :
( ( ( xsd_integer @ SV16 )
= $false )
| ( ( xsd_string @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(134,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,133,131,130,129,128,127,126,125,123,113,112,81,69,68,67]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(137,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(141,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(142,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(143,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(144,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(145,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(146,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(147,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(148,plain,
( ( cowlNothing @ sK2_X )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(149,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(150,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(151,plain,
! [SV18: $i] :
( ( ! [SY23: $i] :
( ( SV18 != SY23 )
| ~ ( cA @ SV18 )
| ( cA @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV19: $i] :
( ( ! [SY24: $i] :
( ( SV19 != SY24 )
| ~ ( cB @ SV19 )
| ( cB @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV20: $i] :
( ( ! [SY25: $i] :
( ( SV20 != SY25 )
| ~ ( cowlNothing @ SV20 )
| ( cowlNothing @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV21: $i] :
( ( ! [SY26: $i] :
( ( SV21 != SY26 )
| ~ ( cowlThing @ SV21 )
| ( cowlThing @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV22: $i] :
( ( ! [SY27: $i] :
( ( SV22 != SY27 )
| ~ ( xsd_integer @ SV22 )
| ( xsd_integer @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV23: $i] :
( ( ! [SY28: $i] :
( ( SV23 != SY28 )
| ~ ( xsd_string @ SV23 )
| ( xsd_string @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(157,plain,
! [SV24: $i] :
( ( ~ ( cA @ SV24 )
| ~ ( cB @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(158,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(159,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV25: $i,SV18: $i] :
( ( ( SV18 != SV25 )
| ~ ( cA @ SV18 )
| ( cA @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV26: $i,SV19: $i] :
( ( ( SV19 != SV26 )
| ~ ( cB @ SV19 )
| ( cB @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV27: $i,SV20: $i] :
( ( ( SV20 != SV27 )
| ~ ( cowlNothing @ SV20 )
| ( cowlNothing @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV28: $i,SV21: $i] :
( ( ( SV21 != SV28 )
| ~ ( cowlThing @ SV21 )
| ( cowlThing @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV29: $i,SV22: $i] :
( ( ( SV22 != SV29 )
| ~ ( xsd_integer @ SV22 )
| ( xsd_integer @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV30: $i,SV23: $i] :
( ( ( SV23 != SV30 )
| ~ ( xsd_string @ SV23 )
| ( xsd_string @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV24: $i] :
( ( ( ~ ( cA @ SV24 ) )
= $true )
| ( ( ~ ( cB @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(167,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(168,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(169,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(170,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(171,plain,
! [SV25: $i,SV18: $i] :
( ( ( ( SV18 != SV25 )
| ~ ( cA @ SV18 ) )
= $true )
| ( ( cA @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(172,plain,
! [SV26: $i,SV19: $i] :
( ( ( ( SV19 != SV26 )
| ~ ( cB @ SV19 ) )
= $true )
| ( ( cB @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(173,plain,
! [SV27: $i,SV20: $i] :
( ( ( ( SV20 != SV27 )
| ~ ( cowlNothing @ SV20 ) )
= $true )
| ( ( cowlNothing @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV28: $i,SV21: $i] :
( ( ( ( SV21 != SV28 )
| ~ ( cowlThing @ SV21 ) )
= $true )
| ( ( cowlThing @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(175,plain,
! [SV29: $i,SV22: $i] :
( ( ( ( SV22 != SV29 )
| ~ ( xsd_integer @ SV22 ) )
= $true )
| ( ( xsd_integer @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(176,plain,
! [SV30: $i,SV23: $i] :
( ( ( ( SV23 != SV30 )
| ~ ( xsd_string @ SV23 ) )
= $true )
| ( ( xsd_string @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(177,plain,
! [SV24: $i] :
( ( ( cA @ SV24 )
= $false )
| ( ( ~ ( cB @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(178,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(179,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(180,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(181,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(182,plain,
! [SV25: $i,SV18: $i] :
( ( ( SV18 != SV25 )
= $true )
| ( ( ~ ( cA @ SV18 ) )
= $true )
| ( ( cA @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV26: $i,SV19: $i] :
( ( ( SV19 != SV26 )
= $true )
| ( ( ~ ( cB @ SV19 ) )
= $true )
| ( ( cB @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV27: $i,SV20: $i] :
( ( ( SV20 != SV27 )
= $true )
| ( ( ~ ( cowlNothing @ SV20 ) )
= $true )
| ( ( cowlNothing @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV28: $i,SV21: $i] :
( ( ( SV21 != SV28 )
= $true )
| ( ( ~ ( cowlThing @ SV21 ) )
= $true )
| ( ( cowlThing @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(186,plain,
! [SV29: $i,SV22: $i] :
( ( ( SV22 != SV29 )
= $true )
| ( ( ~ ( xsd_integer @ SV22 ) )
= $true )
| ( ( xsd_integer @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV30: $i,SV23: $i] :
( ( ( SV23 != SV30 )
= $true )
| ( ( ~ ( xsd_string @ SV23 ) )
= $true )
| ( ( xsd_string @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(188,plain,
! [SV24: $i] :
( ( ( cB @ SV24 )
= $false )
| ( ( cA @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV31: $i] :
( ( ~ ( xsd_string @ SV31 )
| ~ ( xsd_integer @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV32: $i] :
( ( ( xsd_integer @ SV32 )
| ( xsd_string @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV33: $i] :
( ( cowlThing @ SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV34: $i] :
( ( ~ ( cowlNothing @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV25: $i,SV18: $i] :
( ( ( SV18 = SV25 )
= $false )
| ( ( ~ ( cA @ SV18 ) )
= $true )
| ( ( cA @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV26: $i,SV19: $i] :
( ( ( SV19 = SV26 )
= $false )
| ( ( ~ ( cB @ SV19 ) )
= $true )
| ( ( cB @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV27: $i,SV20: $i] :
( ( ( SV20 = SV27 )
= $false )
| ( ( ~ ( cowlNothing @ SV20 ) )
= $true )
| ( ( cowlNothing @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV28: $i,SV21: $i] :
( ( ( SV21 = SV28 )
= $false )
| ( ( ~ ( cowlThing @ SV21 ) )
= $true )
| ( ( cowlThing @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV29: $i,SV22: $i] :
( ( ( SV22 = SV29 )
= $false )
| ( ( ~ ( xsd_integer @ SV22 ) )
= $true )
| ( ( xsd_integer @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV30: $i,SV23: $i] :
( ( ( SV23 = SV30 )
= $false )
| ( ( ~ ( xsd_string @ SV23 ) )
= $true )
| ( ( xsd_string @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV31: $i] :
( ( ( ~ ( xsd_string @ SV31 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(200,plain,
! [SV32: $i] :
( ( ( xsd_integer @ SV32 )
