%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : KRS131+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 10:26:26 AM UTC 2026
% Result : Theorem 0.70s 0.35s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 589 ( 300 unt; 0 typ; 0 def)
% Number of atoms : 3294 ( 893 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 4502 (1576 ~; 828 |; 25 &;2007 @)
% ( 30 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 8 con; 0-2 aty)
% Number of variables : 909 ( 0 ^; 885 !; 24 ?; 909 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cA,type,
cA: $i > $o ).
thf(tp_cNothing,type,
cNothing: $i > $o ).
thf(tp_cnotA,type,
cnotA: $i > $o ).
thf(tp_cowlNothing,type,
cowlNothing: $i > $o ).
thf(tp_cowlThing,type,
cowlThing: $i > $o ).
thf(tp_rp,type,
rp: $i > $i > $o ).
thf(tp_rq,type,
rq: $i > $i > $o ).
thf(tp_sK10_SY30,type,
sK10_SY30: $i > $i ).
thf(tp_sK11_SY26,type,
sK11_SY26: $i > $i ).
thf(tp_sK12_SY28,type,
sK12_SY28: $i > $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK14_SY36,type,
sK14_SY36: $i > $i ).
thf(tp_sK15_SY32,type,
sK15_SY32: $i > $i ).
thf(tp_sK16_SY34,type,
sK16_SY34: $i > $i ).
thf(tp_sK17_SX0,type,
sK17_SX0: $i ).
thf(tp_sK18_SY42,type,
sK18_SY42: $i > $i ).
thf(tp_sK19_SY41,type,
sK19_SY41: $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK20_SY37,type,
sK20_SY37: $i > $i ).
thf(tp_sK21_SX0,type,
sK21_SX0: $i ).
thf(tp_sK22_SY46,type,
sK22_SY46: $i > $i ).
thf(tp_sK23_SY48,type,
sK23_SY48: $i > $i ).
thf(tp_sK24_SY44,type,
sK24_SY44: $i > $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i > $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i > $i ).
thf(tp_sK4_SY16,type,
sK4_SY16: $i > $i ).
thf(tp_sK5_X,type,
sK5_X: $i ).
thf(tp_sK6_SY23,type,
sK6_SY23: $i > $i ).
thf(tp_sK7_SY22,type,
sK7_SY22: $i > $i ).
thf(tp_sK8_SY19,type,
sK8_SY19: $i > $i ).
thf(tp_sK9_SX0,type,
sK9_SX0: $i ).
thf(tp_xsd_integer,type,
xsd_integer: $i > $o ).
thf(tp_xsd_string,type,
xsd_string: $i > $o ).
thf(1,axiom,
! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(2,axiom,
! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(3,axiom,
! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(4,axiom,
! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(5,axiom,
! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(6,axiom,
! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(7,conjecture,
( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( cnotA @ X )
<=> ~ ( cA @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(8,negated_conjecture,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( cnotA @ X )
<=> ~ ( cA @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( cnotA @ X )
<=> ~ ( cA @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ! [X: $i] : ( cowlThing @ X ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(17,plain,
( ( ! [X: $i] :
~ ( cowlNothing @ X ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
=> ~ ( xsd_integer @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(19,plain,
( ( ! [X: $i] :
( ~ ( xsd_integer @ X )
=> ( xsd_string @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
=> ~ ( cA @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(21,plain,
( ( ! [X: $i] :
( ~ ( cA @ X )
=> ( cnotA @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(22,plain,
( ( ~ ! [X: $i] : ( cowlThing @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(23,plain,
( ( ~ ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ ! [X: $i] :
( ( xsd_string @ X )
=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(25,plain,
( ( ~ ! [X: $i] :
( ~ ( xsd_integer @ X )
=> ( xsd_string @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(26,plain,
( ( ~ ! [X: $i] :
( ( cnotA @ X )
=> ~ ( cA @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(27,plain,
( ( ~ ! [X: $i] :
( ~ ( cA @ X )
=> ( cnotA @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(34,plain,
( ( ~ ! [X: $i] : ( cowlThing @ X ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(36,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cnotA @ SX0 )
| ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) )
| ( cnotA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(37,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cowlThing @ SX0 )
| ~ ~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(39,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cA @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) )
| ( cA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(40,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(41,plain,
( ( ! [X: $i] : ( cowlThing @ X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV1: $i] :
( ( ~ ( ~ ( ~ ( xsd_string @ SV1 )
| ~ ( xsd_integer @ SV1 ) )
| ~ ( ~ ~ ( xsd_integer @ SV1 )
| ( xsd_string @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV2: $i] :
( ( ~ ( ~ ( ~ ( cnotA @ SV2 )
| ! [SY13: $i] :
( ~ ( rq @ SV2 @ SY13 )
| ( cNothing @ SY13 ) ) )
| ~ ( ~ ! [SY14: $i] :
( ~ ( rq @ SV2 @ SY14 )
| ( cNothing @ SY14 ) )
| ( cnotA @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV3: $i] :
( ( ~ ( ~ ( cowlThing @ SV3 )
| ~ ~ ( cowlNothing @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV4: $i] :
( ( ~ ( cNothing @ SV4 )
| ~ ~ ! [SY15: $i] :
~ ( rp @ SV4 @ SY15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV5: $i] :
( ( ~ ( ~ ( ~ ( cA @ SV5 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) )
| ~ ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) )
| ( cA @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV6: $i] :
( ( ~ ( cNothing @ SV6 )
| ~ ! [SY18: $i] :
~ ( rp @ SV6 @ SY18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
( ( cowlThing @ sK1_X )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(49,plain,
! [SV1: $i] :
( ( ~ ( ~ ( xsd_string @ SV1 )
| ~ ( xsd_integer @ SV1 ) )
| ~ ( ~ ~ ( xsd_integer @ SV1 )
| ( xsd_string @ SV1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV2: $i] :
( ( ~ ( ~ ( cnotA @ SV2 )
| ! [SY13: $i] :
( ~ ( rq @ SV2 @ SY13 )
| ( cNothing @ SY13 ) ) )
| ~ ( ~ ! [SY14: $i] :
( ~ ( rq @ SV2 @ SY14 )
| ( cNothing @ SY14 ) )
| ( cnotA @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV3: $i] :
( ( ~ ( cowlThing @ SV3 )
| ~ ~ ( cowlNothing @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( ~ ( cNothing @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY15: $i] :
~ ( rp @ SV4 @ SY15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV5: $i] :
( ( ~ ( ~ ( cA @ SV5 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) )
| ~ ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) )
| ( cA @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( ~ ( cNothing @ SV6 ) )
= $true )
| ( ( ~ ! [SY18: $i] :
~ ( rp @ SV6 @ SY18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV1: $i] :
( ( ~ ( ~ ( xsd_string @ SV1 )
| ~ ( xsd_integer @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(56,plain,
! [SV1: $i] :
( ( ~ ( ~ ~ ( xsd_integer @ SV1 )
| ( xsd_string @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(57,plain,
! [SV2: $i] :
( ( ~ ( ~ ( cnotA @ SV2 )
| ! [SY13: $i] :
( ~ ( rq @ SV2 @ SY13 )
| ( cNothing @ SY13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(58,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY14: $i] :
( ~ ( rq @ SV2 @ SY14 )
| ( cNothing @ SY14 ) )
| ( cnotA @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(59,plain,
! [SV3: $i] :
( ( ~ ( cowlThing @ SV3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(60,plain,
! [SV3: $i] :
( ( ~ ~ ( cowlNothing @ SV3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(61,plain,
! [SV4: $i] :
( ( ( cNothing @ SV4 )
= $false )
| ( ( ~ ~ ! [SY15: $i] :
~ ( rp @ SV4 @ SY15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV5: $i] :
( ( ~ ( ~ ( cA @ SV5 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(63,plain,
! [SV5: $i] :
( ( ~ ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) )
| ( cA @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(64,plain,
! [SV6: $i] :
( ( ( cNothing @ SV6 )
= $false )
| ( ( ~ ! [SY18: $i] :
~ ( rp @ SV6 @ SY18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV1: $i] :
( ( ~ ( xsd_string @ SV1 )
| ~ ( xsd_integer @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(66,plain,
! [SV1: $i] :
( ( ~ ~ ( xsd_integer @ SV1 )
| ( xsd_string @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(67,plain,
! [SV2: $i] :
( ( ~ ( cnotA @ SV2 )
| ! [SY13: $i] :
( ~ ( rq @ SV2 @ SY13 )
| ( cNothing @ SY13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(68,plain,
! [SV2: $i] :
( ( ~ ! [SY14: $i] :
( ~ ( rq @ SV2 @ SY14 )
| ( cNothing @ SY14 ) )
| ( cnotA @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(69,plain,
! [SV3: $i] :
( ( cowlThing @ SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(70,plain,
! [SV3: $i] :
( ( ~ ( cowlNothing @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( ~ ! [SY15: $i] :
~ ( rp @ SV4 @ SY15 ) )
= $false )
| ( ( cNothing @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV5: $i] :
( ( ~ ( cA @ SV5 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(73,plain,
! [SV5: $i] :
( ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) )
| ( cA @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(74,plain,
! [SV6: $i] :
( ( ( ! [SY18: $i] :
~ ( rp @ SV6 @ SY18 ) )
= $false )
| ( ( cNothing @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV1: $i] :
( ( ( ~ ( xsd_string @ SV1 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV1: $i] :
( ( ( ~ ~ ( xsd_integer @ SV1 ) )
= $true )
| ( ( xsd_string @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV2: $i] :
( ( ( ~ ( cnotA @ SV2 ) )
= $true )
| ( ( ! [SY13: $i] :
( ~ ( rq @ SV2 @ SY13 )
| ( cNothing @ SY13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV2: $i] :
( ( ( ~ ! [SY14: $i] :
( ~ ( rq @ SV2 @ SY14 )
| ( cNothing @ SY14 ) ) )
= $true )
| ( ( cnotA @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV3: $i] :
( ( cowlNothing @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV4: $i] :
( ( ( ! [SY15: $i] :
~ ( rp @ SV4 @ SY15 ) )
= $true )
| ( ( cNothing @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( ~ ( cA @ SV5 ) )
= $true )
| ( ( ~ ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV5: $i] :
( ( ( ~ ~ ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) ) )
= $true )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV6: $i] :
( ( ( ~ ( rp @ SV6 @ ( sK2_SY18 @ SV6 ) ) )
= $false )
| ( ( cNothing @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[74]) ).
