TSTP Solution File: KRS169+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 03:15:49 EDT 2022
% Result : Theorem 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 368 ( 296 unt; 12 typ; 0 def)
% Number of atoms : 1508 ( 404 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 1777 ( 465 ~; 288 |; 45 &; 968 @)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 485 ( 0 ^ 485 !; 0 ?; 485 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cowlNothing,type,
cowlNothing: $i > $o ).
thf(tp_cowlThing,type,
cowlThing: $i > $o ).
thf(tp_iX,type,
iX: $i ).
thf(tp_iY,type,
iY: $i ).
thf(tp_rhasHead,type,
rhasHead: $i > $i > $o ).
thf(tp_rhasLeader,type,
rhasLeader: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK3_X,type,
sK3_X: $i ).
thf(tp_sK4_X,type,
sK4_X: $i ).
thf(tp_xsd_integer,type,
xsd_integer: $i > $o ).
thf(tp_xsd_string,type,
xsd_string: $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( rhasLeader @ X @ Y )
<=> ( rhasHead @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(2,axiom,
cowlThing @ iY,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(3,axiom,
rhasLeader @ iX @ iY,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(4,axiom,
cowlThing @ iX,
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 ) )
& ( cowlThing @ iX )
& ( rhasHead @ iX @ iY )
& ( cowlThing @ iY ) ),
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 ) )
& ( cowlThing @ iX )
& ( rhasHead @ iX @ iY )
& ( cowlThing @ iY ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( cowlThing @ X )
& ~ ( cowlNothing @ X ) )
& ! [X: $i] :
( ( xsd_string @ X )
<=> ~ ( xsd_integer @ X ) )
& ( cowlThing @ iX )
& ( rhasHead @ iX @ iY )
& ( cowlThing @ iY ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i] :
( ( rhasLeader @ X @ Y )
<=> ( rhasHead @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( cowlThing @ iY )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( cowlThing @ iX )
= $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,
( ( cowlThing @ iX )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(21,plain,
( ( rhasHead @ iX @ iY )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(22,plain,
( ( cowlThing @ iY )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[9]) ).
thf(23,plain,
( ( ~ ! [X: $i] : ( cowlThing @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(24,plain,
( ( ~ ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(25,plain,
( ( ~ ! [X: $i] :
( ( xsd_string @ X )
=> ~ ( xsd_integer @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(26,plain,
( ( ~ ! [X: $i] :
( ~ ( xsd_integer @ X )
=> ( xsd_string @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(27,plain,
( ( ~ ( cowlThing @ iX ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(28,plain,
( ( ~ ( rhasHead @ iX @ iY ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(29,plain,
( ( ~ ( cowlThing @ iY ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(30,plain,
( ( ~ ( cowlThing @ sK1_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(31,plain,
( ( cowlNothing @ sK2_X )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(32,plain,
( ( ( xsd_string @ sK3_X )
& ( xsd_integer @ sK3_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(33,plain,
( ( ~ ( xsd_integer @ sK4_X )
& ~ ( xsd_string @ sK4_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(35,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(36,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(37,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(39,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(40,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(41,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(43,plain,
( ( ~ ( cowlThing @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(46,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(47,plain,
( ( cowlThing @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(53,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(55,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(57,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(58,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(59,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(60,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(62,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV1: $i] :
( ( ! [SY6: $i] :
( ~ ( rhasHead @ SV1 @ SY6 )
| ( rhasLeader @ SV1 @ SY6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY7: $i] :
( ~ ( rhasLeader @ SV2 @ SY7 )
| ( rhasHead @ SV2 @ SY7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV3: $i] :
( ( cowlThing @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV4: $i] :
( ( ~ ( cowlNothing @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV5: $i] :
( ( ~ ( xsd_string @ SV5 )
| ~ ( xsd_integer @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV6: $i] :
( ( ( xsd_integer @ SV6 )
| ( xsd_string @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( rhasHead @ SV1 @ SV7 )
| ( rhasLeader @ SV1 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV8: $i,SV2: $i] :
( ( ~ ( rhasLeader @ SV2 @ SV8 )
| ( rhasHead @ SV2 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV4: $i] :
( ( cowlNothing @ SV4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( ~ ( xsd_string @ SV5 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV6: $i] :
( ( ( xsd_integer @ SV6 )
= $true )
| ( ( xsd_string @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( rhasHead @ SV1 @ SV7 ) )
= $true )
| ( ( rhasLeader @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV8: $i,SV2: $i] :
( ( ( ~ ( rhasLeader @ SV2 @ SV8 ) )
= $true )
| ( ( rhasHead @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV5: $i] :
( ( ( xsd_string @ SV5 )
= $false )
| ( ( ~ ( xsd_integer @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV7: $i,SV1: $i] :
( ( ( rhasHead @ SV1 @ SV7 )
= $false )
| ( ( rhasLeader @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(78,plain,
! [SV8: $i,SV2: $i] :
( ( ( rhasLeader @ SV2 @ SV8 )
= $false )
| ( ( rhasHead @ SV2 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(79,plain,
! [SV5: $i] :
( ( ( xsd_integer @ SV5 )
= $false )
| ( ( xsd_string @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(80,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,79,78,77,73,71,65,47,41,40]) ).
