%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYN917+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 11:07:08 AM UTC 2026
% Result : Theorem 2.28s 0.57s
% Output : CNFRefutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 1
% Syntax : Number of formulae : 663 ( 471 unt; 0 typ; 0 def)
% Number of atoms : 3798 ( 885 equ; 0 cnn)
% Maximal formula atoms : 94 ( 5 avg)
% Number of connectives : 4896 (1717 ~; 846 |; 189 &;1814 @)
% ( 30 <=>; 300 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 43 usr; 35 con; 0-2 aty)
% Number of variables : 1048 ( 0 ^; 886 !; 162 ?;1048 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c,type,
c: $o ).
thf(tp_f,type,
f: $i > $o ).
thf(tp_g,type,
g: $i > $o ).
thf(tp_h,type,
h: $i > $o ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_q,type,
q: $i > $o ).
thf(tp_r,type,
r: $i > $i > $o ).
thf(tp_sK10_SY62,type,
sK10_SY62: $i > $i ).
thf(tp_sK11_SX0,type,
sK11_SX0: $i ).
thf(tp_sK12_SX0,type,
sK12_SX0: $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK14_SX0,type,
sK14_SX0: $i ).
thf(tp_sK15_SX0,type,
sK15_SX0: $i ).
thf(tp_sK16_SX0,type,
sK16_SX0: $i ).
thf(tp_sK17_SX0,type,
sK17_SX0: $i ).
thf(tp_sK18_SX1,type,
sK18_SX1: $i ).
thf(tp_sK19_SX0,type,
sK19_SX0: $i ).
thf(tp_sK1_SX1,type,
sK1_SX1: $i > $i ).
thf(tp_sK20_SX0,type,
sK20_SX0: $i ).
thf(tp_sK21_SX0,type,
sK21_SX0: $i ).
thf(tp_sK22_SX1,type,
sK22_SX1: $i ).
thf(tp_sK23_SX0,type,
sK23_SX0: $i ).
thf(tp_sK24_SX0,type,
sK24_SX0: $i ).
thf(tp_sK25_SX0,type,
sK25_SX0: $i ).
thf(tp_sK26_SX0,type,
sK26_SX0: $i ).
thf(tp_sK27_SX0,type,
sK27_SX0: $i ).
thf(tp_sK28_SX0,type,
sK28_SX0: $i ).
thf(tp_sK29_SX0,type,
sK29_SX0: $i ).
thf(tp_sK2_SX1,type,
sK2_SX1: $i > $i ).
thf(tp_sK30_SX0,type,
sK30_SX0: $i ).
thf(tp_sK31_SX0,type,
sK31_SX0: $i ).
thf(tp_sK32_SX0,type,
sK32_SX0: $i ).
thf(tp_sK33_SX0,type,
sK33_SX0: $i ).
thf(tp_sK34_SX0,type,
sK34_SX0: $i ).
thf(tp_sK35_SX0,type,
sK35_SX0: $i ).
thf(tp_sK36_SX0,type,
sK36_SX0: $i ).
thf(tp_sK3_SX1,type,
sK3_SX1: $i > $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY57,type,
sK5_SY57: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_sK9_SX0,type,
sK9_SX0: $i ).