thf(84,plain,
! [SV1: $i] :
( ( ( xsd_string @ SV1 )
= $false )
| ( ( ~ ( xsd_integer @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV1: $i] :
( ( ( ~ ( xsd_integer @ SV1 ) )
= $false )
| ( ( xsd_string @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV2: $i] :
( ( ( cnotA @ SV2 )
= $false )
| ( ( ! [SY13: $i] :
( ~ ( rq @ SV2 @ SY13 )
| ( cNothing @ SY13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV2: $i] :
( ( ( ! [SY14: $i] :
( ~ ( rq @ SV2 @ SY14 )
| ( cNothing @ SY14 ) ) )
= $false )
| ( ( cnotA @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV7: $i,SV4: $i] :
( ( ( ~ ( rp @ SV4 @ SV7 ) )
= $true )
| ( ( cNothing @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV5: $i] :
( ( ( cA @ SV5 )
= $false )
| ( ( ~ ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV5: $i] :
( ( ( ~ ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) ) )
= $false )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV6: $i] :
( ( ( rp @ SV6 @ ( sK2_SY18 @ SV6 ) )
= $true )
| ( ( cNothing @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(92,plain,
! [SV1: $i] :
( ( ( xsd_integer @ SV1 )
= $false )
| ( ( xsd_string @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV1: $i] :
( ( ( xsd_integer @ SV1 )
= $true )
| ( ( xsd_string @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(94,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( rq @ SV2 @ SV8 )
| ( cNothing @ SV8 ) )
= $true )
| ( ( cnotA @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV2: $i] :
( ( ( ~ ( rq @ SV2 @ ( sK3_SY14 @ SV2 ) )
| ( cNothing @ ( sK3_SY14 @ SV2 ) ) )
= $false )
| ( ( cnotA @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(96,plain,
! [SV7: $i,SV4: $i] :
( ( ( rp @ SV4 @ SV7 )
= $false )
| ( ( cNothing @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV5: $i] :
( ( ( ! [SY16: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY16 )
| ~ ( cowlThing @ SY16 ) ) )
= $false )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV5: $i] :
( ( ( ! [SY17: $i] :
~ ~ ( ~ ( rq @ SV5 @ SY17 )
| ~ ( cowlThing @ SY17 ) ) )
= $true )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(99,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( rq @ SV2 @ SV8 ) )
= $true )
| ( ( cNothing @ SV8 )
= $true )
| ( ( cnotA @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV2: $i] :
( ( ( ~ ( rq @ SV2 @ ( sK3_SY14 @ SV2 ) ) )
= $false )
| ( ( cnotA @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV2: $i] :
( ( ( cNothing @ ( sK3_SY14 @ SV2 ) )
= $false )
| ( ( cnotA @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ( cowlThing @ ( sK4_SY16 @ SV5 ) ) ) )
= $false )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(103,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV5 @ SV9 )
| ~ ( cowlThing @ SV9 ) ) )
= $true )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV8: $i,SV2: $i] :
( ( ( rq @ SV2 @ SV8 )
= $false )
| ( ( cNothing @ SV8 )
= $true )
| ( ( cnotA @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV2: $i] :
( ( ( rq @ SV2 @ ( sK3_SY14 @ SV2 ) )
= $true )
| ( ( cnotA @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(106,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( rq @ SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ( cowlThing @ ( sK4_SY16 @ SV5 ) ) ) )
= $true )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(107,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( ~ ( rq @ SV5 @ SV9 )
| ~ ( cowlThing @ SV9 ) ) )
= $false )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV5: $i] :
( ( ( ~ ( rq @ SV5 @ ( sK4_SY16 @ SV5 ) )
| ~ ( cowlThing @ ( sK4_SY16 @ SV5 ) ) )
= $false )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(109,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( rq @ SV5 @ SV9 )
| ~ ( cowlThing @ SV9 ) )
= $true )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(110,plain,
! [SV5: $i] :
( ( ( ~ ( rq @ SV5 @ ( sK4_SY16 @ SV5 ) ) )
= $false )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( ~ ( cowlThing @ ( sK4_SY16 @ SV5 ) ) )
= $false )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(112,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( rq @ SV5 @ SV9 ) )
= $true )
| ( ( ~ ( cowlThing @ SV9 ) )
= $true )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV5: $i] :
( ( ( rq @ SV5 @ ( sK4_SY16 @ SV5 ) )
= $true )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(114,plain,
! [SV5: $i] :
( ( ( cowlThing @ ( sK4_SY16 @ SV5 ) )
= $true )
| ( ( cA @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(115,plain,
! [SV9: $i,SV5: $i] :
( ( ( rq @ SV5 @ SV9 )
= $false )
| ( ( ~ ( cowlThing @ SV9 ) )
= $true )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV5: $i,SV9: $i] :
( ( ( cowlThing @ SV9 )
= $false )
| ( ( rq @ SV5 @ SV9 )
= $false )
| ( ( cA @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(117,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[48,116,114,113,105,104,101,96,93,92,91,79,69]) ).
thf(118,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(119,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(120,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(121,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(122,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(123,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(124,plain,
( ( ~ ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(125,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(126,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cA @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) )
| ( cA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(127,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cnotA @ SX0 )
| ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) )
| ( cnotA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(128,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(129,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cowlThing @ SX0 )
| ~ ~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(130,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(131,plain,
( ( ! [X: $i] :
~ ( cowlNothing @ X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(132,plain,
! [SV10: $i] :
( ( ~ ( ~ ( ~ ( xsd_string @ SV10 )
| ~ ( xsd_integer @ SV10 ) )
| ~ ( ~ ~ ( xsd_integer @ SV10 )
| ( xsd_string @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV11: $i] :
( ( ~ ( ~ ( ~ ( cA @ SV11 )
| ~ ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) )
| ~ ( ~ ~ ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) )
| ( cA @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV12: $i] :
( ( ~ ( ~ ( ~ ( cnotA @ SV12 )
| ! [SY21: $i] :
( ~ ( rq @ SV12 @ SY21 )
| ( cNothing @ SY21 ) ) )
| ~ ( ~ ! [SY22: $i] :
( ~ ( rq @ SV12 @ SY22 )
| ( cNothing @ SY22 ) )
| ( cnotA @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV13: $i] :
( ( ~ ( cNothing @ SV13 )
| ~ ! [SY23: $i] :
~ ( rp @ SV13 @ SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV14: $i] :
( ( ~ ( ~ ( cowlThing @ SV14 )
| ~ ~ ( cowlNothing @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV15: $i] :
( ( ~ ( cNothing @ SV15 )
| ~ ~ ! [SY24: $i] :
~ ( rp @ SV15 @ SY24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(138,plain,
( ( ~ ( cowlNothing @ sK5_X ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[131]) ).
thf(139,plain,
! [SV10: $i] :
( ( ~ ( ~ ( xsd_string @ SV10 )
| ~ ( xsd_integer @ SV10 ) )
| ~ ( ~ ~ ( xsd_integer @ SV10 )
| ( xsd_string @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV11: $i] :
( ( ~ ( ~ ( cA @ SV11 )
| ~ ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) )
| ~ ( ~ ~ ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) )
| ( cA @ SV11 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(141,plain,
! [SV12: $i] :
( ( ~ ( ~ ( cnotA @ SV12 )
| ! [SY21: $i] :
( ~ ( rq @ SV12 @ SY21 )
| ( cNothing @ SY21 ) ) )
| ~ ( ~ ! [SY22: $i] :
( ~ ( rq @ SV12 @ SY22 )
| ( cNothing @ SY22 ) )
| ( cnotA @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(142,plain,
! [SV13: $i] :
( ( ( ~ ( cNothing @ SV13 ) )
= $true )
| ( ( ~ ! [SY23: $i] :
~ ( rp @ SV13 @ SY23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV14: $i] :
( ( ~ ( cowlThing @ SV14 )
| ~ ~ ( cowlNothing @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV15: $i] :
( ( ( ~ ( cNothing @ SV15 ) )
= $true )
| ( ( ~ ~ ! [SY24: $i] :
~ ( rp @ SV15 @ SY24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(145,plain,
( ( cowlNothing @ sK5_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(146,plain,
! [SV10: $i] :
( ( ~ ( ~ ( xsd_string @ SV10 )
| ~ ( xsd_integer @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(147,plain,
! [SV10: $i] :
( ( ~ ( ~ ~ ( xsd_integer @ SV10 )
| ( xsd_string @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(148,plain,
! [SV11: $i] :
( ( ~ ( ~ ( cA @ SV11 )
| ~ ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(149,plain,
! [SV11: $i] :
( ( ~ ( ~ ~ ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) )
| ( cA @ SV11 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(150,plain,
! [SV12: $i] :
( ( ~ ( ~ ( cnotA @ SV12 )
| ! [SY21: $i] :
( ~ ( rq @ SV12 @ SY21 )
| ( cNothing @ SY21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY22: $i] :
( ~ ( rq @ SV12 @ SY22 )
| ( cNothing @ SY22 ) )
| ( cnotA @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(152,plain,
! [SV13: $i] :
( ( ( cNothing @ SV13 )
= $false )
| ( ( ~ ! [SY23: $i] :
~ ( rp @ SV13 @ SY23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV14: $i] :
( ( ~ ( cowlThing @ SV14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(154,plain,
! [SV14: $i] :
( ( ~ ~ ( cowlNothing @ SV14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(155,plain,
! [SV15: $i] :
( ( ( cNothing @ SV15 )
= $false )
| ( ( ~ ~ ! [SY24: $i] :
~ ( rp @ SV15 @ SY24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV10: $i] :
( ( ~ ( xsd_string @ SV10 )
| ~ ( xsd_integer @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(157,plain,
! [SV10: $i] :
( ( ~ ~ ( xsd_integer @ SV10 )
| ( xsd_string @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(158,plain,
! [SV11: $i] :
( ( ~ ( cA @ SV11 )
| ~ ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(159,plain,
! [SV11: $i] :
( ( ~ ~ ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) )
| ( cA @ SV11 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(160,plain,
! [SV12: $i] :
( ( ~ ( cnotA @ SV12 )
| ! [SY21: $i] :
( ~ ( rq @ SV12 @ SY21 )
| ( cNothing @ SY21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(161,plain,
! [SV12: $i] :
( ( ~ ! [SY22: $i] :
( ~ ( rq @ SV12 @ SY22 )
| ( cNothing @ SY22 ) )
| ( cnotA @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(162,plain,
! [SV13: $i] :
( ( ( ! [SY23: $i] :
~ ( rp @ SV13 @ SY23 ) )
= $false )
| ( ( cNothing @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV14: $i] :
( ( cowlThing @ SV14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(164,plain,
! [SV14: $i] :
( ( ~ ( cowlNothing @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(165,plain,
! [SV15: $i] :
( ( ( ~ ! [SY24: $i] :
~ ( rp @ SV15 @ SY24 ) )
= $false )
| ( ( cNothing @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV10: $i] :
( ( ( ~ ( xsd_string @ SV10 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV10: $i] :
( ( ( ~ ~ ( xsd_integer @ SV10 ) )
= $true )
| ( ( xsd_string @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV11: $i] :
( ( ( ~ ( cA @ SV11 ) )
= $true )
| ( ( ~ ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV11: $i] :
( ( ( ~ ~ ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) ) )
= $true )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV12: $i] :
( ( ( ~ ( cnotA @ SV12 ) )
= $true )
| ( ( ! [SY21: $i] :
( ~ ( rq @ SV12 @ SY21 )
| ( cNothing @ SY21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV12: $i] :
( ( ( ~ ! [SY22: $i] :
( ~ ( rq @ SV12 @ SY22 )
| ( cNothing @ SY22 ) ) )
= $true )
| ( ( cnotA @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV13: $i] :
( ( ( ~ ( rp @ SV13 @ ( sK6_SY23 @ SV13 ) ) )
= $false )
| ( ( cNothing @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[162]) ).