thf(81,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(82,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(83,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(84,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(85,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(87,plain,
( ( cowlNothing @ sK2_X )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(88,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(89,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(90,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(91,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(92,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(94,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(95,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(98,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(99,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(105,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(106,plain,
! [SV9: $i] :
( ( ! [SY8: $i] :
( ~ ( rhasHead @ SV9 @ SY8 )
| ( rhasLeader @ SV9 @ SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV10: $i] :
( ( ! [SY9: $i] :
( ~ ( rhasLeader @ SV10 @ SY9 )
| ( rhasHead @ SV10 @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV11: $i] :
( ( cowlThing @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV12: $i] :
( ( ~ ( cowlNothing @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV13: $i] :
( ( ~ ( xsd_string @ SV13 )
| ~ ( xsd_integer @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV14: $i] :
( ( ( xsd_integer @ SV14 )
| ( xsd_string @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV15: $i,SV9: $i] :
( ( ~ ( rhasHead @ SV9 @ SV15 )
| ( rhasLeader @ SV9 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV16: $i,SV10: $i] :
( ( ~ ( rhasLeader @ SV10 @ SV16 )
| ( rhasHead @ SV10 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV12: $i] :
( ( cowlNothing @ SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV13: $i] :
( ( ( ~ ( xsd_string @ SV13 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(116,plain,
! [SV14: $i] :
( ( ( xsd_integer @ SV14 )
= $true )
| ( ( xsd_string @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV15: $i,SV9: $i] :
( ( ( ~ ( rhasHead @ SV9 @ SV15 ) )
= $true )
| ( ( rhasLeader @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV16: $i,SV10: $i] :
( ( ( ~ ( rhasLeader @ SV10 @ SV16 ) )
= $true )
| ( ( rhasHead @ SV10 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV13: $i] :
( ( ( xsd_string @ SV13 )
= $false )
| ( ( ~ ( xsd_integer @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(120,plain,
! [SV15: $i,SV9: $i] :
( ( ( rhasHead @ SV9 @ SV15 )
= $false )
| ( ( rhasLeader @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(121,plain,
! [SV16: $i,SV10: $i] :
( ( ( rhasLeader @ SV10 @ SV16 )
= $false )
| ( ( rhasHead @ SV10 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(122,plain,
! [SV13: $i] :
( ( ( xsd_integer @ SV13 )
= $false )
| ( ( xsd_string @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(123,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[83,122,121,120,116,114,108,87,85,84]) ).