= $true )
| ( ( xsd_string @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(201,plain,
! [SV34: $i] :
( ( cowlNothing @ SV34 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV25: $i,SV18: $i] :
( ( ( cA @ SV18 )
= $false )
| ( ( SV18 = SV25 )
= $false )
| ( ( cA @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV26: $i,SV19: $i] :
( ( ( cB @ SV19 )
= $false )
| ( ( SV19 = SV26 )
= $false )
| ( ( cB @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV27: $i,SV20: $i] :
( ( ( cowlNothing @ SV20 )
= $false )
| ( ( SV20 = SV27 )
= $false )
| ( ( cowlNothing @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV28: $i,SV21: $i] :
( ( ( cowlThing @ SV21 )
= $false )
| ( ( SV21 = SV28 )
= $false )
| ( ( cowlThing @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV29: $i,SV22: $i] :
( ( ( xsd_integer @ SV22 )
= $false )
| ( ( SV22 = SV29 )
= $false )
| ( ( xsd_integer @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV30: $i,SV23: $i] :
( ( ( xsd_string @ SV23 )
= $false )
| ( ( SV23 = SV30 )
= $false )
| ( ( xsd_string @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV31: $i] :
( ( ( xsd_string @ SV31 )
= $false )
| ( ( ~ ( xsd_integer @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV31: $i] :
( ( ( xsd_integer @ SV31 )
= $false )
| ( ( xsd_string @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(210,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[143,209,207,206,205,204,203,202,201,200,191,188,148,146,145,144]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(213,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(214,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(217,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(218,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(219,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(220,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(221,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(222,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(223,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(224,plain,
( ( ( xsd_string @ sK3_X )
& ( xsd_integer @ sK3_X ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(225,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(226,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(227,plain,
( ( ~ ( ~ ( xsd_string @ sK3_X )
| ~ ( xsd_integer @ sK3_X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(228,plain,
! [SV35: $i] :
( ( ! [SY29: $i] :
( ( SV35 != SY29 )
| ~ ( cA @ SV35 )
| ( cA @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV36: $i] :
( ( ! [SY30: $i] :
( ( SV36 != SY30 )
| ~ ( cB @ SV36 )
| ( cB @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV37: $i] :
( ( ! [SY31: $i] :
( ( SV37 != SY31 )
| ~ ( cowlNothing @ SV37 )
| ( cowlNothing @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(231,plain,
! [SV38: $i] :
( ( ! [SY32: $i] :
( ( SV38 != SY32 )
| ~ ( cowlThing @ SV38 )
| ( cowlThing @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(232,plain,
! [SV39: $i] :
( ( ! [SY33: $i] :
( ( SV39 != SY33 )
| ~ ( xsd_integer @ SV39 )
| ( xsd_integer @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV40: $i] :
( ( ! [SY34: $i] :
( ( SV40 != SY34 )
| ~ ( xsd_string @ SV40 )
| ( xsd_string @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV41: $i] :
( ( ~ ( cA @ SV41 )
| ~ ( cB @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(235,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(236,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(237,plain,
( ( ~ ( xsd_string @ sK3_X )
| ~ ( xsd_integer @ sK3_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(238,plain,
! [SV42: $i,SV35: $i] :
( ( ( SV35 != SV42 )
| ~ ( cA @ SV35 )
| ( cA @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(239,plain,
! [SV43: $i,SV36: $i] :
( ( ( SV36 != SV43 )
| ~ ( cB @ SV36 )
| ( cB @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(240,plain,
! [SV44: $i,SV37: $i] :
( ( ( SV37 != SV44 )
| ~ ( cowlNothing @ SV37 )
| ( cowlNothing @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV45: $i,SV38: $i] :
( ( ( SV38 != SV45 )
| ~ ( cowlThing @ SV38 )
| ( cowlThing @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV46: $i,SV39: $i] :
( ( ( SV39 != SV46 )
| ~ ( xsd_integer @ SV39 )
| ( xsd_integer @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV47: $i,SV40: $i] :
( ( ( SV40 != SV47 )
| ~ ( xsd_string @ SV40 )
| ( xsd_string @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV41: $i] :
( ( ( ~ ( cA @ SV41 ) )
= $true )
| ( ( ~ ( cB @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(245,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(246,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(247,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(248,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(249,plain,
( ( ~ ( xsd_string @ sK3_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(250,plain,
( ( ~ ( xsd_integer @ sK3_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(251,plain,
! [SV42: $i,SV35: $i] :
( ( ( ( SV35 != SV42 )
| ~ ( cA @ SV35 ) )
= $true )
| ( ( cA @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(252,plain,
! [SV43: $i,SV36: $i] :
( ( ( ( SV36 != SV43 )
| ~ ( cB @ SV36 ) )
= $true )
| ( ( cB @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(253,plain,
! [SV44: $i,SV37: $i] :
( ( ( ( SV37 != SV44 )
| ~ ( cowlNothing @ SV37 ) )
= $true )
| ( ( cowlNothing @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(254,plain,
! [SV45: $i,SV38: $i] :
( ( ( ( SV38 != SV45 )
| ~ ( cowlThing @ SV38 ) )
= $true )
| ( ( cowlThing @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(255,plain,
! [SV46: $i,SV39: $i] :
( ( ( ( SV39 != SV46 )
| ~ ( xsd_integer @ SV39 ) )
= $true )
| ( ( xsd_integer @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(256,plain,
! [SV47: $i,SV40: $i] :
( ( ( ( SV40 != SV47 )
| ~ ( xsd_string @ SV40 ) )
= $true )
| ( ( xsd_string @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV41: $i] :
( ( ( cA @ SV41 )
= $false )
| ( ( ~ ( cB @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(258,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(259,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(260,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(261,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(262,plain,
( ( xsd_string @ sK3_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(263,plain,
( ( xsd_integer @ sK3_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(264,plain,
! [SV42: $i,SV35: $i] :
( ( ( SV35 != SV42 )
= $true )
| ( ( ~ ( cA @ SV35 ) )
= $true )
| ( ( cA @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(265,plain,
! [SV43: $i,SV36: $i] :
( ( ( SV36 != SV43 )
= $true )
| ( ( ~ ( cB @ SV36 ) )
= $true )
| ( ( cB @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(266,plain,
! [SV44: $i,SV37: $i] :
( ( ( SV37 != SV44 )
= $true )
| ( ( ~ ( cowlNothing @ SV37 ) )
= $true )
| ( ( cowlNothing @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(267,plain,
! [SV45: $i,SV38: $i] :
( ( ( SV38 != SV45 )
= $true )