thf(173,plain,
! [SV14: $i] :
( ( cowlNothing @ SV14 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV15: $i] :
( ( ( ! [SY24: $i] :
~ ( rp @ SV15 @ SY24 ) )
= $true )
| ( ( cNothing @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(175,plain,
! [SV10: $i] :
( ( ( xsd_string @ SV10 )
= $false )
| ( ( ~ ( xsd_integer @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV10: $i] :
( ( ( ~ ( xsd_integer @ SV10 ) )
= $false )
| ( ( xsd_string @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV11: $i] :
( ( ( cA @ SV11 )
= $false )
| ( ( ~ ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV11: $i] :
( ( ( ~ ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) ) )
= $false )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(179,plain,
! [SV12: $i] :
( ( ( cnotA @ SV12 )
= $false )
| ( ( ! [SY21: $i] :
( ~ ( rq @ SV12 @ SY21 )
| ( cNothing @ SY21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV12: $i] :
( ( ( ! [SY22: $i] :
( ~ ( rq @ SV12 @ SY22 )
| ( cNothing @ SY22 ) ) )
= $false )
| ( ( cnotA @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV13: $i] :
( ( ( rp @ SV13 @ ( sK6_SY23 @ SV13 ) )
= $true )
| ( ( cNothing @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(182,plain,
! [SV16: $i,SV15: $i] :
( ( ( ~ ( rp @ SV15 @ SV16 ) )
= $true )
| ( ( cNothing @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(183,plain,
! [SV10: $i] :
( ( ( xsd_integer @ SV10 )
= $false )
| ( ( xsd_string @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(184,plain,
! [SV10: $i] :
( ( ( xsd_integer @ SV10 )
= $true )
| ( ( xsd_string @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(185,plain,
! [SV11: $i] :
( ( ( ! [SY19: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY19 )
| ~ ( cowlThing @ SY19 ) ) )
= $false )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV11: $i] :
( ( ( ! [SY20: $i] :
~ ~ ( ~ ( rq @ SV11 @ SY20 )
| ~ ( cowlThing @ SY20 ) ) )
= $true )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(187,plain,
! [SV17: $i,SV12: $i] :
( ( ( ~ ( rq @ SV12 @ SV17 )
| ( cNothing @ SV17 ) )
= $true )
| ( ( cnotA @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV12: $i] :
( ( ( ~ ( rq @ SV12 @ ( sK7_SY22 @ SV12 ) )
| ( cNothing @ ( sK7_SY22 @ SV12 ) ) )
= $false )
| ( ( cnotA @ SV12 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[180]) ).
thf(189,plain,
! [SV16: $i,SV15: $i] :
( ( ( rp @ SV15 @ SV16 )
= $false )
| ( ( cNothing @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(190,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV11 @ ( sK8_SY19 @ SV11 ) )
| ~ ( cowlThing @ ( sK8_SY19 @ SV11 ) ) ) )
= $false )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[185]) ).
thf(191,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV11 @ SV18 )
| ~ ( cowlThing @ SV18 ) ) )
= $true )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV17: $i,SV12: $i] :
( ( ( ~ ( rq @ SV12 @ SV17 ) )
= $true )
| ( ( cNothing @ SV17 )
= $true )
| ( ( cnotA @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV12: $i] :
( ( ( ~ ( rq @ SV12 @ ( sK7_SY22 @ SV12 ) ) )
= $false )
| ( ( cnotA @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(194,plain,
! [SV12: $i] :
( ( ( cNothing @ ( sK7_SY22 @ SV12 ) )
= $false )
| ( ( cnotA @ SV12 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(195,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( rq @ SV11 @ ( sK8_SY19 @ SV11 ) )
| ~ ( cowlThing @ ( sK8_SY19 @ SV11 ) ) ) )
= $true )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(196,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( ~ ( rq @ SV11 @ SV18 )
| ~ ( cowlThing @ SV18 ) ) )
= $false )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV17: $i,SV12: $i] :
( ( ( rq @ SV12 @ SV17 )
= $false )
| ( ( cNothing @ SV17 )
= $true )
| ( ( cnotA @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV12: $i] :
( ( ( rq @ SV12 @ ( sK7_SY22 @ SV12 ) )
= $true )
| ( ( cnotA @ SV12 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(199,plain,
! [SV11: $i] :
( ( ( ~ ( rq @ SV11 @ ( sK8_SY19 @ SV11 ) )
| ~ ( cowlThing @ ( sK8_SY19 @ SV11 ) ) )
= $false )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( rq @ SV11 @ SV18 )
| ~ ( cowlThing @ SV18 ) )
= $true )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(201,plain,
! [SV11: $i] :
( ( ( ~ ( rq @ SV11 @ ( sK8_SY19 @ SV11 ) ) )
= $false )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(202,plain,
! [SV11: $i] :
( ( ( ~ ( cowlThing @ ( sK8_SY19 @ SV11 ) ) )
= $false )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(203,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( rq @ SV11 @ SV18 ) )
= $true )
| ( ( ~ ( cowlThing @ SV18 ) )
= $true )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV11: $i] :
( ( ( rq @ SV11 @ ( sK8_SY19 @ SV11 ) )
= $true )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(205,plain,
! [SV11: $i] :
( ( ( cowlThing @ ( sK8_SY19 @ SV11 ) )
= $true )
| ( ( cA @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(206,plain,
! [SV18: $i,SV11: $i] :
( ( ( rq @ SV11 @ SV18 )
= $false )
| ( ( ~ ( cowlThing @ SV18 ) )
= $true )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV11: $i,SV18: $i] :
( ( ( cowlThing @ SV18 )
= $false )
| ( ( rq @ SV11 @ SV18 )
= $false )
| ( ( cA @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(208,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[145,207,205,204,198,197,194,189,184,183,181,173,163]) ).
thf(209,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(210,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(211,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(212,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(213,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(214,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(215,plain,
( ( ~ ! [X: $i] :
( ( xsd_string @ X )
=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(216,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(217,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cnotA @ SX0 )
| ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) )
| ( cnotA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(218,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cowlThing @ SX0 )
| ~ ~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(219,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(220,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(221,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cA @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) )
| ( cA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(222,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(223,plain,
! [SV19: $i] :
( ( ~ ( ~ ( ~ ( xsd_string @ SV19 )
| ~ ( xsd_integer @ SV19 ) )
| ~ ( ~ ~ ( xsd_integer @ SV19 )
| ( xsd_string @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(224,plain,
! [SV20: $i] :
( ( ~ ( ~ ( ~ ( cnotA @ SV20 )
| ! [SY25: $i] :
( ~ ( rq @ SV20 @ SY25 )
| ( cNothing @ SY25 ) ) )
| ~ ( ~ ! [SY26: $i] :
( ~ ( rq @ SV20 @ SY26 )
| ( cNothing @ SY26 ) )
| ( cnotA @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV21: $i] :
( ( ~ ( ~ ( cowlThing @ SV21 )
| ~ ~ ( cowlNothing @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(226,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(227,plain,
! [SV22: $i] :
( ( ~ ( cNothing @ SV22 )
| ~ ~ ! [SY27: $i] :
~ ( rp @ SV22 @ SY27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ~ ( cA @ SV23 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) )
| ( cA @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(229,plain,
! [SV24: $i] :
( ( ~ ( cNothing @ SV24 )
| ~ ! [SY30: $i] :
~ ( rp @ SV24 @ SY30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV19: $i] :
( ( ~ ( ~ ( xsd_string @ SV19 )
| ~ ( xsd_integer @ SV19 ) )
| ~ ( ~ ~ ( xsd_integer @ SV19 )
| ( xsd_string @ SV19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(231,plain,
! [SV20: $i] :
( ( ~ ( ~ ( cnotA @ SV20 )
| ! [SY25: $i] :
( ~ ( rq @ SV20 @ SY25 )
| ( cNothing @ SY25 ) ) )
| ~ ( ~ ! [SY26: $i] :
( ~ ( rq @ SV20 @ SY26 )
| ( cNothing @ SY26 ) )
| ( cnotA @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(232,plain,
! [SV21: $i] :
( ( ~ ( cowlThing @ SV21 )
| ~ ~ ( cowlNothing @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(233,plain,
( ( ~ ( xsd_string @ sK9_SX0 )
| ~ ( xsd_integer @ sK9_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[226]) ).