thf(124,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(125,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(126,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(127,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(128,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(130,plain,
( ( ( xsd_string @ sK3_X )
& ( xsd_integer @ sK3_X ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(131,plain,
( ( ~ ( ~ ( xsd_string @ sK3_X )
| ~ ( xsd_integer @ sK3_X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(132,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(133,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(134,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(135,plain,
( ( ~ ( xsd_string @ sK3_X )
| ~ ( xsd_integer @ sK3_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(136,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
( ( ~ ( xsd_string @ sK3_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(140,plain,
( ( ~ ( xsd_integer @ sK3_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(141,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(142,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(143,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(144,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(145,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(146,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(147,plain,
( ( xsd_string @ sK3_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(148,plain,
( ( xsd_integer @ sK3_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(151,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(152,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(153,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(154,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV17: $i] :
( ( ! [SY10: $i] :
( ~ ( rhasHead @ SV17 @ SY10 )
| ( rhasLeader @ SV17 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV18: $i] :
( ( ! [SY11: $i] :
( ~ ( rhasLeader @ SV18 @ SY11 )
| ( rhasHead @ SV18 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV19: $i] :
( ( ~ ( xsd_string @ SV19 )
| ~ ( xsd_integer @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV20: $i] :
( ( ( xsd_integer @ SV20 )
| ( xsd_string @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(159,plain,
! [SV21: $i] :
( ( cowlThing @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV22: $i] :
( ( ~ ( cowlNothing @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(161,plain,
! [SV23: $i,SV17: $i] :
( ( ~ ( rhasHead @ SV17 @ SV23 )
| ( rhasLeader @ SV17 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV24: $i,SV18: $i] :
( ( ~ ( rhasLeader @ SV18 @ SV24 )
| ( rhasHead @ SV18 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV19: $i] :
( ( ( ~ ( xsd_string @ SV19 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(164,plain,
! [SV20: $i] :
( ( ( xsd_integer @ SV20 )
= $true )
| ( ( xsd_string @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(165,plain,
! [SV22: $i] :
( ( cowlNothing @ SV22 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV23: $i,SV17: $i] :
( ( ( ~ ( rhasHead @ SV17 @ SV23 ) )
= $true )
| ( ( rhasLeader @ SV17 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV24: $i,SV18: $i] :
( ( ( ~ ( rhasLeader @ SV18 @ SV24 ) )
= $true )
| ( ( rhasHead @ SV18 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV19: $i] :
( ( ( xsd_string @ SV19 )
= $false )
| ( ( ~ ( xsd_integer @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(169,plain,
! [SV23: $i,SV17: $i] :
( ( ( rhasHead @ SV17 @ SV23 )
= $false )
| ( ( rhasLeader @ SV17 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(170,plain,
! [SV24: $i,SV18: $i] :
( ( ( rhasLeader @ SV18 @ SV24 )
= $false )
| ( ( rhasHead @ SV18 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(171,plain,
! [SV19: $i] :
( ( ( xsd_integer @ SV19 )
= $false )
| ( ( xsd_string @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(172,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[126,171,170,169,165,164,159,148,147,128,127]) ).
thf(173,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(174,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(175,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(176,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(177,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(178,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(179,plain,
( ( ~ ( xsd_integer @ sK4_X )
& ~ ( xsd_string @ sK4_X ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(180,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(181,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(182,plain,
( ( ~ ( ~ ~ ( xsd_integer @ sK4_X )
| ~ ~ ( xsd_string @ sK4_X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(183,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(184,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(185,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(186,plain,
( ( ~ ~ ( xsd_integer @ sK4_X )
| ~ ~ ( xsd_string @ sK4_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(187,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(188,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(189,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(190,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(191,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[185]) ).