| ( ( ~ ( cowlThing @ SV38 ) )
= $true )
| ( ( cowlThing @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV46: $i,SV39: $i] :
( ( ( SV39 != SV46 )
= $true )
| ( ( ~ ( xsd_integer @ SV39 ) )
= $true )
| ( ( xsd_integer @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(269,plain,
! [SV47: $i,SV40: $i] :
( ( ( SV40 != SV47 )
= $true )
| ( ( ~ ( xsd_string @ SV40 ) )
= $true )
| ( ( xsd_string @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(270,plain,
! [SV41: $i] :
( ( ( cB @ SV41 )
= $false )
| ( ( cA @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(271,plain,
! [SV48: $i] :
( ( ~ ( xsd_string @ SV48 )
| ~ ( xsd_integer @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(272,plain,
! [SV49: $i] :
( ( ( xsd_integer @ SV49 )
| ( xsd_string @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(273,plain,
! [SV50: $i] :
( ( cowlThing @ SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(274,plain,
! [SV51: $i] :
( ( ~ ( cowlNothing @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(275,plain,
! [SV42: $i,SV35: $i] :
( ( ( SV35 = SV42 )
= $false )
| ( ( ~ ( cA @ SV35 ) )
= $true )
| ( ( cA @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV43: $i,SV36: $i] :
( ( ( SV36 = SV43 )
= $false )
| ( ( ~ ( cB @ SV36 ) )
= $true )
| ( ( cB @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV44: $i,SV37: $i] :
( ( ( SV37 = SV44 )
= $false )
| ( ( ~ ( cowlNothing @ SV37 ) )
= $true )
| ( ( cowlNothing @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(278,plain,
! [SV45: $i,SV38: $i] :
( ( ( SV38 = SV45 )
= $false )
| ( ( ~ ( cowlThing @ SV38 ) )
= $true )
| ( ( cowlThing @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV46: $i,SV39: $i] :
( ( ( SV39 = SV46 )
= $false )
| ( ( ~ ( xsd_integer @ SV39 ) )
= $true )
| ( ( xsd_integer @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV47: $i,SV40: $i] :
( ( ( SV40 = SV47 )
= $false )
| ( ( ~ ( xsd_string @ SV40 ) )
= $true )
| ( ( xsd_string @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV48: $i] :
( ( ( ~ ( xsd_string @ SV48 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(282,plain,
! [SV49: $i] :
( ( ( xsd_integer @ SV49 )
= $true )
| ( ( xsd_string @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(283,plain,
! [SV51: $i] :
( ( cowlNothing @ SV51 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(284,plain,
! [SV42: $i,SV35: $i] :
( ( ( cA @ SV35 )
= $false )
| ( ( SV35 = SV42 )
= $false )
| ( ( cA @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV43: $i,SV36: $i] :
( ( ( cB @ SV36 )
= $false )
| ( ( SV36 = SV43 )
= $false )
| ( ( cB @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(286,plain,
! [SV44: $i,SV37: $i] :
( ( ( cowlNothing @ SV37 )
= $false )
| ( ( SV37 = SV44 )
= $false )
| ( ( cowlNothing @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(287,plain,
! [SV45: $i,SV38: $i] :
( ( ( cowlThing @ SV38 )
= $false )
| ( ( SV38 = SV45 )
= $false )
| ( ( cowlThing @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(288,plain,
! [SV46: $i,SV39: $i] :
( ( ( xsd_integer @ SV39 )
= $false )
| ( ( SV39 = SV46 )
= $false )
| ( ( xsd_integer @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(289,plain,
! [SV47: $i,SV40: $i] :
( ( ( xsd_string @ SV40 )
= $false )
| ( ( SV40 = SV47 )
= $false )
| ( ( xsd_string @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(290,plain,
! [SV48: $i] :
( ( ( xsd_string @ SV48 )
= $false )
| ( ( ~ ( xsd_integer @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(291,plain,
! [SV48: $i] :
( ( ( xsd_integer @ SV48 )
= $false )
| ( ( xsd_string @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(292,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[219,291,289,288,287,286,285,284,283,282,273,270,263,262,222,221,220]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(299,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(300,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(301,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(302,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(303,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(304,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(305,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(306,plain,
( ( ~ ( xsd_integer @ sK4_X )
& ~ ( xsd_string @ sK4_X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(307,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(308,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(309,plain,
( ( ~ ( ~ ~ ( xsd_integer @ sK4_X )
| ~ ~ ( xsd_string @ sK4_X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(310,plain,
! [SV52: $i] :
( ( ! [SY35: $i] :
( ( SV52 != SY35 )
| ~ ( cA @ SV52 )
| ( cA @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(311,plain,
! [SV53: $i] :
( ( ! [SY36: $i] :
( ( SV53 != SY36 )
| ~ ( cB @ SV53 )
| ( cB @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(312,plain,
! [SV54: $i] :
( ( ! [SY37: $i] :
( ( SV54 != SY37 )
| ~ ( cowlNothing @ SV54 )
| ( cowlNothing @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(313,plain,
! [SV55: $i] :
( ( ! [SY38: $i] :
( ( SV55 != SY38 )
| ~ ( cowlThing @ SV55 )
| ( cowlThing @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(314,plain,
! [SV56: $i] :
( ( ! [SY39: $i] :
( ( SV56 != SY39 )
| ~ ( xsd_integer @ SV56 )
| ( xsd_integer @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(315,plain,
! [SV57: $i] :
( ( ! [SY40: $i] :
( ( SV57 != SY40 )
| ~ ( xsd_string @ SV57 )
| ( xsd_string @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(316,plain,
! [SV58: $i] :
( ( ~ ( cA @ SV58 )
| ~ ( cB @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(317,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(318,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(319,plain,
( ( ~ ~ ( xsd_integer @ sK4_X )
| ~ ~ ( xsd_string @ sK4_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(320,plain,
! [SV59: $i,SV52: $i] :
( ( ( SV52 != SV59 )
| ~ ( cA @ SV52 )
| ( cA @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(321,plain,
! [SV60: $i,SV53: $i] :
( ( ( SV53 != SV60 )
| ~ ( cB @ SV53 )
| ( cB @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(322,plain,
! [SV61: $i,SV54: $i] :
( ( ( SV54 != SV61 )
| ~ ( cowlNothing @ SV54 )
| ( cowlNothing @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(323,plain,
! [SV62: $i,SV55: $i] :
( ( ( SV55 != SV62 )
| ~ ( cowlThing @ SV55 )
| ( cowlThing @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(324,plain,
! [SV63: $i,SV56: $i] :
( ( ( SV56 != SV63 )
| ~ ( xsd_integer @ SV56 )
| ( xsd_integer @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(325,plain,
! [SV64: $i,SV57: $i] :
( ( ( SV57 != SV64 )
| ~ ( xsd_string @ SV57 )
| ( xsd_string @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(326,plain,
! [SV58: $i] :
( ( ( ~ ( cA @ SV58 ) )
= $true )
| ( ( ~ ( cB @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(327,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(328,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(329,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(330,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(331,plain,