thf(1,conjecture,
( ( ( ! [X: $i] :
( ( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [Y: $i] :
( ( f @ Y )
& ~ ( g @ Y ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
& ( ( ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( r @ X @ Y )
& ( r @ Y @ Z ) )
=> ( r @ X @ Z ) ) )
=> ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ X @ X ) ) )
& ( ( ( ! [X: $i] :
( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [X: $i] :
( ( f @ X )
& ~ ( g @ X ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
& ? [X: $i] :
! [Y: $i] :
( ( ( p @ Y )
=> ( q @ X ) )
=> ( ( p @ X )
=> ( q @ X ) ) )
& ( ! [X: $i] :
( ( p @ X )
& ( q @ X ) )
<=> ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) ) )
& ( ( ! [X: $i] : ( p @ X )
| ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) )
& ( ? [X: $i] :
( ( p @ X )
| ( q @ X ) )
<=> ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) ) )
& ? [Y: $i] :
( ( p @ Y )
=> ! [X: $i] : ( p @ X ) )
& ( ? [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
& ? [X: $i] : ( q @ X ) ) )
& ! [Y: $i] :
( ! [X: $i] : ( p @ X )
=> ( p @ Y ) )
& ( ! [X: $i] : ( p @ X )
=> ? [X: $i] : ( p @ X ) )
& ( ~ ? [Y: $i] : ( p @ Y )
=> ! [Y: $i] :
( ? [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
& ( ! [X: $i] :
( ( p @ X )
| c )
<=> ( ! [X: $i] : ( p @ X )
| c ) )
& ( ? [X: $i] :
( ( p @ X )
& c )
<=> ( ? [X: $i] : ( p @ X )
& c ) )
& ( ? [X: $i] : c
<=> c )
& ( ! [X: $i] : c
<=> c )
& ( ? [X: $i] :
( c
=> ( p @ X ) )
<=> ( c
=> ? [X: $i] : ( p @ X ) ) )
& ( ? [X: $i] :
( ( p @ X )
=> c )
<=> ( ! [X: $i] : ( p @ X )
=> c ) )
& ( ! [X: $i] :
( c
=> ( p @ X ) )
<=> ( c
=> ! [X: $i] : ( p @ X ) ) )
& ( ! [X: $i] :
( ( p @ X )
=> c )
<=> ( ? [X: $i] : ( p @ X )
=> c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
( ( ( ( ! [X: $i] :
( ( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [Y: $i] :
( ( f @ Y )
& ~ ( g @ Y ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
& ( ( ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( r @ X @ Y )
& ( r @ Y @ Z ) )
=> ( r @ X @ Z ) ) )
=> ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ X @ X ) ) )
& ( ( ( ! [X: $i] :
( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [X: $i] :
( ( f @ X )
& ~ ( g @ X ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
& ? [X: $i] :
! [Y: $i] :
( ( ( p @ Y )
=> ( q @ X ) )
=> ( ( p @ X )
=> ( q @ X ) ) )
& ( ! [X: $i] :
( ( p @ X )
& ( q @ X ) )
<=> ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) ) )
& ( ( ! [X: $i] : ( p @ X )
| ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) )
& ( ? [X: $i] :
( ( p @ X )
| ( q @ X ) )
<=> ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) ) )
& ? [Y: $i] :
( ( p @ Y )
=> ! [X: $i] : ( p @ X ) )
& ( ? [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
& ? [X: $i] : ( q @ X ) ) )
& ! [Y: $i] :
( ! [X: $i] : ( p @ X )
=> ( p @ Y ) )
& ( ! [X: $i] : ( p @ X )
=> ? [X: $i] : ( p @ X ) )
& ( ~ ? [Y: $i] : ( p @ Y )
=> ! [Y: $i] :
( ? [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
& ( ! [X: $i] :
( ( p @ X )
| c )
<=> ( ! [X: $i] : ( p @ X )
| c ) )
& ( ? [X: $i] :
( ( p @ X )
& c )
<=> ( ? [X: $i] : ( p @ X )
& c ) )
& ( ? [X: $i] : c
<=> c )
& ( ! [X: $i] : c
<=> c )
& ( ? [X: $i] :
( c
=> ( p @ X ) )
<=> ( c
=> ? [X: $i] : ( p @ X ) ) )
& ( ? [X: $i] :
( ( p @ X )
=> c )
<=> ( ! [X: $i] : ( p @ X )
=> c ) )
& ( ! [X: $i] :
( c
=> ( p @ X ) )
<=> ( c
=> ! [X: $i] : ( p @ X ) ) )
& ( ! [X: $i] :
( ( p @ X )
=> c )
<=> ( ? [X: $i] : ( p @ X )
=> c ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ! [X: $i] :
( ( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [Y: $i] :
( ( f @ Y )
& ~ ( g @ Y ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
& ( ( ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( r @ X @ Y )
& ( r @ Y @ Z ) )
=> ( r @ X @ Z ) ) )
=> ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ X @ X ) ) )
& ( ( ( ! [X: $i] :
( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [X: $i] :
( ( f @ X )
& ~ ( g @ X ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
& ? [X: $i] :
! [Y: $i] :
( ( ( p @ Y )
=> ( q @ X ) )
=> ( ( p @ X )
=> ( q @ X ) ) )
& ( ! [X: $i] :
( ( p @ X )
& ( q @ X ) )
<=> ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) ) )
& ( ( ! [X: $i] : ( p @ X )
| ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) )
& ( ? [X: $i] :
( ( p @ X )
| ( q @ X ) )
<=> ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) ) )
& ? [Y: $i] :
( ( p @ Y )
=> ! [X: $i] : ( p @ X ) )
& ( ? [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
& ? [X: $i] : ( q @ X ) ) )
& ! [Y: $i] :
( ! [X: $i] : ( p @ X )
=> ( p @ Y ) )
& ( ! [X: $i] : ( p @ X )
=> ? [X: $i] : ( p @ X ) )
& ( ~ ? [Y: $i] : ( p @ Y )
=> ! [Y: $i] :
( ? [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
& ( ! [X: $i] :
( ( p @ X )
| c )
<=> ( ! [X: $i] : ( p @ X )
| c ) )
& ( ? [X: $i] :
( ( p @ X )
& c )
<=> ( ? [X: $i] : ( p @ X )
& c ) )
& ( ? [X: $i] : c
<=> c )
& ( ! [X: $i] : c
<=> c )
& ( ? [X: $i] :
( c
=> ( p @ X ) )
<=> ( c
=> ? [X: $i] : ( p @ X ) ) )
& ( ? [X: $i] :
( ( p @ X )
=> c )
<=> ( ! [X: $i] : ( p @ X )
=> c ) )
& ( ! [X: $i] :
( c
=> ( p @ X ) )
<=> ( c
=> ! [X: $i] : ( p @ X ) ) )
& ( ! [X: $i] :
( ( p @ X )
=> c )
<=> ( ? [X: $i] : ( p @ X )
=> c ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ! [X: $i] :
( ( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [Y: $i] :
( ( f @ Y )
& ~ ( g @ Y ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ( ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( r @ X @ Y )
& ( r @ Y @ Z ) )
=> ( r @ X @ Z ) ) )
=> ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ X @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ( ( ! [X: $i] :
( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [X: $i] :
( ( f @ X )
& ~ ( g @ X ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(7,plain,
( ( ? [X: $i] :
! [Y: $i] :
( ( ( p @ Y )
=> ( q @ X ) )
=> ( ( p @ X )
=> ( q @ X ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(8,plain,
( ( ! [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(9,plain,
( ( ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
& ( q @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(10,plain,
( ( ( ! [X: $i] : ( p @ X )
| ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(11,plain,
( ( ? [X: $i] :
( ( p @ X )
| ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(12,plain,
( ( ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) )
=> ? [X: $i] :
( ( p @ X )
| ( q @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(13,plain,
( ( ? [Y: $i] :
( ( p @ Y )
=> ! [X: $i] : ( p @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(14,plain,
( ( ? [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
& ? [X: $i] : ( q @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(15,plain,
( ( ! [Y: $i] :
( ! [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(16,plain,
( ( ! [X: $i] : ( p @ X )
=> ? [X: $i] : ( p @ X ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(17,plain,
( ( ~ ? [Y: $i] : ( p @ Y )
=> ! [Y: $i] :
( ? [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(18,plain,
( ( ! [X: $i] :
( ( p @ X )
| c )
=> ( ! [X: $i] : ( p @ X )
| c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(19,plain,
( ( ( ! [X: $i] : ( p @ X )
| c )
=> ! [X: $i] :
( ( p @ X )
| c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(20,plain,
( ( ? [X: $i] :
( ( p @ X )
& c )
=> ( ? [X: $i] : ( p @ X )
& c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(21,plain,
( ( ( ? [X: $i] : ( p @ X )
& c )
=> ? [X: $i] :
( ( p @ X )
& c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(22,plain,
( ( ? [X: $i] : c
=> c )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(23,plain,
( ( c
=> ? [X: $i] : c )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(24,plain,
( ( ! [X: $i] : c
=> c )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(25,plain,
( ( c
=> ! [X: $i] : c )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(26,plain,
( ( ? [X: $i] :
( c
=> ( p @ X ) )
=> ( c
=> ? [X: $i] : ( p @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(27,plain,
( ( ( c
=> ? [X: $i] : ( p @ X ) )
=> ? [X: $i] :
( c
=> ( p @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(28,plain,
( ( ? [X: $i] :
( ( p @ X )
=> c )
=> ( ! [X: $i] : ( p @ X )
=> c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(29,plain,
( ( ( ! [X: $i] : ( p @ X )
=> c )
=> ? [X: $i] :
( ( p @ X )
=> c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(30,plain,
( ( ! [X: $i] :
( c
=> ( p @ X ) )
=> ( c