thf(192,plain,
( ( ~ ~ ( xsd_integer @ sK4_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(193,plain,
( ( ~ ~ ( xsd_string @ sK4_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(194,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(195,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(196,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(197,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(198,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(199,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(200,plain,
( ( ~ ( xsd_integer @ sK4_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(201,plain,
( ( ~ ( xsd_string @ sK4_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(202,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(203,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(204,plain,
! [SV25: $i] :
( ( cowlThing @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV26: $i] :
( ( ~ ( cowlNothing @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(206,plain,
! [SV27: $i] :
( ( ! [SY12: $i] :
( ~ ( rhasHead @ SV27 @ SY12 )
| ( rhasLeader @ SV27 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(207,plain,
! [SV28: $i] :
( ( ! [SY13: $i] :
( ~ ( rhasLeader @ SV28 @ SY13 )
| ( rhasHead @ SV28 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(208,plain,
( ( xsd_integer @ sK4_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(209,plain,
( ( xsd_string @ sK4_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(210,plain,
! [SV29: $i] :
( ( ~ ( xsd_string @ SV29 )
| ~ ( xsd_integer @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(211,plain,
! [SV30: $i] :
( ( ( xsd_integer @ SV30 )
| ( xsd_string @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(212,plain,
! [SV26: $i] :
( ( cowlNothing @ SV26 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(213,plain,
! [SV31: $i,SV27: $i] :
( ( ~ ( rhasHead @ SV27 @ SV31 )
| ( rhasLeader @ SV27 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(214,plain,
! [SV32: $i,SV28: $i] :
( ( ~ ( rhasLeader @ SV28 @ SV32 )
| ( rhasHead @ SV28 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(215,plain,
! [SV29: $i] :
( ( ( ~ ( xsd_string @ SV29 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(216,plain,
! [SV30: $i] :
( ( ( xsd_integer @ SV30 )
= $true )
| ( ( xsd_string @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(217,plain,
! [SV31: $i,SV27: $i] :
( ( ( ~ ( rhasHead @ SV27 @ SV31 ) )
= $true )
| ( ( rhasLeader @ SV27 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV32: $i,SV28: $i] :
( ( ( ~ ( rhasLeader @ SV28 @ SV32 ) )
= $true )
| ( ( rhasHead @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV29: $i] :
( ( ( xsd_string @ SV29 )
= $false )
| ( ( ~ ( xsd_integer @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV31: $i,SV27: $i] :
( ( ( rhasHead @ SV27 @ SV31 )
= $false )
| ( ( rhasLeader @ SV27 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(221,plain,
! [SV32: $i,SV28: $i] :
( ( ( rhasLeader @ SV28 @ SV32 )
= $false )
| ( ( rhasHead @ SV28 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(222,plain,
! [SV29: $i] :
( ( ( xsd_integer @ SV29 )
= $false )
| ( ( xsd_string @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(223,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[175,222,221,220,216,212,209,208,204,177,176]) ).
thf(224,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(225,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(226,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(227,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(228,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(229,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(230,plain,
( ( ~ ( cowlThing @ iX ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(231,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(232,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(233,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(234,plain,
( ( cowlThing @ iX )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(235,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(236,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(237,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(238,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(239,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(240,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(241,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(242,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(243,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(244,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(245,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(246,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(247,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(248,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(249,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(250,plain,
! [SV33: $i] :
( ( ! [SY14: $i] :
( ~ ( rhasHead @ SV33 @ SY14 )
| ( rhasLeader @ SV33 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(251,plain,
! [SV34: $i] :
( ( ! [SY15: $i] :
( ~ ( rhasLeader @ SV34 @ SY15 )
| ( rhasHead @ SV34 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(252,plain,
! [SV35: $i] :
( ( cowlThing @ SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(253,plain,
! [SV36: $i] :
( ( ~ ( cowlNothing @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV37: $i] :
( ( ~ ( xsd_string @ SV37 )
| ~ ( xsd_integer @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(255,plain,
! [SV38: $i] :
( ( ( xsd_integer @ SV38 )
| ( xsd_string @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(256,plain,
! [SV39: $i,SV33: $i] :
( ( ~ ( rhasHead @ SV33 @ SV39 )
| ( rhasLeader @ SV33 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(257,plain,
! [SV40: $i,SV34: $i] :
( ( ~ ( rhasLeader @ SV34 @ SV40 )
| ( rhasHead @ SV34 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(258,plain,
! [SV36: $i] :
( ( cowlNothing @ SV36 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(259,plain,
! [SV37: $i] :
( ( ( ~ ( xsd_string @ SV37 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(260,plain,
! [SV38: $i] :
( ( ( xsd_integer @ SV38 )
= $true )
| ( ( xsd_string @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(261,plain,
! [SV39: $i,SV33: $i] :
( ( ( ~ ( rhasHead @ SV33 @ SV39 ) )
= $true )
| ( ( rhasLeader @ SV33 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(262,plain,
! [SV40: $i,SV34: $i] :
( ( ( ~ ( rhasLeader @ SV34 @ SV40 ) )
= $true )
| ( ( rhasHead @ SV34 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(263,plain,
! [SV37: $i] :
( ( ( xsd_string @ SV37 )
= $false )
| ( ( ~ ( xsd_integer @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(264,plain,
! [SV39: $i,SV33: $i] :
( ( ( rhasHead @ SV33 @ SV39 )
= $false )
| ( ( rhasLeader @ SV33 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(265,plain,
! [SV40: $i,SV34: $i] :
( ( ( rhasLeader @ SV34 @ SV40 )
= $false )
| ( ( rhasHead @ SV34 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(266,plain,
! [SV37: $i] :
( ( ( xsd_integer @ SV37 )
= $false )
| ( ( xsd_string @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(267,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[226,266,265,264,260,258,252,234,228,227]) ).