( ( ~ ~ ( xsd_integer @ sK4_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(332,plain,
( ( ~ ~ ( xsd_string @ sK4_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(333,plain,
! [SV59: $i,SV52: $i] :
( ( ( ( SV52 != SV59 )
| ~ ( cA @ SV52 ) )
= $true )
| ( ( cA @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(334,plain,
! [SV60: $i,SV53: $i] :
( ( ( ( SV53 != SV60 )
| ~ ( cB @ SV53 ) )
= $true )
| ( ( cB @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(335,plain,
! [SV61: $i,SV54: $i] :
( ( ( ( SV54 != SV61 )
| ~ ( cowlNothing @ SV54 ) )
= $true )
| ( ( cowlNothing @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(336,plain,
! [SV62: $i,SV55: $i] :
( ( ( ( SV55 != SV62 )
| ~ ( cowlThing @ SV55 ) )
= $true )
| ( ( cowlThing @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(337,plain,
! [SV63: $i,SV56: $i] :
( ( ( ( SV56 != SV63 )
| ~ ( xsd_integer @ SV56 ) )
= $true )
| ( ( xsd_integer @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(338,plain,
! [SV64: $i,SV57: $i] :
( ( ( ( SV57 != SV64 )
| ~ ( xsd_string @ SV57 ) )
= $true )
| ( ( xsd_string @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(339,plain,
! [SV58: $i] :
( ( ( cA @ SV58 )
= $false )
| ( ( ~ ( cB @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(340,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(341,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(342,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(343,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(344,plain,
( ( ~ ( xsd_integer @ sK4_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(345,plain,
( ( ~ ( xsd_string @ sK4_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(346,plain,
! [SV59: $i,SV52: $i] :
( ( ( SV52 != SV59 )
= $true )
| ( ( ~ ( cA @ SV52 ) )
= $true )
| ( ( cA @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(347,plain,
! [SV60: $i,SV53: $i] :
( ( ( SV53 != SV60 )
= $true )
| ( ( ~ ( cB @ SV53 ) )
= $true )
| ( ( cB @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(348,plain,
! [SV61: $i,SV54: $i] :
( ( ( SV54 != SV61 )
= $true )
| ( ( ~ ( cowlNothing @ SV54 ) )
= $true )
| ( ( cowlNothing @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(349,plain,
! [SV62: $i,SV55: $i] :
( ( ( SV55 != SV62 )
= $true )
| ( ( ~ ( cowlThing @ SV55 ) )
= $true )
| ( ( cowlThing @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(350,plain,
! [SV63: $i,SV56: $i] :
( ( ( SV56 != SV63 )
= $true )
| ( ( ~ ( xsd_integer @ SV56 ) )
= $true )
| ( ( xsd_integer @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(351,plain,
! [SV64: $i,SV57: $i] :
( ( ( SV57 != SV64 )
= $true )
| ( ( ~ ( xsd_string @ SV57 ) )
= $true )
| ( ( xsd_string @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(352,plain,
! [SV58: $i] :
( ( ( cB @ SV58 )
= $false )
| ( ( cA @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(353,plain,
! [SV65: $i] :
( ( ~ ( xsd_string @ SV65 )
| ~ ( xsd_integer @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(354,plain,
! [SV66: $i] :
( ( ( xsd_integer @ SV66 )
| ( xsd_string @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(355,plain,
! [SV67: $i] :
( ( cowlThing @ SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(356,plain,
! [SV68: $i] :
( ( ~ ( cowlNothing @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(357,plain,
( ( xsd_integer @ sK4_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(358,plain,
( ( xsd_string @ sK4_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(359,plain,
! [SV59: $i,SV52: $i] :
( ( ( SV52 = SV59 )
= $false )
| ( ( ~ ( cA @ SV52 ) )
= $true )
| ( ( cA @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(360,plain,
! [SV60: $i,SV53: $i] :
( ( ( SV53 = SV60 )
= $false )
| ( ( ~ ( cB @ SV53 ) )
= $true )
| ( ( cB @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(361,plain,
! [SV61: $i,SV54: $i] :
( ( ( SV54 = SV61 )
= $false )
| ( ( ~ ( cowlNothing @ SV54 ) )
= $true )
| ( ( cowlNothing @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(362,plain,
! [SV62: $i,SV55: $i] :
( ( ( SV55 = SV62 )
= $false )
| ( ( ~ ( cowlThing @ SV55 ) )
= $true )
| ( ( cowlThing @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(363,plain,
! [SV63: $i,SV56: $i] :
( ( ( SV56 = SV63 )
= $false )
| ( ( ~ ( xsd_integer @ SV56 ) )
= $true )
| ( ( xsd_integer @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV64: $i,SV57: $i] :
( ( ( SV57 = SV64 )
= $false )
| ( ( ~ ( xsd_string @ SV57 ) )
= $true )
| ( ( xsd_string @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(365,plain,
! [SV65: $i] :
( ( ( ~ ( xsd_string @ SV65 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(366,plain,
! [SV66: $i] :
( ( ( xsd_integer @ SV66 )
= $true )
| ( ( xsd_string @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(367,plain,
! [SV68: $i] :
( ( cowlNothing @ SV68 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV59: $i,SV52: $i] :
( ( ( cA @ SV52 )
= $false )
| ( ( SV52 = SV59 )
= $false )
| ( ( cA @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(369,plain,
! [SV60: $i,SV53: $i] :
( ( ( cB @ SV53 )
= $false )
| ( ( SV53 = SV60 )
= $false )
| ( ( cB @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(370,plain,
! [SV61: $i,SV54: $i] :
( ( ( cowlNothing @ SV54 )
= $false )
| ( ( SV54 = SV61 )
= $false )
| ( ( cowlNothing @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(371,plain,
! [SV62: $i,SV55: $i] :
( ( ( cowlThing @ SV55 )
= $false )
| ( ( SV55 = SV62 )
= $false )
| ( ( cowlThing @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(372,plain,
! [SV63: $i,SV56: $i] :
( ( ( xsd_integer @ SV56 )
= $false )
| ( ( SV56 = SV63 )
= $false )
| ( ( xsd_integer @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(373,plain,
! [SV64: $i,SV57: $i] :
( ( ( xsd_string @ SV57 )
= $false )
| ( ( SV57 = SV64 )
= $false )
| ( ( xsd_string @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(374,plain,
! [SV65: $i] :
( ( ( xsd_string @ SV65 )
= $false )
| ( ( ~ ( xsd_integer @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(375,plain,
! [SV65: $i] :
( ( ( xsd_integer @ SV65 )
= $false )
| ( ( xsd_string @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(376,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[301,375,373,372,371,370,369,368,367,366,358,357,355,352,304,303,302]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(378,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(380,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(381,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(383,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(384,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(385,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(386,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(387,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(388,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(389,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(390,plain,
( ( ~ ( cowlThing @ ia ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(391,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(392,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(393,plain,