=> ! [X: $i] : ( p @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(31,plain,
( ( ( c
=> ! [X: $i] : ( p @ X ) )
=> ! [X: $i] :
( c
=> ( p @ X ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( p @ X )
=> c )
=> ( ? [X: $i] : ( p @ X )
=> c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(33,plain,
( ( ( ? [X: $i] : ( p @ X )
=> c )
=> ! [X: $i] :
( ( p @ X )
=> c ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(34,plain,
( ( ~ ( ( ! [X: $i] :
( ( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [Y: $i] :
( ( f @ Y )
& ~ ( g @ Y ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(35,plain,
( ( ~ ( ( ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( r @ X @ Y )
& ( r @ Y @ Z ) )
=> ( r @ X @ Z ) ) )
=> ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ X @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(36,plain,
( ( ~ ( ( ( ! [X: $i] :
( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [X: $i] :
( ( f @ X )
& ~ ( g @ X ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(37,plain,
( ( ~ ? [X: $i] :
! [Y: $i] :
( ( ( p @ Y )
=> ( q @ X ) )
=> ( ( p @ X )
=> ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(38,plain,
( ( ~ ( ! [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(39,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
& ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(40,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
| ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(41,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
| ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(42,plain,
( ( ~ ( ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) )
=> ? [X: $i] :
( ( p @ X )
| ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(43,plain,
( ( ~ ? [Y: $i] :
( ( p @ Y )
=> ! [X: $i] : ( p @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(44,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
& ? [X: $i] : ( q @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(45,plain,
( ( ~ ! [Y: $i] :
( ! [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(46,plain,
( ( ~ ( ! [X: $i] : ( p @ X )
=> ? [X: $i] : ( p @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(47,plain,
( ( ~ ( ~ ? [Y: $i] : ( p @ Y )
=> ! [Y: $i] :
( ? [X: $i] : ( p @ X )
=> ( p @ Y ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(48,plain,
( ( ~ ( ! [X: $i] :
( ( p @ X )
| c )
=> ( ! [X: $i] : ( p @ X )
| c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(49,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
| c )
=> ! [X: $i] :
( ( p @ X )
| c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(50,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
& c )
=> ( ? [X: $i] : ( p @ X )
& c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(51,plain,
( ( ~ ( ( ? [X: $i] : ( p @ X )
& c )
=> ? [X: $i] :
( ( p @ X )
& c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(52,plain,
( ( ~ ( ? [X: $i] : c
=> c ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(53,plain,
( ( ~ ( c
=> ? [X: $i] : c ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(54,plain,
( ( ~ ( ! [X: $i] : c
=> c ) )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(55,plain,
( ( ~ ( c
=> ! [X: $i] : c ) )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(56,plain,
( ( ~ ( ? [X: $i] :
( c
=> ( p @ X ) )
=> ( c
=> ? [X: $i] : ( p @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(57,plain,
( ( ~ ( ( c
=> ? [X: $i] : ( p @ X ) )
=> ? [X: $i] :
( c
=> ( p @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(58,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
=> c )
=> ( ! [X: $i] : ( p @ X )
=> c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(59,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
=> c )
=> ? [X: $i] :
( ( p @ X )
=> c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(60,plain,
( ( ~ ( ! [X: $i] :
( c
=> ( p @ X ) )
=> ( c
=> ! [X: $i] : ( p @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(61,plain,
( ( ~ ( ( c
=> ! [X: $i] : ( p @ X ) )
=> ! [X: $i] :
( c
=> ( p @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(62,plain,
( ( ~ ( ! [X: $i] :
( ( p @ X )
=> c )
=> ( ? [X: $i] : ( p @ X )
=> c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(63,plain,
( ( ~ ( ( ? [X: $i] : ( p @ X )
=> c )
=> ! [X: $i] :
( ( p @ X )