thf(234,plain,
! [SV22: $i] :
( ( ( ~ ( cNothing @ SV22 ) )
= $true )
| ( ( ~ ~ ! [SY27: $i] :
~ ( rp @ SV22 @ SY27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(235,plain,
! [SV23: $i] :
( ( ~ ( ~ ( cA @ SV23 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) )
| ( cA @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(236,plain,
! [SV24: $i] :
( ( ( ~ ( cNothing @ SV24 ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ( rp @ SV24 @ SY30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(237,plain,
! [SV19: $i] :
( ( ~ ( ~ ( xsd_string @ SV19 )
| ~ ( xsd_integer @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(238,plain,
! [SV19: $i] :
( ( ~ ( ~ ~ ( xsd_integer @ SV19 )
| ( xsd_string @ SV19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(239,plain,
! [SV20: $i] :
( ( ~ ( ~ ( cnotA @ SV20 )
| ! [SY25: $i] :
( ~ ( rq @ SV20 @ SY25 )
| ( cNothing @ SY25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV20: $i] :
( ( ~ ( ~ ! [SY26: $i] :
( ~ ( rq @ SV20 @ SY26 )
| ( cNothing @ SY26 ) )
| ( cnotA @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(241,plain,
! [SV21: $i] :
( ( ~ ( cowlThing @ SV21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(242,plain,
! [SV21: $i] :
( ( ~ ~ ( cowlNothing @ SV21 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(243,plain,
( ( ~ ( xsd_string @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(244,plain,
( ( ~ ( xsd_integer @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(245,plain,
! [SV22: $i] :
( ( ( cNothing @ SV22 )
= $false )
| ( ( ~ ~ ! [SY27: $i] :
~ ( rp @ SV22 @ SY27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(246,plain,
! [SV23: $i] :
( ( ~ ( ~ ( cA @ SV23 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(247,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) )
| ( cA @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(248,plain,
! [SV24: $i] :
( ( ( cNothing @ SV24 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ( rp @ SV24 @ SY30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(249,plain,
! [SV19: $i] :
( ( ~ ( xsd_string @ SV19 )
| ~ ( xsd_integer @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(250,plain,
! [SV19: $i] :
( ( ~ ~ ( xsd_integer @ SV19 )
| ( xsd_string @ SV19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(251,plain,
! [SV20: $i] :
( ( ~ ( cnotA @ SV20 )
| ! [SY25: $i] :
( ~ ( rq @ SV20 @ SY25 )
| ( cNothing @ SY25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(252,plain,
! [SV20: $i] :
( ( ~ ! [SY26: $i] :
( ~ ( rq @ SV20 @ SY26 )
| ( cNothing @ SY26 ) )
| ( cnotA @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(253,plain,
! [SV21: $i] :
( ( cowlThing @ SV21 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(254,plain,
! [SV21: $i] :
( ( ~ ( cowlNothing @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(255,plain,
( ( xsd_string @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(256,plain,
( ( xsd_integer @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(257,plain,
! [SV22: $i] :
( ( ( ~ ! [SY27: $i] :
~ ( rp @ SV22 @ SY27 ) )
= $false )
| ( ( cNothing @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(258,plain,
! [SV23: $i] :
( ( ~ ( cA @ SV23 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(259,plain,
! [SV23: $i] :
( ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) )
| ( cA @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(260,plain,
! [SV24: $i] :
( ( ( ! [SY30: $i] :
~ ( rp @ SV24 @ SY30 ) )
= $false )
| ( ( cNothing @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(261,plain,
! [SV19: $i] :
( ( ( ~ ( xsd_string @ SV19 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(262,plain,
! [SV19: $i] :
( ( ( ~ ~ ( xsd_integer @ SV19 ) )
= $true )
| ( ( xsd_string @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(263,plain,
! [SV20: $i] :
( ( ( ~ ( cnotA @ SV20 ) )
= $true )
| ( ( ! [SY25: $i] :
( ~ ( rq @ SV20 @ SY25 )
| ( cNothing @ SY25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(264,plain,
! [SV20: $i] :
( ( ( ~ ! [SY26: $i] :
( ~ ( rq @ SV20 @ SY26 )
| ( cNothing @ SY26 ) ) )
= $true )
| ( ( cnotA @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(265,plain,
! [SV21: $i] :
( ( cowlNothing @ SV21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV22: $i] :
( ( ( ! [SY27: $i] :
~ ( rp @ SV22 @ SY27 ) )
= $true )
| ( ( cNothing @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(267,plain,
! [SV23: $i] :
( ( ( ~ ( cA @ SV23 ) )
= $true )
| ( ( ~ ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(268,plain,
! [SV23: $i] :
( ( ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) ) )
= $true )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV24: $i] :
( ( ( ~ ( rp @ SV24 @ ( sK10_SY30 @ SV24 ) ) )
= $false )
| ( ( cNothing @ SV24 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[260]) ).
thf(270,plain,
! [SV19: $i] :
( ( ( xsd_string @ SV19 )
= $false )
| ( ( ~ ( xsd_integer @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(271,plain,
! [SV19: $i] :
( ( ( ~ ( xsd_integer @ SV19 ) )
= $false )
| ( ( xsd_string @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(272,plain,
! [SV20: $i] :
( ( ( cnotA @ SV20 )
= $false )
| ( ( ! [SY25: $i] :
( ~ ( rq @ SV20 @ SY25 )
| ( cNothing @ SY25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(273,plain,
! [SV20: $i] :
( ( ( ! [SY26: $i] :
( ~ ( rq @ SV20 @ SY26 )
| ( cNothing @ SY26 ) ) )
= $false )
| ( ( cnotA @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(274,plain,
! [SV25: $i,SV22: $i] :
( ( ( ~ ( rp @ SV22 @ SV25 ) )
= $true )
| ( ( cNothing @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(275,plain,
! [SV23: $i] :
( ( ( cA @ SV23 )
= $false )
| ( ( ~ ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV23: $i] :
( ( ( ~ ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) ) )
= $false )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV24: $i] :
( ( ( rp @ SV24 @ ( sK10_SY30 @ SV24 ) )
= $true )
| ( ( cNothing @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(278,plain,
! [SV19: $i] :
( ( ( xsd_integer @ SV19 )
= $false )
| ( ( xsd_string @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(279,plain,
! [SV19: $i] :
( ( ( xsd_integer @ SV19 )
= $true )
| ( ( xsd_string @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(280,plain,
! [SV26: $i,SV20: $i] :
( ( ( ~ ( rq @ SV20 @ SV26 )
| ( cNothing @ SV26 ) )
= $true )
| ( ( cnotA @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(281,plain,
! [SV20: $i] :
( ( ( ~ ( rq @ SV20 @ ( sK11_SY26 @ SV20 ) )
| ( cNothing @ ( sK11_SY26 @ SV20 ) ) )
= $false )
| ( ( cnotA @ SV20 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[273]) ).
thf(282,plain,
! [SV25: $i,SV22: $i] :
( ( ( rp @ SV22 @ SV25 )
= $false )
| ( ( cNothing @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(283,plain,
! [SV23: $i] :
( ( ( ! [SY28: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY28 )
| ~ ( cowlThing @ SY28 ) ) )
= $false )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(284,plain,
! [SV23: $i] :
( ( ( ! [SY29: $i] :
~ ~ ( ~ ( rq @ SV23 @ SY29 )
| ~ ( cowlThing @ SY29 ) ) )
= $true )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(285,plain,
! [SV26: $i,SV20: $i] :
( ( ( ~ ( rq @ SV20 @ SV26 ) )
= $true )
| ( ( cNothing @ SV26 )
= $true )
| ( ( cnotA @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(286,plain,
! [SV20: $i] :
( ( ( ~ ( rq @ SV20 @ ( sK11_SY26 @ SV20 ) ) )
= $false )
| ( ( cnotA @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV20: $i] :
( ( ( cNothing @ ( sK11_SY26 @ SV20 ) )
= $false )
| ( ( cnotA @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(288,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV23 @ ( sK12_SY28 @ SV23 ) )
| ~ ( cowlThing @ ( sK12_SY28 @ SV23 ) ) ) )
= $false )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[283]) ).
thf(289,plain,
! [SV27: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV23 @ SV27 )
| ~ ( cowlThing @ SV27 ) ) )
= $true )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(290,plain,
! [SV26: $i,SV20: $i] :
( ( ( rq @ SV20 @ SV26 )
= $false )
| ( ( cNothing @ SV26 )
= $true )
| ( ( cnotA @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(291,plain,
! [SV20: $i] :
( ( ( rq @ SV20 @ ( sK11_SY26 @ SV20 ) )
= $true )
| ( ( cnotA @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(292,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( rq @ SV23 @ ( sK12_SY28 @ SV23 ) )
| ~ ( cowlThing @ ( sK12_SY28 @ SV23 ) ) ) )
= $true )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(293,plain,
! [SV27: $i,SV23: $i] :
( ( ( ~ ( ~ ( rq @ SV23 @ SV27 )
| ~ ( cowlThing @ SV27 ) ) )
= $false )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV23: $i] :
( ( ( ~ ( rq @ SV23 @ ( sK12_SY28 @ SV23 ) )
| ~ ( cowlThing @ ( sK12_SY28 @ SV23 ) ) )
= $false )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(295,plain,
! [SV27: $i,SV23: $i] :
( ( ( ~ ( rq @ SV23 @ SV27 )
| ~ ( cowlThing @ SV27 ) )
= $true )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(296,plain,
! [SV23: $i] :
( ( ( ~ ( rq @ SV23 @ ( sK12_SY28 @ SV23 ) ) )
= $false )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(297,plain,
! [SV23: $i] :
( ( ( ~ ( cowlThing @ ( sK12_SY28 @ SV23 ) ) )
= $false )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(298,plain,
! [SV27: $i,SV23: $i] :
( ( ( ~ ( rq @ SV23 @ SV27 ) )
= $true )
| ( ( ~ ( cowlThing @ SV27 ) )
= $true )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(299,plain,
! [SV23: $i] :
( ( ( rq @ SV23 @ ( sK12_SY28 @ SV23 ) )
= $true )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(300,plain,
! [SV23: $i] :
( ( ( cowlThing @ ( sK12_SY28 @ SV23 ) )
= $true )
| ( ( cA @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(301,plain,
! [SV27: $i,SV23: $i] :
( ( ( rq @ SV23 @ SV27 )
= $false )
| ( ( ~ ( cowlThing @ SV27 ) )
= $true )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(302,plain,
! [SV23: $i,SV27: $i] :
( ( ( cowlThing @ SV27 )
= $false )
| ( ( rq @ SV23 @ SV27 )
= $false )
| ( ( cA @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(303,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[253,302,300,299,291,290,287,282,279,278,277,265,256,255]) ).