! [SV69: $i] :
( ( ! [SY41: $i] :
( ( SV69 != SY41 )
| ~ ( cA @ SV69 )
| ( cA @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(394,plain,
! [SV70: $i] :
( ( ! [SY42: $i] :
( ( SV70 != SY42 )
| ~ ( cB @ SV70 )
| ( cB @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(395,plain,
! [SV71: $i] :
( ( ! [SY43: $i] :
( ( SV71 != SY43 )
| ~ ( cowlNothing @ SV71 )
| ( cowlNothing @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(396,plain,
! [SV72: $i] :
( ( ! [SY44: $i] :
( ( SV72 != SY44 )
| ~ ( cowlThing @ SV72 )
| ( cowlThing @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(397,plain,
! [SV73: $i] :
( ( ! [SY45: $i] :
( ( SV73 != SY45 )
| ~ ( xsd_integer @ SV73 )
| ( xsd_integer @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(398,plain,
! [SV74: $i] :
( ( ! [SY46: $i] :
( ( SV74 != SY46 )
| ~ ( xsd_string @ SV74 )
| ( xsd_string @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(399,plain,
! [SV75: $i] :
( ( ~ ( cA @ SV75 )
| ~ ( cB @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(400,plain,
( ( cowlThing @ ia )
= $false ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(401,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(402,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(403,plain,
! [SV76: $i,SV69: $i] :
( ( ( SV69 != SV76 )
| ~ ( cA @ SV69 )
| ( cA @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(404,plain,
! [SV77: $i,SV70: $i] :
( ( ( SV70 != SV77 )
| ~ ( cB @ SV70 )
| ( cB @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(405,plain,
! [SV78: $i,SV71: $i] :
( ( ( SV71 != SV78 )
| ~ ( cowlNothing @ SV71 )
| ( cowlNothing @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(406,plain,
! [SV79: $i,SV72: $i] :
( ( ( SV72 != SV79 )
| ~ ( cowlThing @ SV72 )
| ( cowlThing @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(407,plain,
! [SV80: $i,SV73: $i] :
( ( ( SV73 != SV80 )
| ~ ( xsd_integer @ SV73 )
| ( xsd_integer @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(408,plain,
! [SV81: $i,SV74: $i] :
( ( ( SV74 != SV81 )
| ~ ( xsd_string @ SV74 )
| ( xsd_string @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(409,plain,
! [SV75: $i] :
( ( ( ~ ( cA @ SV75 ) )
= $true )
| ( ( ~ ( cB @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(410,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(411,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(412,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(413,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(414,plain,
! [SV76: $i,SV69: $i] :
( ( ( ( SV69 != SV76 )
| ~ ( cA @ SV69 ) )
= $true )
| ( ( cA @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(415,plain,
! [SV77: $i,SV70: $i] :
( ( ( ( SV70 != SV77 )
| ~ ( cB @ SV70 ) )
= $true )
| ( ( cB @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(416,plain,
! [SV78: $i,SV71: $i] :
( ( ( ( SV71 != SV78 )
| ~ ( cowlNothing @ SV71 ) )
= $true )
| ( ( cowlNothing @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(417,plain,
! [SV79: $i,SV72: $i] :
( ( ( ( SV72 != SV79 )
| ~ ( cowlThing @ SV72 ) )
= $true )
| ( ( cowlThing @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(418,plain,
! [SV80: $i,SV73: $i] :
( ( ( ( SV73 != SV80 )
| ~ ( xsd_integer @ SV73 ) )
= $true )
| ( ( xsd_integer @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(419,plain,
! [SV81: $i,SV74: $i] :
( ( ( ( SV74 != SV81 )
| ~ ( xsd_string @ SV74 ) )
= $true )
| ( ( xsd_string @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(420,plain,
! [SV75: $i] :
( ( ( cA @ SV75 )
= $false )
| ( ( ~ ( cB @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(421,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(422,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(423,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(424,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(425,plain,
! [SV76: $i,SV69: $i] :
( ( ( SV69 != SV76 )
= $true )
| ( ( ~ ( cA @ SV69 ) )
= $true )
| ( ( cA @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(426,plain,
! [SV77: $i,SV70: $i] :
( ( ( SV70 != SV77 )
= $true )
| ( ( ~ ( cB @ SV70 ) )
= $true )
| ( ( cB @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(427,plain,
! [SV78: $i,SV71: $i] :
( ( ( SV71 != SV78 )
= $true )
| ( ( ~ ( cowlNothing @ SV71 ) )
= $true )
| ( ( cowlNothing @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(428,plain,
! [SV79: $i,SV72: $i] :
( ( ( SV72 != SV79 )
= $true )
| ( ( ~ ( cowlThing @ SV72 ) )
= $true )
| ( ( cowlThing @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(429,plain,
! [SV80: $i,SV73: $i] :
( ( ( SV73 != SV80 )
= $true )
| ( ( ~ ( xsd_integer @ SV73 ) )
= $true )
| ( ( xsd_integer @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(430,plain,
! [SV81: $i,SV74: $i] :
( ( ( SV74 != SV81 )
= $true )
| ( ( ~ ( xsd_string @ SV74 ) )
= $true )
| ( ( xsd_string @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(431,plain,
! [SV75: $i] :
( ( ( cB @ SV75 )
= $false )
| ( ( cA @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV82: $i] :
( ( cowlThing @ SV82 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(433,plain,
! [SV83: $i] :
( ( ~ ( cowlNothing @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(434,plain,
! [SV84: $i] :
( ( ~ ( xsd_string @ SV84 )
| ~ ( xsd_integer @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(435,plain,
! [SV85: $i] :
( ( ( xsd_integer @ SV85 )
| ( xsd_string @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(436,plain,
! [SV76: $i,SV69: $i] :
( ( ( SV69 = SV76 )
= $false )
| ( ( ~ ( cA @ SV69 ) )
= $true )
| ( ( cA @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(437,plain,
! [SV77: $i,SV70: $i] :
( ( ( SV70 = SV77 )
= $false )
| ( ( ~ ( cB @ SV70 ) )
= $true )
| ( ( cB @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(438,plain,
! [SV78: $i,SV71: $i] :
( ( ( SV71 = SV78 )
= $false )
| ( ( ~ ( cowlNothing @ SV71 ) )
= $true )
| ( ( cowlNothing @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(439,plain,
! [SV79: $i,SV72: $i] :
( ( ( SV72 = SV79 )
= $false )
| ( ( ~ ( cowlThing @ SV72 ) )
= $true )
| ( ( cowlThing @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(440,plain,
! [SV80: $i,SV73: $i] :
( ( ( SV73 = SV80 )
= $false )
| ( ( ~ ( xsd_integer @ SV73 ) )
= $true )
| ( ( xsd_integer @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(441,plain,
! [SV81: $i,SV74: $i] :
( ( ( SV74 = SV81 )
= $false )
| ( ( ~ ( xsd_string @ SV74 ) )
= $true )
| ( ( xsd_string @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(442,plain,
! [SV83: $i] :
( ( cowlNothing @ SV83 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(443,plain,
! [SV84: $i] :
( ( ( ~ ( xsd_string @ SV84 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(444,plain,
! [SV85: $i] :
( ( ( xsd_integer @ SV85 )
= $true )
| ( ( xsd_string @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(445,plain,
! [SV76: $i,SV69: $i] :
( ( ( cA @ SV69 )
= $false )
| ( ( SV69 = SV76 )
= $false )
| ( ( cA @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(446,plain,