thf(268,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(269,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(270,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(271,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(272,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(273,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(274,plain,
( ( ~ ( rhasHead @ iX @ iY ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(275,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(276,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(277,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(278,plain,
( ( rhasHead @ iX @ iY )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(279,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(280,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(281,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(282,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(283,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(284,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(285,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(286,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(287,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(288,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(289,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(290,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(291,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(292,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(293,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(294,plain,
! [SV41: $i] :
( ( cowlThing @ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(295,plain,
! [SV42: $i] :
( ( ~ ( cowlNothing @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(296,plain,
! [SV43: $i] :
( ( ~ ( xsd_string @ SV43 )
| ~ ( xsd_integer @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(297,plain,
! [SV44: $i] :
( ( ( xsd_integer @ SV44 )
| ( xsd_string @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(298,plain,
! [SV45: $i] :
( ( ! [SY16: $i] :
( ~ ( rhasHead @ SV45 @ SY16 )
| ( rhasLeader @ SV45 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(299,plain,
! [SV46: $i] :
( ( ! [SY17: $i] :
( ~ ( rhasLeader @ SV46 @ SY17 )
| ( rhasHead @ SV46 @ SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(300,plain,
! [SV42: $i] :
( ( cowlNothing @ SV42 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(301,plain,
! [SV43: $i] :
( ( ( ~ ( xsd_string @ SV43 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(302,plain,
! [SV44: $i] :
( ( ( xsd_integer @ SV44 )
= $true )
| ( ( xsd_string @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(303,plain,
! [SV47: $i,SV45: $i] :
( ( ~ ( rhasHead @ SV45 @ SV47 )
| ( rhasLeader @ SV45 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(304,plain,
! [SV48: $i,SV46: $i] :
( ( ~ ( rhasLeader @ SV46 @ SV48 )
| ( rhasHead @ SV46 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(305,plain,
! [SV43: $i] :
( ( ( xsd_string @ SV43 )
= $false )
| ( ( ~ ( xsd_integer @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(306,plain,
! [SV47: $i,SV45: $i] :
( ( ( ~ ( rhasHead @ SV45 @ SV47 ) )
= $true )
| ( ( rhasLeader @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(307,plain,
! [SV48: $i,SV46: $i] :
( ( ( ~ ( rhasLeader @ SV46 @ SV48 ) )
= $true )
| ( ( rhasHead @ SV46 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(308,plain,
! [SV43: $i] :
( ( ( xsd_integer @ SV43 )
= $false )
| ( ( xsd_string @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(309,plain,
! [SV47: $i,SV45: $i] :
( ( ( rhasHead @ SV45 @ SV47 )
= $false )
| ( ( rhasLeader @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(310,plain,
! [SV48: $i,SV46: $i] :
( ( ( rhasLeader @ SV46 @ SV48 )
= $false )
| ( ( rhasHead @ SV46 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(311,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[270,310,309,308,302,300,294,278,272,271]) ).