=> c ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(64,plain,
( ( ~ ( ( ! [X: $i] :
( ( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [Y: $i] :
( ( f @ Y )
& ~ ( g @ Y ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(65,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(67,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(68,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(69,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(70,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(71,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(72,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(74,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(75,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( f @ SV1 )
| ~ ( h @ SV1 ) )
| ( g @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( f @ SV2 )
| ~ ( g @ SV2 ) )
| ~ ~ ( h @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( f @ SV1 )
| ~ ( h @ SV1 ) ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( f @ SV2 )
| ~ ( g @ SV2 ) )
| ~ ~ ( h @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV3: $i] :
( ( ~ ( ~ ~ ( ~ ( f @ SV3 )
| ~ ( g @ SV3 ) )
| ( h @ SV3 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
( ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( f @ SV1 )
| ~ ( h @ SV1 ) ) )
= $false )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ( f @ SV2 )
| ~ ( g @ SV2 ) )
| ~ ~ ( h @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( f @ SV3 )
| ~ ( g @ SV3 ) )
| ( h @ SV3 ) ) )
= $true )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV4: $i] :
( ( ( ~ ( f @ SV4 )
| ( g @ SV4 ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV1: $i] :
( ( ( ~ ( f @ SV1 )
| ~ ( h @ SV1 ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( f @ SV2 )
| ~ ( g @ SV2 ) ) )
= $true )
| ( ( ~ ~ ( h @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( f @ SV3 )
| ~ ( g @ SV3 ) )
| ( h @ SV3 ) )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV4: $i] :
( ( ( ~ ( f @ SV4 ) )
= $true )
| ( ( g @ SV4 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV1: $i] :
( ( ( ~ ( f @ SV1 ) )
= $true )
| ( ( ~ ( h @ SV1 ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( f @ SV2 )
| ~ ( g @ SV2 ) ) )
= $false )
| ( ( ~ ~ ( h @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(95,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( f @ SV3 )
| ~ ( g @ SV3 ) ) )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV3: $i] :
( ( ( h @ SV3 )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(97,plain,
! [SV4: $i] :
( ( ( f @ SV4 )
= $false )
| ( ( g @ SV4 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV1: $i] :
( ( ( f @ SV1 )
= $false )
| ( ( ~ ( h @ SV1 ) )
= $true )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV2: $i] :
( ( ( ~ ( f @ SV2 )
| ~ ( g @ SV2 ) )
= $true )
| ( ( ~ ~ ( h @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( f @ SV3 )
| ~ ( g @ SV3 ) ) )
= $true )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV3: $i] :
( ( ( ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $false )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV4: $i,SV5: $i] :
( ( ( ~ ( f @ SV5 )
| ( h @ SV5 ) )
= $true )
| ( ( g @ SV4 )
= $true )
| ( ( f @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( h @ SV1 )
= $false )
| ( ( f @ SV1 )
= $false )
| ( ( g @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV2: $i] :
( ( ( ~ ( f @ SV2 ) )
= $true )
| ( ( ~ ( g @ SV2 ) )
= $true )
| ( ( ~ ~ ( h @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV3: $i] :
( ( ( ~ ( f @ SV3 )
| ~ ( g @ SV3 ) )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( f @ ( sK1_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK1_SX1 @ SV3 ) ) ) )
= $false )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(107,plain,
! [SV4: $i,SV5: $i] :
( ( ( ~ ( f @ SV5 ) )
= $true )
| ( ( h @ SV5 )
= $true )
| ( ( g @ SV4 )
= $true )
| ( ( f @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV2: $i] :
( ( ( f @ SV2 )
= $false )
| ( ( ~ ( g @ SV2 ) )
= $true )
| ( ( ~ ~ ( h @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV3: $i] :
( ( ( ~ ( f @ SV3 ) )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(110,plain,
! [SV3: $i] :
( ( ( ~ ( g @ SV3 ) )
= $false )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[105]) ).