! [SV77: $i,SV70: $i] :
( ( ( cB @ SV70 )
= $false )
| ( ( SV70 = SV77 )
= $false )
| ( ( cB @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(447,plain,
! [SV78: $i,SV71: $i] :
( ( ( cowlNothing @ SV71 )
= $false )
| ( ( SV71 = SV78 )
= $false )
| ( ( cowlNothing @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(448,plain,
! [SV79: $i,SV72: $i] :
( ( ( cowlThing @ SV72 )
= $false )
| ( ( SV72 = SV79 )
= $false )
| ( ( cowlThing @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(449,plain,
! [SV80: $i,SV73: $i] :
( ( ( xsd_integer @ SV73 )
= $false )
| ( ( SV73 = SV80 )
= $false )
| ( ( xsd_integer @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(450,plain,
! [SV81: $i,SV74: $i] :
( ( ( xsd_string @ SV74 )
= $false )
| ( ( SV74 = SV81 )
= $false )
| ( ( xsd_string @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(451,plain,
! [SV84: $i] :
( ( ( xsd_string @ SV84 )
= $false )
| ( ( ~ ( xsd_integer @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(452,plain,
! [SV84: $i] :
( ( ( xsd_integer @ SV84 )
= $false )
| ( ( xsd_string @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(453,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[385,452,450,449,448,447,446,445,444,442,432,431,400,388,387,386]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(456,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(458,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(460,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(461,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(462,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(463,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(464,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(465,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(466,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(467,plain,
( ( ~ ( cowlThing @ ib ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(468,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(469,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(470,plain,
! [SV86: $i] :
( ( ! [SY47: $i] :
( ( SV86 != SY47 )
| ~ ( cA @ SV86 )
| ( cA @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(471,plain,
! [SV87: $i] :
( ( ! [SY48: $i] :
( ( SV87 != SY48 )
| ~ ( cB @ SV87 )
| ( cB @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(472,plain,
! [SV88: $i] :
( ( ! [SY49: $i] :
( ( SV88 != SY49 )
| ~ ( cowlNothing @ SV88 )
| ( cowlNothing @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(473,plain,
! [SV89: $i] :
( ( ! [SY50: $i] :
( ( SV89 != SY50 )
| ~ ( cowlThing @ SV89 )
| ( cowlThing @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(474,plain,
! [SV90: $i] :
( ( ! [SY51: $i] :
( ( SV90 != SY51 )
| ~ ( xsd_integer @ SV90 )
| ( xsd_integer @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(475,plain,
! [SV91: $i] :
( ( ! [SY52: $i] :
( ( SV91 != SY52 )
| ~ ( xsd_string @ SV91 )
| ( xsd_string @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(476,plain,
! [SV92: $i] :
( ( ~ ( cA @ SV92 )
| ~ ( cB @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(477,plain,
( ( cowlThing @ ib )
= $false ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(478,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(479,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(480,plain,
! [SV93: $i,SV86: $i] :
( ( ( SV86 != SV93 )
| ~ ( cA @ SV86 )
| ( cA @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(481,plain,
! [SV94: $i,SV87: $i] :
( ( ( SV87 != SV94 )
| ~ ( cB @ SV87 )
| ( cB @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(482,plain,
! [SV95: $i,SV88: $i] :
( ( ( SV88 != SV95 )
| ~ ( cowlNothing @ SV88 )
| ( cowlNothing @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(483,plain,
! [SV96: $i,SV89: $i] :
( ( ( SV89 != SV96 )
| ~ ( cowlThing @ SV89 )
| ( cowlThing @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(484,plain,
! [SV97: $i,SV90: $i] :
( ( ( SV90 != SV97 )
| ~ ( xsd_integer @ SV90 )
| ( xsd_integer @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(485,plain,
! [SV98: $i,SV91: $i] :
( ( ( SV91 != SV98 )
| ~ ( xsd_string @ SV91 )
| ( xsd_string @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(486,plain,
! [SV92: $i] :
( ( ( ~ ( cA @ SV92 ) )
= $true )
| ( ( ~ ( cB @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(487,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(488,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(489,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(490,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(491,plain,
! [SV93: $i,SV86: $i] :
( ( ( ( SV86 != SV93 )
| ~ ( cA @ SV86 ) )
= $true )
| ( ( cA @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(492,plain,
! [SV94: $i,SV87: $i] :
( ( ( ( SV87 != SV94 )
| ~ ( cB @ SV87 ) )
= $true )
| ( ( cB @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(493,plain,
! [SV95: $i,SV88: $i] :
( ( ( ( SV88 != SV95 )
| ~ ( cowlNothing @ SV88 ) )
= $true )
| ( ( cowlNothing @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(494,plain,
! [SV96: $i,SV89: $i] :
( ( ( ( SV89 != SV96 )
| ~ ( cowlThing @ SV89 ) )
= $true )
| ( ( cowlThing @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(495,plain,
! [SV97: $i,SV90: $i] :
( ( ( ( SV90 != SV97 )
| ~ ( xsd_integer @ SV90 ) )
= $true )
| ( ( xsd_integer @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(496,plain,
! [SV98: $i,SV91: $i] :
( ( ( ( SV91 != SV98 )
| ~ ( xsd_string @ SV91 ) )
= $true )
| ( ( xsd_string @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(497,plain,
! [SV92: $i] :
( ( ( cA @ SV92 )
= $false )
| ( ( ~ ( cB @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(498,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(499,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(500,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(501,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(502,plain,
! [SV93: $i,SV86: $i] :
( ( ( SV86 != SV93 )
= $true )
| ( ( ~ ( cA @ SV86 ) )
= $true )
| ( ( cA @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(503,plain,
! [SV94: $i,SV87: $i] :
( ( ( SV87 != SV94 )
= $true )
| ( ( ~ ( cB @ SV87 ) )
= $true )
| ( ( cB @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(504,plain,
! [SV95: $i,SV88: $i] :
( ( ( SV88 != SV95 )
= $true )
| ( ( ~ ( cowlNothing @ SV88 ) )
= $true )
| ( ( cowlNothing @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(505,plain,
! [SV96: $i,SV89: $i] :
( ( ( SV89 != SV96 )
= $true )
| ( ( ~ ( cowlThing @ SV89 ) )
= $true )
| ( ( cowlThing @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(506,plain,
! [SV97: $i,SV90: $i] :
( ( ( SV90 != SV97 )
= $true )
| ( ( ~ ( xsd_integer @ SV90 ) )
= $true )
| ( ( xsd_integer @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(507,plain,
! [SV98: $i,SV91: $i] :
( ( ( SV91 != SV98 )
= $true )
| ( ( ~ ( xsd_string @ SV91 ) )
= $true )
| ( ( xsd_string @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(508,plain,
! [SV92: $i] :
( ( ( cB @ SV92 )
= $false )
| ( ( cA @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(509,plain,