thf(304,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(305,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(306,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(307,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(308,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(309,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(310,plain,
( ( ~ ! [X: $i] :
( ~ ( xsd_integer @ X )
=> ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(311,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cowlThing @ SX0 )
| ~ ~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(312,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cnotA @ SX0 )
| ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) )
| ( cnotA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(313,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(314,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cA @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) )
| ( cA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(316,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(317,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(318,plain,
! [SV28: $i] :
( ( ~ ( ~ ( cowlThing @ SV28 )
| ~ ~ ( cowlNothing @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(319,plain,
! [SV29: $i] :
( ( ~ ( ~ ( ~ ( cnotA @ SV29 )
| ! [SY31: $i] :
( ~ ( rq @ SV29 @ SY31 )
| ( cNothing @ SY31 ) ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( rq @ SV29 @ SY32 )
| ( cNothing @ SY32 ) )
| ( cnotA @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(320,plain,
! [SV30: $i] :
( ( ~ ( cNothing @ SV30 )
| ~ ~ ! [SY33: $i] :
~ ( rp @ SV30 @ SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(321,plain,
! [SV31: $i] :
( ( ~ ( ~ ( ~ ( cA @ SV31 )
| ~ ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) )
| ~ ( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) )
| ( cA @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(322,plain,
! [SV32: $i] :
( ( ~ ( cNothing @ SV32 )
| ~ ! [SY36: $i] :
~ ( rp @ SV32 @ SY36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(323,plain,
( ( ! [SX0: $i] :
( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(324,plain,
! [SV33: $i] :
( ( ~ ( ~ ( ~ ( xsd_string @ SV33 )
| ~ ( xsd_integer @ SV33 ) )
| ~ ( ~ ~ ( xsd_integer @ SV33 )
| ( xsd_string @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(325,plain,
! [SV28: $i] :
( ( ~ ( cowlThing @ SV28 )
| ~ ~ ( cowlNothing @ SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(326,plain,
! [SV29: $i] :
( ( ~ ( ~ ( cnotA @ SV29 )
| ! [SY31: $i] :
( ~ ( rq @ SV29 @ SY31 )
| ( cNothing @ SY31 ) ) )
| ~ ( ~ ! [SY32: $i] :
( ~ ( rq @ SV29 @ SY32 )
| ( cNothing @ SY32 ) )
| ( cnotA @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(327,plain,
! [SV30: $i] :
( ( ( ~ ( cNothing @ SV30 ) )
= $true )
| ( ( ~ ~ ! [SY33: $i] :
~ ( rp @ SV30 @ SY33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(328,plain,
! [SV31: $i] :
( ( ~ ( ~ ( cA @ SV31 )
| ~ ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) )
| ~ ( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) )
| ( cA @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(329,plain,
! [SV32: $i] :
( ( ( ~ ( cNothing @ SV32 ) )
= $true )
| ( ( ~ ! [SY36: $i] :
~ ( rp @ SV32 @ SY36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(330,plain,
( ( ~ ~ ( xsd_integer @ sK13_SX0 )
| ( xsd_string @ sK13_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[323]) ).
thf(331,plain,
! [SV33: $i] :
( ( ~ ( ~ ( xsd_string @ SV33 )
| ~ ( xsd_integer @ SV33 ) )
| ~ ( ~ ~ ( xsd_integer @ SV33 )
| ( xsd_string @ SV33 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(332,plain,
! [SV28: $i] :
( ( ~ ( cowlThing @ SV28 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(333,plain,
! [SV28: $i] :
( ( ~ ~ ( cowlNothing @ SV28 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(334,plain,
! [SV29: $i] :
( ( ~ ( ~ ( cnotA @ SV29 )
| ! [SY31: $i] :
( ~ ( rq @ SV29 @ SY31 )
| ( cNothing @ SY31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(335,plain,
! [SV29: $i] :
( ( ~ ( ~ ! [SY32: $i] :
( ~ ( rq @ SV29 @ SY32 )
| ( cNothing @ SY32 ) )
| ( cnotA @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[326]) ).
thf(336,plain,
! [SV30: $i] :
( ( ( cNothing @ SV30 )
= $false )
| ( ( ~ ~ ! [SY33: $i] :
~ ( rp @ SV30 @ SY33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(337,plain,
! [SV31: $i] :
( ( ~ ( ~ ( cA @ SV31 )
| ~ ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(338,plain,
! [SV31: $i] :
( ( ~ ( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) )
| ( cA @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(339,plain,
! [SV32: $i] :
( ( ( cNothing @ SV32 )
= $false )
| ( ( ~ ! [SY36: $i] :
~ ( rp @ SV32 @ SY36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(340,plain,
( ( ~ ~ ( xsd_integer @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(341,plain,
( ( xsd_string @ sK13_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(342,plain,
! [SV33: $i] :
( ( ~ ( ~ ( xsd_string @ SV33 )
| ~ ( xsd_integer @ SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(343,plain,
! [SV33: $i] :
( ( ~ ( ~ ~ ( xsd_integer @ SV33 )
| ( xsd_string @ SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(344,plain,
! [SV28: $i] :
( ( cowlThing @ SV28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(345,plain,
! [SV28: $i] :
( ( ~ ( cowlNothing @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(346,plain,
! [SV29: $i] :
( ( ~ ( cnotA @ SV29 )
| ! [SY31: $i] :
( ~ ( rq @ SV29 @ SY31 )
| ( cNothing @ SY31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(347,plain,
! [SV29: $i] :
( ( ~ ! [SY32: $i] :
( ~ ( rq @ SV29 @ SY32 )
| ( cNothing @ SY32 ) )
| ( cnotA @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(348,plain,
! [SV30: $i] :
( ( ( ~ ! [SY33: $i] :
~ ( rp @ SV30 @ SY33 ) )
= $false )
| ( ( cNothing @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(349,plain,
! [SV31: $i] :
( ( ~ ( cA @ SV31 )
| ~ ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(350,plain,
! [SV31: $i] :
( ( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) )
| ( cA @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(351,plain,
! [SV32: $i] :
( ( ( ! [SY36: $i] :
~ ( rp @ SV32 @ SY36 ) )
= $false )
| ( ( cNothing @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(352,plain,
( ( ~ ( xsd_integer @ sK13_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(353,plain,
! [SV33: $i] :
( ( ~ ( xsd_string @ SV33 )
| ~ ( xsd_integer @ SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(354,plain,
! [SV33: $i] :
( ( ~ ~ ( xsd_integer @ SV33 )
| ( xsd_string @ SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(355,plain,
! [SV28: $i] :
( ( cowlNothing @ SV28 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(356,plain,
! [SV29: $i] :
( ( ( ~ ( cnotA @ SV29 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( rq @ SV29 @ SY31 )
| ( cNothing @ SY31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(357,plain,
! [SV29: $i] :
( ( ( ~ ! [SY32: $i] :
( ~ ( rq @ SV29 @ SY32 )
| ( cNothing @ SY32 ) ) )
= $true )
| ( ( cnotA @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(358,plain,
! [SV30: $i] :
( ( ( ! [SY33: $i] :
~ ( rp @ SV30 @ SY33 ) )
= $true )
| ( ( cNothing @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(359,plain,
! [SV31: $i] :
( ( ( ~ ( cA @ SV31 ) )
= $true )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(360,plain,
! [SV31: $i] :
( ( ( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) ) )
= $true )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(361,plain,
! [SV32: $i] :
( ( ( ~ ( rp @ SV32 @ ( sK14_SY36 @ SV32 ) ) )
= $false )
| ( ( cNothing @ SV32 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[351]) ).
thf(362,plain,
( ( xsd_integer @ sK13_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(363,plain,
! [SV33: $i] :
( ( ( ~ ( xsd_string @ SV33 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(364,plain,
! [SV33: $i] :
( ( ( ~ ~ ( xsd_integer @ SV33 ) )
= $true )
| ( ( xsd_string @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(365,plain,
! [SV29: $i] :
( ( ( cnotA @ SV29 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( rq @ SV29 @ SY31 )
| ( cNothing @ SY31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(366,plain,
! [SV29: $i] :
( ( ( ! [SY32: $i] :
( ~ ( rq @ SV29 @ SY32 )
| ( cNothing @ SY32 ) ) )
= $false )
| ( ( cnotA @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(367,plain,
! [SV34: $i,SV30: $i] :
( ( ( ~ ( rp @ SV30 @ SV34 ) )
= $true )
| ( ( cNothing @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(368,plain,
! [SV31: $i] :
( ( ( cA @ SV31 )
= $false )
| ( ( ~ ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(369,plain,
! [SV31: $i] :
( ( ( ~ ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) ) )
= $false )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(370,plain,
! [SV32: $i] :
( ( ( rp @ SV32 @ ( sK14_SY36 @ SV32 ) )
= $true )
| ( ( cNothing @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(371,plain,
! [SV33: $i] :
( ( ( xsd_string @ SV33 )
= $false )
| ( ( ~ ( xsd_integer @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(372,plain,
! [SV33: $i] :
( ( ( ~ ( xsd_integer @ SV33 ) )
= $false )
| ( ( xsd_string @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(373,plain,
! [SV35: $i,SV29: $i] :
( ( ( ~ ( rq @ SV29 @ SV35 )
| ( cNothing @ SV35 ) )
= $true )
| ( ( cnotA @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(374,plain,
! [SV29: $i] :
( ( ( ~ ( rq @ SV29 @ ( sK15_SY32 @ SV29 ) )
| ( cNothing @ ( sK15_SY32 @ SV29 ) ) )
= $false )
| ( ( cnotA @ SV29 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[366]) ).
thf(375,plain,
! [SV34: $i,SV30: $i] :
( ( ( rp @ SV30 @ SV34 )
= $false )
| ( ( cNothing @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(376,plain,
! [SV31: $i] :
( ( ( ! [SY34: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY34 )
| ~ ( cowlThing @ SY34 ) ) )
= $false )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(377,plain,
! [SV31: $i] :
( ( ( ! [SY35: $i] :
~ ~ ( ~ ( rq @ SV31 @ SY35 )
| ~ ( cowlThing @ SY35 ) ) )
= $true )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(378,plain,
! [SV33: $i] :
( ( ( xsd_integer @ SV33 )
= $false )
| ( ( xsd_string @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(379,plain,
! [SV33: $i] :
( ( ( xsd_integer @ SV33 )
= $true )
| ( ( xsd_string @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(380,plain,
! [SV35: $i,SV29: $i] :
( ( ( ~ ( rq @ SV29 @ SV35 ) )
= $true )
| ( ( cNothing @ SV35 )
= $true )
| ( ( cnotA @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(381,plain,
! [SV29: $i] :
( ( ( ~ ( rq @ SV29 @ ( sK15_SY32 @ SV29 ) ) )
= $false )
| ( ( cnotA @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(382,plain,
! [SV29: $i] :
( ( ( cNothing @ ( sK15_SY32 @ SV29 ) )
= $false )
| ( ( cnotA @ SV29 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(383,plain,
! [SV31: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV31 @ ( sK16_SY34 @ SV31 ) )
| ~ ( cowlThing @ ( sK16_SY34 @ SV31 ) ) ) )
= $false )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[376]) ).