thf(312,plain,
( ( ! [X: $i] : ( cowlThing @ X )
& ! [X: $i] :
~ ( cowlNothing @ X ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(313,plain,
( ( ! [X: $i] :
( ~ ( xsd_string @ X )
| ~ ( xsd_integer @ X ) )
& ! [X: $i] :
( ( xsd_integer @ X )
| ( xsd_string @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(314,plain,
( ( cowlThing @ iX )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(315,plain,
( ( rhasLeader @ iX @ iY )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(316,plain,
( ( cowlThing @ iY )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(317,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( rhasHead @ X @ Y )
| ( rhasLeader @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( rhasLeader @ X @ Y )
| ( rhasHead @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(318,plain,
( ( ~ ( cowlThing @ iY ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(319,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(320,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(321,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(322,plain,
( ( cowlThing @ iY )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(323,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 )
| ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(324,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(325,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) )
| ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(326,plain,
( ( ~ ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(327,plain,
( ( ~ ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(328,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(329,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(330,plain,
( ( ~ ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(331,plain,
( ( ~ ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(332,plain,
( ( ! [SX0: $i] : ( cowlThing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(333,plain,
( ( ! [SX0: $i] :
~ ( cowlNothing @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(334,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasHead @ SX0 @ SX1 )
| ( rhasLeader @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(335,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rhasLeader @ SX0 @ SX1 )
| ( rhasHead @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(336,plain,
( ( ! [SX0: $i] :
( ~ ( xsd_string @ SX0 )
| ~ ( xsd_integer @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(337,plain,
( ( ! [SX0: $i] :
( ( xsd_integer @ SX0 )
| ( xsd_string @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(338,plain,
! [SV49: $i] :
( ( cowlThing @ SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(339,plain,
! [SV50: $i] :
( ( ~ ( cowlNothing @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(340,plain,
! [SV51: $i] :
( ( ! [SY18: $i] :
( ~ ( rhasHead @ SV51 @ SY18 )
| ( rhasLeader @ SV51 @ SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(341,plain,
! [SV52: $i] :
( ( ! [SY19: $i] :
( ~ ( rhasLeader @ SV52 @ SY19 )
| ( rhasHead @ SV52 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(342,plain,
! [SV53: $i] :
( ( ~ ( xsd_string @ SV53 )
| ~ ( xsd_integer @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(343,plain,
! [SV54: $i] :
( ( ( xsd_integer @ SV54 )
| ( xsd_string @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(344,plain,
! [SV50: $i] :
( ( cowlNothing @ SV50 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(345,plain,
! [SV55: $i,SV51: $i] :
( ( ~ ( rhasHead @ SV51 @ SV55 )
| ( rhasLeader @ SV51 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(346,plain,
! [SV56: $i,SV52: $i] :
( ( ~ ( rhasLeader @ SV52 @ SV56 )
| ( rhasHead @ SV52 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(347,plain,
! [SV53: $i] :
( ( ( ~ ( xsd_string @ SV53 ) )
= $true )
| ( ( ~ ( xsd_integer @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(348,plain,
! [SV54: $i] :
( ( ( xsd_integer @ SV54 )
= $true )
| ( ( xsd_string @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(349,plain,
! [SV55: $i,SV51: $i] :
( ( ( ~ ( rhasHead @ SV51 @ SV55 ) )
= $true )
| ( ( rhasLeader @ SV51 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(350,plain,
! [SV56: $i,SV52: $i] :
( ( ( ~ ( rhasLeader @ SV52 @ SV56 ) )
= $true )
| ( ( rhasHead @ SV52 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(351,plain,
! [SV53: $i] :
( ( ( xsd_string @ SV53 )
= $false )
| ( ( ~ ( xsd_integer @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(352,plain,
! [SV55: $i,SV51: $i] :
( ( ( rhasHead @ SV51 @ SV55 )
= $false )
| ( ( rhasLeader @ SV51 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(353,plain,
! [SV56: $i,SV52: $i] :
( ( ( rhasLeader @ SV52 @ SV56 )
= $false )
| ( ( rhasHead @ SV52 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(354,plain,
! [SV53: $i] :
( ( ( xsd_integer @ SV53 )
= $false )
| ( ( xsd_string @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(355,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[314,354,353,352,348,344,338,322,316,315]) ).
thf(356,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[355,80,123,172,223,267,311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : KRS169+1 : TPTP v8.1.0. Released v3.1.0.
% 0.09/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 7 13:26:00 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 6
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full).............
% 0.18/0.54
% 0.18/0.54 ********************************
% 0.18/0.54 * All subproblems solved! *
% 0.18/0.54 ********************************
% 0.18/0.54 % 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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:355,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.57
% 0.18/0.57 %**** Beginning of derivation protocol ****
% 0.18/0.57 % SZS output start CNFRefutation
% See solution above
% 0.18/0.58
% 0.18/0.58 %**** End of derivation protocol ****
% 0.18/0.58 %**** no. of clauses in derivation: 356 ****
% 0.18/0.58 %**** clause counter: 355 ****
% 0.18/0.58
% 0.18/0.58 % 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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:355,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------