! [SV99: $i] :
( ( ~ ( xsd_string @ SV99 )
| ~ ( xsd_integer @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(510,plain,
! [SV100: $i] :
( ( ( xsd_integer @ SV100 )
| ( xsd_string @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(511,plain,
! [SV101: $i] :
( ( cowlThing @ SV101 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(512,plain,
! [SV102: $i] :
( ( ~ ( cowlNothing @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(513,plain,
! [SV93: $i,SV86: $i] :
( ( ( SV86 = SV93 )
= $false )
| ( ( ~ ( cA @ SV86 ) )
= $true )
| ( ( cA @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(514,plain,
! [SV94: $i,SV87: $i] :
( ( ( SV87 = SV94 )
= $false )
| ( ( ~ ( cB @ SV87 ) )
= $true )
| ( ( cB @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(515,plain,
! [SV95: $i,SV88: $i] :
( ( ( SV88 = SV95 )
= $false )
| ( ( ~ ( cowlNothing @ SV88 ) )
= $true )
| ( ( cowlNothing @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(516,plain,
! [SV96: $i,SV89: $i] :
( ( ( SV89 = SV96 )
= $false )
| ( ( ~ ( cowlThing @ SV89 ) )
= $true )
| ( ( cowlThing @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(517,plain,
! [SV97: $i,SV90: $i] :
( ( ( SV90 = SV97 )
= $false )
| ( ( ~ ( xsd_integer @ SV90 ) )
= $true )
| ( ( xsd_integer @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(518,plain,
! [SV98: $i,SV91: $i] :
( ( ( SV91 = SV98 )
= $false )
| ( ( ~ ( xsd_string @ SV91 ) )
= $true )
| ( ( xsd_string @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(519,plain,
! [SV99: $i] :
( ( ( ~ ( xsd_string @ SV99 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(520,plain,
! [SV100: $i] :
( ( ( xsd_integer @ SV100 )
= $true )
| ( ( xsd_string @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(521,plain,
! [SV102: $i] :
( ( cowlNothing @ SV102 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(522,plain,
! [SV93: $i,SV86: $i] :
( ( ( cA @ SV86 )
= $false )
| ( ( SV86 = SV93 )
= $false )
| ( ( cA @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(523,plain,
! [SV94: $i,SV87: $i] :
( ( ( cB @ SV87 )
= $false )
| ( ( SV87 = SV94 )
= $false )
| ( ( cB @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(524,plain,
! [SV95: $i,SV88: $i] :
( ( ( cowlNothing @ SV88 )
= $false )
| ( ( SV88 = SV95 )
= $false )
| ( ( cowlNothing @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(525,plain,
! [SV96: $i,SV89: $i] :
( ( ( cowlThing @ SV89 )
= $false )
| ( ( SV89 = SV96 )
= $false )
| ( ( cowlThing @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(526,plain,
! [SV97: $i,SV90: $i] :
( ( ( xsd_integer @ SV90 )
= $false )
| ( ( SV90 = SV97 )
= $false )
| ( ( xsd_integer @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(527,plain,
! [SV98: $i,SV91: $i] :
( ( ( xsd_string @ SV91 )
= $false )
| ( ( SV91 = SV98 )
= $false )
| ( ( xsd_string @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(528,plain,
! [SV99: $i] :
( ( ( xsd_string @ SV99 )
= $false )
| ( ( ~ ( xsd_integer @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(529,plain,
! [SV99: $i] :
( ( ( xsd_integer @ SV99 )
= $false )
| ( ( xsd_string @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(530,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[462,529,527,526,525,524,523,522,521,520,511,508,477,465,464,463]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cA @ A )
| ( cA @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cB @ A )
| ( cB @ B ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlNothing @ A )
| ( cowlNothing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( cowlThing @ A )
| ( cowlThing @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_integer @ A )
| ( xsd_integer @ B ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ~ ( xsd_string @ A )
| ( xsd_string @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(537,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(538,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(539,plain,
( ( cA @ ia )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(540,plain,
( ( cowlThing @ ia )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(541,plain,
( ( cB @ ib )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(542,plain,
( ( cowlThing @ ib )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(543,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
| ~ ( cB @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(544,plain,
( ( ia = ib )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(545,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(546,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(547,plain,
! [SV103: $i] :
( ( ! [SY53: $i] :
( ( SV103 != SY53 )
| ~ ( cA @ SV103 )
| ( cA @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(548,plain,
! [SV104: $i] :
( ( ! [SY54: $i] :
( ( SV104 != SY54 )
| ~ ( cB @ SV104 )
| ( cB @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(549,plain,
! [SV105: $i] :
( ( ! [SY55: $i] :
( ( SV105 != SY55 )
| ~ ( cowlNothing @ SV105 )
| ( cowlNothing @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(550,plain,
! [SV106: $i] :
( ( ! [SY56: $i] :
( ( SV106 != SY56 )
| ~ ( cowlThing @ SV106 )
| ( cowlThing @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(551,plain,
! [SV107: $i] :
( ( ! [SY57: $i] :
( ( SV107 != SY57 )
| ~ ( xsd_integer @ SV107 )
| ( xsd_integer @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(552,plain,
! [SV108: $i] :
( ( ! [SY58: $i] :
( ( SV108 != SY58 )
| ~ ( xsd_string @ SV108 )
| ( xsd_string @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(553,plain,
! [SV109: $i] :
( ( ~ ( cA @ SV109 )
| ~ ( cB @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(554,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(555,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(556,plain,
! [SV110: $i,SV103: $i] :
( ( ( SV103 != SV110 )
| ~ ( cA @ SV103 )
| ( cA @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(557,plain,
! [SV111: $i,SV104: $i] :
( ( ( SV104 != SV111 )
| ~ ( cB @ SV104 )
| ( cB @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(558,plain,
! [SV112: $i,SV105: $i] :
( ( ( SV105 != SV112 )
| ~ ( cowlNothing @ SV105 )
| ( cowlNothing @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(559,plain,
! [SV113: $i,SV106: $i] :
( ( ( SV106 != SV113 )
| ~ ( cowlThing @ SV106 )
| ( cowlThing @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(560,plain,
! [SV114: $i,SV107: $i] :
( ( ( SV107 != SV114 )
| ~ ( xsd_integer @ SV107 )
| ( xsd_integer @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(561,plain,
! [SV115: $i,SV108: $i] :
( ( ( SV108 != SV115 )
| ~ ( xsd_string @ SV108 )
| ( xsd_string @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(562,plain,
! [SV109: $i] :
( ( ( ~ ( cA @ SV109 ) )
= $true )
| ( ( ~ ( cB @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(563,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(564,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(565,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(566,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(567,plain,
! [SV110: $i,SV103: $i] :