thf(384,plain,
! [SV36: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV31 @ SV36 )
| ~ ( cowlThing @ SV36 ) ) )
= $true )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(385,plain,
! [SV35: $i,SV29: $i] :
( ( ( rq @ SV29 @ SV35 )
= $false )
| ( ( cNothing @ SV35 )
= $true )
| ( ( cnotA @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(386,plain,
! [SV29: $i] :
( ( ( rq @ SV29 @ ( sK15_SY32 @ SV29 ) )
= $true )
| ( ( cnotA @ SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(387,plain,
! [SV31: $i] :
( ( ( ~ ( ~ ( rq @ SV31 @ ( sK16_SY34 @ SV31 ) )
| ~ ( cowlThing @ ( sK16_SY34 @ SV31 ) ) ) )
= $true )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(388,plain,
! [SV36: $i,SV31: $i] :
( ( ( ~ ( ~ ( rq @ SV31 @ SV36 )
| ~ ( cowlThing @ SV36 ) ) )
= $false )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(389,plain,
! [SV31: $i] :
( ( ( ~ ( rq @ SV31 @ ( sK16_SY34 @ SV31 ) )
| ~ ( cowlThing @ ( sK16_SY34 @ SV31 ) ) )
= $false )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(390,plain,
! [SV36: $i,SV31: $i] :
( ( ( ~ ( rq @ SV31 @ SV36 )
| ~ ( cowlThing @ SV36 ) )
= $true )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(391,plain,
! [SV31: $i] :
( ( ( ~ ( rq @ SV31 @ ( sK16_SY34 @ SV31 ) ) )
= $false )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(392,plain,
! [SV31: $i] :
( ( ( ~ ( cowlThing @ ( sK16_SY34 @ SV31 ) ) )
= $false )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(393,plain,
! [SV36: $i,SV31: $i] :
( ( ( ~ ( rq @ SV31 @ SV36 ) )
= $true )
| ( ( ~ ( cowlThing @ SV36 ) )
= $true )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(394,plain,
! [SV31: $i] :
( ( ( rq @ SV31 @ ( sK16_SY34 @ SV31 ) )
= $true )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(395,plain,
! [SV31: $i] :
( ( ( cowlThing @ ( sK16_SY34 @ SV31 ) )
= $true )
| ( ( cA @ SV31 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(396,plain,
! [SV36: $i,SV31: $i] :
( ( ( rq @ SV31 @ SV36 )
= $false )
| ( ( ~ ( cowlThing @ SV36 ) )
= $true )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(397,plain,
! [SV31: $i,SV36: $i] :
( ( ( cowlThing @ SV36 )
= $false )
| ( ( rq @ SV31 @ SV36 )
= $false )
| ( ( cA @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(398,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[341,397,395,394,386,385,382,379,378,375,370,362,355,344]) ).
thf(399,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(400,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(401,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(402,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(403,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(404,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(405,plain,
( ( ~ ! [X: $i] :
( ( cnotA @ X )
=> ~ ( cA @ X ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(406,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cA @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) )
| ( cA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(407,plain,
( ( ~ ! [SX0: $i] :
( ~ ( cnotA @ SX0 )
| ~ ( cA @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(408,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(409,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(410,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cowlThing @ SX0 )
| ~ ~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(411,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cnotA @ SX0 )
| ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) )
| ( cnotA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(412,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(413,plain,
! [SV37: $i] :
( ( ~ ( ~ ( ~ ( cA @ SV37 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) )
| ~ ( ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) )
| ( cA @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(414,plain,
( ( ! [SX0: $i] :
( ~ ( cnotA @ SX0 )
| ~ ( cA @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(415,plain,
! [SV38: $i] :
( ( ~ ( cNothing @ SV38 )
| ~ ~ ! [SY39: $i] :
~ ( rp @ SV38 @ SY39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(416,plain,
! [SV39: $i] :
( ( ~ ( ~ ( ~ ( xsd_string @ SV39 )
| ~ ( xsd_integer @ SV39 ) )
| ~ ( ~ ~ ( xsd_integer @ SV39 )
| ( xsd_string @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(417,plain,
! [SV40: $i] :
( ( ~ ( ~ ( cowlThing @ SV40 )
| ~ ~ ( cowlNothing @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(418,plain,
! [SV41: $i] :
( ( ~ ( ~ ( ~ ( cnotA @ SV41 )
| ! [SY40: $i] :
( ~ ( rq @ SV41 @ SY40 )
| ( cNothing @ SY40 ) ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( rq @ SV41 @ SY41 )
| ( cNothing @ SY41 ) )
| ( cnotA @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(419,plain,
! [SV42: $i] :
( ( ~ ( cNothing @ SV42 )
| ~ ! [SY42: $i] :
~ ( rp @ SV42 @ SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(420,plain,
! [SV37: $i] :
( ( ~ ( ~ ( cA @ SV37 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) )
| ~ ( ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) )
| ( cA @ SV37 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(421,plain,
( ( ~ ( cnotA @ sK17_SX0 )
| ~ ( cA @ sK17_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[414]) ).
thf(422,plain,
! [SV38: $i] :
( ( ( ~ ( cNothing @ SV38 ) )
= $true )
| ( ( ~ ~ ! [SY39: $i] :
~ ( rp @ SV38 @ SY39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(423,plain,
! [SV39: $i] :
( ( ~ ( ~ ( xsd_string @ SV39 )
| ~ ( xsd_integer @ SV39 ) )
| ~ ( ~ ~ ( xsd_integer @ SV39 )
| ( xsd_string @ SV39 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(424,plain,
! [SV40: $i] :
( ( ~ ( cowlThing @ SV40 )
| ~ ~ ( cowlNothing @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(425,plain,
! [SV41: $i] :
( ( ~ ( ~ ( cnotA @ SV41 )
| ! [SY40: $i] :
( ~ ( rq @ SV41 @ SY40 )
| ( cNothing @ SY40 ) ) )
| ~ ( ~ ! [SY41: $i] :
( ~ ( rq @ SV41 @ SY41 )
| ( cNothing @ SY41 ) )
| ( cnotA @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(426,plain,
! [SV42: $i] :
( ( ( ~ ( cNothing @ SV42 ) )
= $true )
| ( ( ~ ! [SY42: $i] :
~ ( rp @ SV42 @ SY42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(427,plain,
! [SV37: $i] :
( ( ~ ( ~ ( cA @ SV37 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(428,plain,
! [SV37: $i] :
( ( ~ ( ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) )
| ( cA @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(429,plain,
( ( ~ ( cnotA @ sK17_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(430,plain,
( ( ~ ( cA @ sK17_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(431,plain,
! [SV38: $i] :
( ( ( cNothing @ SV38 )
= $false )
| ( ( ~ ~ ! [SY39: $i] :
~ ( rp @ SV38 @ SY39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(432,plain,
! [SV39: $i] :
( ( ~ ( ~ ( xsd_string @ SV39 )
| ~ ( xsd_integer @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(433,plain,
! [SV39: $i] :
( ( ~ ( ~ ~ ( xsd_integer @ SV39 )
| ( xsd_string @ SV39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(434,plain,
! [SV40: $i] :
( ( ~ ( cowlThing @ SV40 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(435,plain,
! [SV40: $i] :
( ( ~ ~ ( cowlNothing @ SV40 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(436,plain,
! [SV41: $i] :
( ( ~ ( ~ ( cnotA @ SV41 )
| ! [SY40: $i] :
( ~ ( rq @ SV41 @ SY40 )
| ( cNothing @ SY40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(437,plain,
! [SV41: $i] :
( ( ~ ( ~ ! [SY41: $i] :
( ~ ( rq @ SV41 @ SY41 )
| ( cNothing @ SY41 ) )
| ( cnotA @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(438,plain,
! [SV42: $i] :
( ( ( cNothing @ SV42 )
= $false )
| ( ( ~ ! [SY42: $i] :
~ ( rp @ SV42 @ SY42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(439,plain,
! [SV37: $i] :
( ( ~ ( cA @ SV37 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(440,plain,
! [SV37: $i] :
( ( ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) )
| ( cA @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(441,plain,
( ( cnotA @ sK17_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(442,plain,
( ( cA @ sK17_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(443,plain,
! [SV38: $i] :
( ( ( ~ ! [SY39: $i] :
~ ( rp @ SV38 @ SY39 ) )
= $false )
| ( ( cNothing @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(444,plain,
! [SV39: $i] :
( ( ~ ( xsd_string @ SV39 )
| ~ ( xsd_integer @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(445,plain,
! [SV39: $i] :
( ( ~ ~ ( xsd_integer @ SV39 )
| ( xsd_string @ SV39 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(446,plain,
! [SV40: $i] :
( ( cowlThing @ SV40 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(447,plain,
! [SV40: $i] :
( ( ~ ( cowlNothing @ SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(448,plain,
! [SV41: $i] :
( ( ~ ( cnotA @ SV41 )
| ! [SY40: $i] :
( ~ ( rq @ SV41 @ SY40 )
| ( cNothing @ SY40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(449,plain,
! [SV41: $i] :
( ( ~ ! [SY41: $i] :
( ~ ( rq @ SV41 @ SY41 )
| ( cNothing @ SY41 ) )
| ( cnotA @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(450,plain,
! [SV42: $i] :
( ( ( ! [SY42: $i] :
~ ( rp @ SV42 @ SY42 ) )
= $false )
| ( ( cNothing @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(451,plain,
! [SV37: $i] :
( ( ( ~ ( cA @ SV37 ) )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(452,plain,
! [SV37: $i] :
( ( ( ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) ) )
= $true )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(453,plain,
! [SV38: $i] :
( ( ( ! [SY39: $i] :
~ ( rp @ SV38 @ SY39 ) )
= $true )
| ( ( cNothing @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(454,plain,
! [SV39: $i] :
( ( ( ~ ( xsd_string @ SV39 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(455,plain,
! [SV39: $i] :
( ( ( ~ ~ ( xsd_integer @ SV39 ) )
= $true )
| ( ( xsd_string @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(456,plain,
! [SV40: $i] :
( ( cowlNothing @ SV40 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(457,plain,
! [SV41: $i] :
( ( ( ~ ( cnotA @ SV41 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( rq @ SV41 @ SY40 )
| ( cNothing @ SY40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(458,plain,
! [SV41: $i] :
( ( ( ~ ! [SY41: $i] :
( ~ ( rq @ SV41 @ SY41 )
| ( cNothing @ SY41 ) ) )
= $true )
| ( ( cnotA @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(459,plain,
! [SV42: $i] :
( ( ( ~ ( rp @ SV42 @ ( sK18_SY42 @ SV42 ) ) )
= $false )
| ( ( cNothing @ SV42 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[450]) ).
thf(460,plain,
! [SV37: $i] :
( ( ( cA @ SV37 )
= $false )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(461,plain,
! [SV37: $i] :
( ( ( ~ ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) ) )
= $false )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(462,plain,
! [SV43: $i,SV38: $i] :
( ( ( ~ ( rp @ SV38 @ SV43 ) )
= $true )
| ( ( cNothing @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(463,plain,
! [SV39: $i] :
( ( ( xsd_string @ SV39 )
= $false )
| ( ( ~ ( xsd_integer @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(464,plain,
! [SV39: $i] :
( ( ( ~ ( xsd_integer @ SV39 ) )
= $false )
| ( ( xsd_string @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(465,plain,
! [SV41: $i] :
( ( ( cnotA @ SV41 )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( rq @ SV41 @ SY40 )
| ( cNothing @ SY40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(466,plain,
! [SV41: $i] :
( ( ( ! [SY41: $i] :
( ~ ( rq @ SV41 @ SY41 )
| ( cNothing @ SY41 ) ) )
= $false )
| ( ( cnotA @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(467,plain,
! [SV42: $i] :
( ( ( rp @ SV42 @ ( sK18_SY42 @ SV42 ) )
= $true )
| ( ( cNothing @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(468,plain,
! [SV37: $i] :
( ( ( ! [SY37: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY37 )
| ~ ( cowlThing @ SY37 ) ) )
= $false )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(469,plain,
! [SV37: $i] :
( ( ( ! [SY38: $i] :
~ ~ ( ~ ( rq @ SV37 @ SY38 )
| ~ ( cowlThing @ SY38 ) ) )
= $true )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(470,plain,
! [SV43: $i,SV38: $i] :
( ( ( rp @ SV38 @ SV43 )
= $false )
| ( ( cNothing @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(471,plain,
! [SV39: $i] :
( ( ( xsd_integer @ SV39 )
= $false )
| ( ( xsd_string @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(472,plain,
! [SV39: $i] :
( ( ( xsd_integer @ SV39 )
= $true )
| ( ( xsd_string @ SV39 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(473,plain,
! [SV44: $i,SV41: $i] :
( ( ( ~ ( rq @ SV41 @ SV44 )
| ( cNothing @ SV44 ) )
= $true )
| ( ( cnotA @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(474,plain,
! [SV41: $i] :
( ( ( ~ ( rq @ SV41 @ ( sK19_SY41 @ SV41 ) )
| ( cNothing @ ( sK19_SY41 @ SV41 ) ) )
= $false )
| ( ( cnotA @ SV41 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[466]) ).
thf(475,plain,
! [SV37: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV37 @ ( sK20_SY37 @ SV37 ) )
| ~ ( cowlThing @ ( sK20_SY37 @ SV37 ) ) ) )
= $false )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[468]) ).
thf(476,plain,
! [SV45: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV37 @ SV45 )
| ~ ( cowlThing @ SV45 ) ) )
= $true )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(477,plain,
! [SV44: $i,SV41: $i] :
( ( ( ~ ( rq @ SV41 @ SV44 ) )
= $true )
| ( ( cNothing @ SV44 )
= $true )
| ( ( cnotA @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(478,plain,
! [SV41: $i] :
( ( ( ~ ( rq @ SV41 @ ( sK19_SY41 @ SV41 ) ) )
= $false )
| ( ( cnotA @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(479,plain,
! [SV41: $i] :
( ( ( cNothing @ ( sK19_SY41 @ SV41 ) )
= $false )
| ( ( cnotA @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(480,plain,
! [SV37: $i] :
( ( ( ~ ( ~ ( rq @ SV37 @ ( sK20_SY37 @ SV37 ) )
| ~ ( cowlThing @ ( sK20_SY37 @ SV37 ) ) ) )
= $true )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(481,plain,
! [SV45: $i,SV37: $i] :
( ( ( ~ ( ~ ( rq @ SV37 @ SV45 )
| ~ ( cowlThing @ SV45 ) ) )
= $false )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(482,plain,
! [SV44: $i,SV41: $i] :
( ( ( rq @ SV41 @ SV44 )
= $false )
| ( ( cNothing @ SV44 )
= $true )
| ( ( cnotA @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(483,plain,
! [SV41: $i] :
( ( ( rq @ SV41 @ ( sK19_SY41 @ SV41 ) )
= $true )
| ( ( cnotA @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(484,plain,
! [SV37: $i] :
( ( ( ~ ( rq @ SV37 @ ( sK20_SY37 @ SV37 ) )
| ~ ( cowlThing @ ( sK20_SY37 @ SV37 ) ) )
= $false )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(485,plain,
! [SV45: $i,SV37: $i] :
( ( ( ~ ( rq @ SV37 @ SV45 )
| ~ ( cowlThing @ SV45 ) )
= $true )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(486,plain,
! [SV37: $i] :
( ( ( ~ ( rq @ SV37 @ ( sK20_SY37 @ SV37 ) ) )
= $false )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(487,plain,
! [SV37: $i] :
( ( ( ~ ( cowlThing @ ( sK20_SY37 @ SV37 ) ) )
= $false )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(488,plain,
! [SV45: $i,SV37: $i] :
( ( ( ~ ( rq @ SV37 @ SV45 ) )
= $true )
| ( ( ~ ( cowlThing @ SV45 ) )
= $true )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(489,plain,
! [SV37: $i] :
( ( ( rq @ SV37 @ ( sK20_SY37 @ SV37 ) )
= $true )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(490,plain,
! [SV37: $i] :
( ( ( cowlThing @ ( sK20_SY37 @ SV37 ) )
= $true )
| ( ( cA @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(491,plain,
! [SV45: $i,SV37: $i] :
( ( ( rq @ SV37 @ SV45 )
= $false )
| ( ( ~ ( cowlThing @ SV45 ) )
= $true )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(492,plain,
! [SV37: $i,SV45: $i] :
( ( ( cowlThing @ SV45 )
= $false )
| ( ( rq @ SV37 @ SV45 )
= $false )
| ( ( cA @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(493,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[441,492,490,489,483,482,479,472,471,470,467,456,446,442]) ).
thf(494,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(495,plain,
( ( ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(496,plain,
( ( ! [X: $i] :
( ( cA @ X )
<=> ? [Y: $i] :
( ( rq @ X @ Y )
& ( cowlThing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(497,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ~ ? [Y: $i] : ( rp @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(498,plain,
( ( ! [X: $i] :
( ( cNothing @ X )
=> ? [Y0: $i] : ( rp @ X @ Y0 ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(499,plain,
( ( ! [X: $i] :
( ( cnotA @ X )
<=> ! [Y: $i] :
( ( rq @ X @ Y )
=> ( cNothing @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(500,plain,
( ( ~ ! [X: $i] :
( ~ ( cA @ X )
=> ( cnotA @ X ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(501,plain,
( ( ! [SX0: $i] :
~ ( ~ ( cowlThing @ SX0 )
| ~ ~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(502,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( cA @ SX0 )
| ( cnotA @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(503,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(504,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cA @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( rq @ SX0 @ SX1 )
| ~ ( cowlThing @ SX1 ) )
| ( cA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(505,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ( ~ ~ ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(506,plain,
( ( ! [SX0: $i] :
( ~ ( cNothing @ SX0 )
| ~ ! [SX1: $i] :
~ ( rp @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(507,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( cnotA @ SX0 )
| ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rq @ SX0 @ SX1 )
| ( cNothing @ SX1 ) )
| ( cnotA @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(508,plain,
! [SV46: $i] :
( ( ~ ( ~ ( cowlThing @ SV46 )
| ~ ~ ( cowlNothing @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(509,plain,
( ( ! [SX0: $i] :
( ~ ~ ( cA @ SX0 )
| ( cnotA @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(510,plain,
! [SV47: $i] :
( ( ~ ( cNothing @ SV47 )
| ~ ~ ! [SY43: $i] :
~ ( rp @ SV47 @ SY43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(511,plain,
! [SV48: $i] :
( ( ~ ( ~ ( ~ ( cA @ SV48 )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) )
| ( cA @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(512,plain,
! [SV49: $i] :
( ( ~ ( ~ ( ~ ( xsd_string @ SV49 )
| ~ ( xsd_integer @ SV49 ) )
| ~ ( ~ ~ ( xsd_integer @ SV49 )
| ( xsd_string @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(513,plain,
! [SV50: $i] :
( ( ~ ( cNothing @ SV50 )
| ~ ! [SY46: $i] :
~ ( rp @ SV50 @ SY46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(514,plain,
! [SV51: $i] :
( ( ~ ( ~ ( ~ ( cnotA @ SV51 )
| ! [SY47: $i] :
( ~ ( rq @ SV51 @ SY47 )
| ( cNothing @ SY47 ) ) )
| ~ ( ~ ! [SY48: $i] :
( ~ ( rq @ SV51 @ SY48 )
| ( cNothing @ SY48 ) )
| ( cnotA @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(515,plain,
! [SV46: $i] :
( ( ~ ( cowlThing @ SV46 )
| ~ ~ ( cowlNothing @ SV46 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(516,plain,
( ( ~ ~ ( cA @ sK21_SX0 )
| ( cnotA @ sK21_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[509]) ).