( ( ( ( SV103 != SV110 )
| ~ ( cA @ SV103 ) )
= $true )
| ( ( cA @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(568,plain,
! [SV111: $i,SV104: $i] :
( ( ( ( SV104 != SV111 )
| ~ ( cB @ SV104 ) )
= $true )
| ( ( cB @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(569,plain,
! [SV112: $i,SV105: $i] :
( ( ( ( SV105 != SV112 )
| ~ ( cowlNothing @ SV105 ) )
= $true )
| ( ( cowlNothing @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(570,plain,
! [SV113: $i,SV106: $i] :
( ( ( ( SV106 != SV113 )
| ~ ( cowlThing @ SV106 ) )
= $true )
| ( ( cowlThing @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(571,plain,
! [SV114: $i,SV107: $i] :
( ( ( ( SV107 != SV114 )
| ~ ( xsd_integer @ SV107 ) )
= $true )
| ( ( xsd_integer @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(572,plain,
! [SV115: $i,SV108: $i] :
( ( ( ( SV108 != SV115 )
| ~ ( xsd_string @ SV108 ) )
= $true )
| ( ( xsd_string @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(573,plain,
! [SV109: $i] :
( ( ( cA @ SV109 )
= $false )
| ( ( ~ ( cB @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(574,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(575,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(576,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(577,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(578,plain,
! [SV110: $i,SV103: $i] :
( ( ( SV103 != SV110 )
= $true )
| ( ( ~ ( cA @ SV103 ) )
= $true )
| ( ( cA @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(579,plain,
! [SV111: $i,SV104: $i] :
( ( ( SV104 != SV111 )
= $true )
| ( ( ~ ( cB @ SV104 ) )
= $true )
| ( ( cB @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(580,plain,
! [SV112: $i,SV105: $i] :
( ( ( SV105 != SV112 )
= $true )
| ( ( ~ ( cowlNothing @ SV105 ) )
= $true )
| ( ( cowlNothing @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(581,plain,
! [SV113: $i,SV106: $i] :
( ( ( SV106 != SV113 )
= $true )
| ( ( ~ ( cowlThing @ SV106 ) )
= $true )
| ( ( cowlThing @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(582,plain,
! [SV114: $i,SV107: $i] :
( ( ( SV107 != SV114 )
= $true )
| ( ( ~ ( xsd_integer @ SV107 ) )
= $true )
| ( ( xsd_integer @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(583,plain,
! [SV115: $i,SV108: $i] :
( ( ( SV108 != SV115 )
= $true )
| ( ( ~ ( xsd_string @ SV108 ) )
= $true )
| ( ( xsd_string @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(584,plain,
! [SV109: $i] :
( ( ( cB @ SV109 )
= $false )
| ( ( cA @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(585,plain,
! [SV116: $i] :
( ( cowlThing @ SV116 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(586,plain,
! [SV117: $i] :
( ( ~ ( cowlNothing @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(587,plain,
! [SV118: $i] :
( ( ~ ( xsd_string @ SV118 )
| ~ ( xsd_integer @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(588,plain,
! [SV119: $i] :
( ( ( xsd_integer @ SV119 )
| ( xsd_string @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(589,plain,
! [SV110: $i,SV103: $i] :
( ( ( SV103 = SV110 )
= $false )
| ( ( ~ ( cA @ SV103 ) )
= $true )
| ( ( cA @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(590,plain,
! [SV111: $i,SV104: $i] :
( ( ( SV104 = SV111 )
= $false )
| ( ( ~ ( cB @ SV104 ) )
= $true )
| ( ( cB @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(591,plain,
! [SV112: $i,SV105: $i] :
( ( ( SV105 = SV112 )
= $false )
| ( ( ~ ( cowlNothing @ SV105 ) )
= $true )
| ( ( cowlNothing @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(592,plain,
! [SV113: $i,SV106: $i] :
( ( ( SV106 = SV113 )
= $false )
| ( ( ~ ( cowlThing @ SV106 ) )
= $true )
| ( ( cowlThing @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(593,plain,
! [SV114: $i,SV107: $i] :
( ( ( SV107 = SV114 )
= $false )
| ( ( ~ ( xsd_integer @ SV107 ) )
= $true )
| ( ( xsd_integer @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(594,plain,
! [SV115: $i,SV108: $i] :
( ( ( SV108 = SV115 )
= $false )
| ( ( ~ ( xsd_string @ SV108 ) )
= $true )
| ( ( xsd_string @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(595,plain,
! [SV117: $i] :
( ( cowlNothing @ SV117 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(596,plain,
! [SV118: $i] :
( ( ( ~ ( xsd_string @ SV118 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(597,plain,
! [SV119: $i] :
( ( ( xsd_integer @ SV119 )
= $true )
| ( ( xsd_string @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(598,plain,
! [SV110: $i,SV103: $i] :
( ( ( cA @ SV103 )
= $false )
| ( ( SV103 = SV110 )
= $false )
| ( ( cA @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(599,plain,
! [SV111: $i,SV104: $i] :
( ( ( cB @ SV104 )
= $false )
| ( ( SV104 = SV111 )
= $false )
| ( ( cB @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(600,plain,
! [SV112: $i,SV105: $i] :
( ( ( cowlNothing @ SV105 )
= $false )
| ( ( SV105 = SV112 )
= $false )
| ( ( cowlNothing @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(601,plain,
! [SV113: $i,SV106: $i] :
( ( ( cowlThing @ SV106 )
= $false )
| ( ( SV106 = SV113 )
= $false )
| ( ( cowlThing @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(602,plain,
! [SV114: $i,SV107: $i] :
( ( ( xsd_integer @ SV107 )
= $false )
| ( ( SV107 = SV114 )
= $false )
| ( ( xsd_integer @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(603,plain,
! [SV115: $i,SV108: $i] :
( ( ( xsd_string @ SV108 )
= $false )
| ( ( SV108 = SV115 )
= $false )
| ( ( xsd_string @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(604,plain,
! [SV118: $i] :
( ( ( xsd_string @ SV118 )
= $false )
| ( ( ~ ( xsd_integer @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(605,plain,
! [SV118: $i] :
( ( ( xsd_integer @ SV118 )
= $false )
| ( ( xsd_string @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(606,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[539,605,603,602,601,600,599,598,597,595,585,584,544,542,541,540]) ).
thf(607,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[606,134,210,292,376,453,530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS163+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.19 % Computer : n011.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Oct 6 11:42:06 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.11/0.43
% 1.11/0.43 No.of.Axioms: 13
% 1.11/0.43
% 1.11/0.43 Length.of.Defs: 0
% 1.11/0.43
% 1.11/0.43 Contains.Choice.Funs: false
% 1.11/0.43 .........
% 1.11/0.43
% 1.11/0.43 ********************************
% 1.11/0.43 * All subproblems solved! *
% 1.11/0.43 ********************************
% 1.11/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:606,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 1.11/0.43
% 1.11/0.43 %**** Beginning of derivation protocol ****
% 1.11/0.43 % SZS output start CNFRefutation
% See solution above
% 1.11/0.44
% 1.11/0.44 %**** End of derivation protocol ****
% 1.11/0.44 %**** no. of clauses in derivation: 607 ****
% 1.11/0.44 %**** clause counter: 606 ****
% 1.11/0.44
% 1.11/0.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:606,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------