thf(517,plain,
! [SV47: $i] :
( ( ( ~ ( cNothing @ SV47 ) )
= $true )
| ( ( ~ ~ ! [SY43: $i] :
~ ( rp @ SV47 @ SY43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(518,plain,
! [SV48: $i] :
( ( ~ ( ~ ( cA @ SV48 )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) )
| ~ ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) )
| ( cA @ SV48 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(519,plain,
! [SV49: $i] :
( ( ~ ( ~ ( xsd_string @ SV49 )
| ~ ( xsd_integer @ SV49 ) )
| ~ ( ~ ~ ( xsd_integer @ SV49 )
| ( xsd_string @ SV49 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(520,plain,
! [SV50: $i] :
( ( ( ~ ( cNothing @ SV50 ) )
= $true )
| ( ( ~ ! [SY46: $i] :
~ ( rp @ SV50 @ SY46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(521,plain,
! [SV51: $i] :
( ( ~ ( ~ ( cnotA @ SV51 )
| ! [SY47: $i] :
( ~ ( rq @ SV51 @ SY47 )
| ( cNothing @ SY47 ) ) )
| ~ ( ~ ! [SY48: $i] :
( ~ ( rq @ SV51 @ SY48 )
| ( cNothing @ SY48 ) )
| ( cnotA @ SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(522,plain,
! [SV46: $i] :
( ( ~ ( cowlThing @ SV46 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(523,plain,
! [SV46: $i] :
( ( ~ ~ ( cowlNothing @ SV46 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(524,plain,
( ( ~ ~ ( cA @ sK21_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(525,plain,
( ( cnotA @ sK21_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(526,plain,
! [SV47: $i] :
( ( ( cNothing @ SV47 )
= $false )
| ( ( ~ ~ ! [SY43: $i] :
~ ( rp @ SV47 @ SY43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(527,plain,
! [SV48: $i] :
( ( ~ ( ~ ( cA @ SV48 )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(528,plain,
! [SV48: $i] :
( ( ~ ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) )
| ( cA @ SV48 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(529,plain,
! [SV49: $i] :
( ( ~ ( ~ ( xsd_string @ SV49 )
| ~ ( xsd_integer @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(530,plain,
! [SV49: $i] :
( ( ~ ( ~ ~ ( xsd_integer @ SV49 )
| ( xsd_string @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(531,plain,
! [SV50: $i] :
( ( ( cNothing @ SV50 )
= $false )
| ( ( ~ ! [SY46: $i] :
~ ( rp @ SV50 @ SY46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(532,plain,
! [SV51: $i] :
( ( ~ ( ~ ( cnotA @ SV51 )
| ! [SY47: $i] :
( ~ ( rq @ SV51 @ SY47 )
| ( cNothing @ SY47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(533,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY48: $i] :
( ~ ( rq @ SV51 @ SY48 )
| ( cNothing @ SY48 ) )
| ( cnotA @ SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(534,plain,
! [SV46: $i] :
( ( cowlThing @ SV46 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(535,plain,
! [SV46: $i] :
( ( ~ ( cowlNothing @ SV46 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(536,plain,
( ( ~ ( cA @ sK21_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(537,plain,
! [SV47: $i] :
( ( ( ~ ! [SY43: $i] :
~ ( rp @ SV47 @ SY43 ) )
= $false )
| ( ( cNothing @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(538,plain,
! [SV48: $i] :
( ( ~ ( cA @ SV48 )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(539,plain,
! [SV48: $i] :
( ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) )
| ( cA @ SV48 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(540,plain,
! [SV49: $i] :
( ( ~ ( xsd_string @ SV49 )
| ~ ( xsd_integer @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(541,plain,
! [SV49: $i] :
( ( ~ ~ ( xsd_integer @ SV49 )
| ( xsd_string @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(542,plain,
! [SV50: $i] :
( ( ( ! [SY46: $i] :
~ ( rp @ SV50 @ SY46 ) )
= $false )
| ( ( cNothing @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(543,plain,
! [SV51: $i] :
( ( ~ ( cnotA @ SV51 )
| ! [SY47: $i] :
( ~ ( rq @ SV51 @ SY47 )
| ( cNothing @ SY47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(544,plain,
! [SV51: $i] :
( ( ~ ! [SY48: $i] :
( ~ ( rq @ SV51 @ SY48 )
| ( cNothing @ SY48 ) )
| ( cnotA @ SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(545,plain,
! [SV46: $i] :
( ( cowlNothing @ SV46 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(546,plain,
( ( cA @ sK21_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(547,plain,
! [SV47: $i] :
( ( ( ! [SY43: $i] :
~ ( rp @ SV47 @ SY43 ) )
= $true )
| ( ( cNothing @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(548,plain,
! [SV48: $i] :
( ( ( ~ ( cA @ SV48 ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(549,plain,
! [SV48: $i] :
( ( ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) ) )
= $true )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(550,plain,
! [SV49: $i] :
( ( ( ~ ( xsd_string @ SV49 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(551,plain,
! [SV49: $i] :
( ( ( ~ ~ ( xsd_integer @ SV49 ) )
= $true )
| ( ( xsd_string @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(552,plain,
! [SV50: $i] :
( ( ( ~ ( rp @ SV50 @ ( sK22_SY46 @ SV50 ) ) )
= $false )
| ( ( cNothing @ SV50 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[542]) ).
thf(553,plain,
! [SV51: $i] :
( ( ( ~ ( cnotA @ SV51 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( rq @ SV51 @ SY47 )
| ( cNothing @ SY47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(554,plain,
! [SV51: $i] :
( ( ( ~ ! [SY48: $i] :
( ~ ( rq @ SV51 @ SY48 )
| ( cNothing @ SY48 ) ) )
= $true )
| ( ( cnotA @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(555,plain,
! [SV52: $i,SV47: $i] :
( ( ( ~ ( rp @ SV47 @ SV52 ) )
= $true )
| ( ( cNothing @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(556,plain,
! [SV48: $i] :
( ( ( cA @ SV48 )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(557,plain,
! [SV48: $i] :
( ( ( ~ ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) ) )
= $false )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(558,plain,
! [SV49: $i] :
( ( ( xsd_string @ SV49 )
= $false )
| ( ( ~ ( xsd_integer @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(559,plain,
! [SV49: $i] :
( ( ( ~ ( xsd_integer @ SV49 ) )
= $false )
| ( ( xsd_string @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(560,plain,
! [SV50: $i] :
( ( ( rp @ SV50 @ ( sK22_SY46 @ SV50 ) )
= $true )
| ( ( cNothing @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(561,plain,
! [SV51: $i] :
( ( ( cnotA @ SV51 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( rq @ SV51 @ SY47 )
| ( cNothing @ SY47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(562,plain,
! [SV51: $i] :
( ( ( ! [SY48: $i] :
( ~ ( rq @ SV51 @ SY48 )
| ( cNothing @ SY48 ) ) )
= $false )
| ( ( cnotA @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(563,plain,
! [SV52: $i,SV47: $i] :
( ( ( rp @ SV47 @ SV52 )
= $false )
| ( ( cNothing @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(564,plain,
! [SV48: $i] :
( ( ( ! [SY44: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY44 )
| ~ ( cowlThing @ SY44 ) ) )
= $false )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(565,plain,
! [SV48: $i] :
( ( ( ! [SY45: $i] :
~ ~ ( ~ ( rq @ SV48 @ SY45 )
| ~ ( cowlThing @ SY45 ) ) )
= $true )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(566,plain,
! [SV49: $i] :
( ( ( xsd_integer @ SV49 )
= $false )
| ( ( xsd_string @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(567,plain,
! [SV49: $i] :
( ( ( xsd_integer @ SV49 )
= $true )
| ( ( xsd_string @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(568,plain,
! [SV53: $i,SV51: $i] :
( ( ( ~ ( rq @ SV51 @ SV53 )
| ( cNothing @ SV53 ) )
= $true )
| ( ( cnotA @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(569,plain,
! [SV51: $i] :
( ( ( ~ ( rq @ SV51 @ ( sK23_SY48 @ SV51 ) )
| ( cNothing @ ( sK23_SY48 @ SV51 ) ) )
= $false )
| ( ( cnotA @ SV51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[562]) ).
thf(570,plain,
! [SV48: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV48 @ ( sK24_SY44 @ SV48 ) )
| ~ ( cowlThing @ ( sK24_SY44 @ SV48 ) ) ) )
= $false )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[564]) ).
thf(571,plain,
! [SV54: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( rq @ SV48 @ SV54 )
| ~ ( cowlThing @ SV54 ) ) )
= $true )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(572,plain,
! [SV53: $i,SV51: $i] :
( ( ( ~ ( rq @ SV51 @ SV53 ) )
= $true )
| ( ( cNothing @ SV53 )
= $true )
| ( ( cnotA @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(573,plain,
! [SV51: $i] :
( ( ( ~ ( rq @ SV51 @ ( sK23_SY48 @ SV51 ) ) )
= $false )
| ( ( cnotA @ SV51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(574,plain,
! [SV51: $i] :
( ( ( cNothing @ ( sK23_SY48 @ SV51 ) )
= $false )
| ( ( cnotA @ SV51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(575,plain,
! [SV48: $i] :
( ( ( ~ ( ~ ( rq @ SV48 @ ( sK24_SY44 @ SV48 ) )
| ~ ( cowlThing @ ( sK24_SY44 @ SV48 ) ) ) )
= $true )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(576,plain,
! [SV54: $i,SV48: $i] :
( ( ( ~ ( ~ ( rq @ SV48 @ SV54 )
| ~ ( cowlThing @ SV54 ) ) )
= $false )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(577,plain,
! [SV53: $i,SV51: $i] :
( ( ( rq @ SV51 @ SV53 )
= $false )
| ( ( cNothing @ SV53 )
= $true )
| ( ( cnotA @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(578,plain,
! [SV51: $i] :
( ( ( rq @ SV51 @ ( sK23_SY48 @ SV51 ) )
= $true )
| ( ( cnotA @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(579,plain,
! [SV48: $i] :
( ( ( ~ ( rq @ SV48 @ ( sK24_SY44 @ SV48 ) )
| ~ ( cowlThing @ ( sK24_SY44 @ SV48 ) ) )
= $false )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(580,plain,
! [SV54: $i,SV48: $i] :
( ( ( ~ ( rq @ SV48 @ SV54 )
| ~ ( cowlThing @ SV54 ) )
= $true )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(581,plain,
! [SV48: $i] :
( ( ( ~ ( rq @ SV48 @ ( sK24_SY44 @ SV48 ) ) )
= $false )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(582,plain,
! [SV48: $i] :
( ( ( ~ ( cowlThing @ ( sK24_SY44 @ SV48 ) ) )
= $false )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(583,plain,
! [SV54: $i,SV48: $i] :
( ( ( ~ ( rq @ SV48 @ SV54 ) )
= $true )
| ( ( ~ ( cowlThing @ SV54 ) )
= $true )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(584,plain,
! [SV48: $i] :
( ( ( rq @ SV48 @ ( sK24_SY44 @ SV48 ) )
= $true )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(585,plain,
! [SV48: $i] :
( ( ( cowlThing @ ( sK24_SY44 @ SV48 ) )
= $true )
| ( ( cA @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(586,plain,
! [SV54: $i,SV48: $i] :
( ( ( rq @ SV48 @ SV54 )
= $false )
| ( ( ~ ( cowlThing @ SV54 ) )
= $true )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(587,plain,
! [SV48: $i,SV54: $i] :
( ( ( cowlThing @ SV54 )
= $false )
| ( ( rq @ SV48 @ SV54 )
= $false )
| ( ( cA @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(588,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[525,587,585,584,578,577,574,567,566,563,560,546,545,534]) ).
thf(589,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[588,117,208,303,398,493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS131+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.17 % Computer : n010.cluster.edu
% 0.14/0.17 % Model : x86_64 x86_64
% 0.14/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.17 % Memory : 8046.5625MB
% 0.14/0.17 % OS : Linux 6.8.0-71-generic
% 0.14/0.17 % CPULimit : 300
% 0.14/0.17 % WCLimit : 300
% 0.14/0.17 % DateTime : Tue Oct 6 11:42:10 UTC 2026
% 0.14/0.17 % CPUTime :
% 0.14/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.35
% 0.70/0.35 No.of.Axioms: 6
% 0.70/0.35
% 0.70/0.35 Length.of.Defs: 0
% 0.70/0.35
% 0.70/0.35 Contains.Choice.Funs: false
% 0.70/0.35 ...........
% 0.70/0.35
% 0.70/0.35 ********************************
% 0.70/0.35 * All subproblems solved! *
% 0.70/0.35 ********************************
% 0.70/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:588,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.35
% 0.70/0.35 %**** Beginning of derivation protocol ****
% 0.70/0.35 % SZS output start CNFRefutation
% See solution above
% 0.70/0.35
% 0.70/0.35 %**** End of derivation protocol ****
% 0.70/0.35 %**** no. of clauses in derivation: 589 ****
% 0.70/0.35 %**** clause counter: 588 ****
% 0.70/0.35
% 0.70/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:588,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------