thf(111,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( f @ ( sK1_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK1_SX1 @ SV3 ) ) ) )
= $true )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(112,plain,
! [SV4: $i,SV5: $i] :
( ( ( f @ SV5 )
= $false )
| ( ( h @ SV5 )
= $true )
| ( ( g @ SV4 )
= $true )
| ( ( f @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(113,plain,
! [SV2: $i] :
( ( ( g @ SV2 )
= $false )
| ( ( f @ SV2 )
= $false )
| ( ( ~ ~ ( h @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV3: $i] :
( ( ( f @ SV3 )
= $true )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(115,plain,
! [SV3: $i] :
( ( ( g @ SV3 )
= $true )
| ( ( ~ ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(116,plain,
! [SV3: $i] :
( ( ( ~ ( f @ ( sK1_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK1_SX1 @ SV3 ) ) )
= $false )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(117,plain,
! [SV2: $i] :
( ( ( ~ ( h @ SV2 ) )
= $false )
| ( ( f @ SV2 )
= $false )
| ( ( g @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV3: $i] :
( ( ( ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $false )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV3: $i] :
( ( ( ! [SX1: $i] :
~ ~ ( ~ ( f @ SX1 )
| ~ ~ ( g @ SX1 ) ) )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(120,plain,
! [SV3: $i] :
( ( ( ~ ( f @ ( sK1_SX1 @ SV3 ) ) )
= $false )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(121,plain,
! [SV3: $i] :
( ( ( ~ ~ ( g @ ( sK1_SX1 @ SV3 ) ) )
= $false )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV2: $i] :
( ( ( h @ SV2 )
= $true )
| ( ( f @ SV2 )
= $false )
| ( ( g @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( f @ ( sK2_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK2_SX1 @ SV3 ) ) ) )
= $false )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(124,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ( f @ ( sK3_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK3_SX1 @ SV3 ) ) ) )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(125,plain,
! [SV3: $i] :
( ( ( f @ ( sK1_SX1 @ SV3 ) )
= $true )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(126,plain,
! [SV3: $i] :
( ( ( ~ ( g @ ( sK1_SX1 @ SV3 ) ) )
= $true )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(127,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( f @ ( sK2_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK2_SX1 @ SV3 ) ) ) )
= $true )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(128,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ( f @ ( sK3_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK3_SX1 @ SV3 ) ) ) )
= $true )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(129,plain,
! [SV3: $i] :
( ( ( g @ ( sK1_SX1 @ SV3 ) )
= $false )
| ( ( h @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV3: $i] :
( ( ( ~ ( f @ ( sK2_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK2_SX1 @ SV3 ) ) )
= $false )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV3: $i] :
( ( ( ~ ( f @ ( sK3_SX1 @ SV3 ) )
| ~ ~ ( g @ ( sK3_SX1 @ SV3 ) ) )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV3: $i] :
( ( ( ~ ( f @ ( sK2_SX1 @ SV3 ) ) )
= $false )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(133,plain,
! [SV3: $i] :
( ( ( ~ ~ ( g @ ( sK2_SX1 @ SV3 ) ) )
= $false )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(134,plain,
! [SV3: $i] :
( ( ( ~ ( f @ ( sK3_SX1 @ SV3 ) ) )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(135,plain,
! [SV3: $i] :
( ( ( ~ ~ ( g @ ( sK3_SX1 @ SV3 ) ) )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(136,plain,
! [SV3: $i] :
( ( ( f @ ( sK2_SX1 @ SV3 ) )
= $true )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(137,plain,
! [SV3: $i] :
( ( ( ~ ( g @ ( sK2_SX1 @ SV3 ) ) )
= $true )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(138,plain,
! [SV3: $i] :
( ( ( f @ ( sK3_SX1 @ SV3 ) )
= $true )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(139,plain,
! [SV3: $i] :
( ( ( ~ ( g @ ( sK3_SX1 @ SV3 ) ) )
= $true )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(140,plain,
! [SV3: $i] :
( ( ( g @ ( sK2_SX1 @ SV3 ) )
= $false )
| ( ( f @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV3: $i] :
( ( ( g @ ( sK3_SX1 @ SV3 ) )
= $false )
| ( ( g @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(142,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[103,141,140,138,136,129,125,122,112]) ).
thf(143,plain,
( ( ~ ( ( ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ Y @ X ) )
& ! [X: $i,Y: $i,Z: $i] :
( ( ( r @ X @ Y )
& ( r @ Y @ Z ) )
=> ( r @ X @ Z ) ) )
=> ! [X: $i,Y: $i] :
( ( r @ X @ Y )
=> ( r @ X @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(144,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(145,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(146,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(148,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(149,plain,
( ( ! [SY57: $i] :
( ~ ( r @ sK4_SX0 @ SY57 )
| ( r @ sK4_SX0 @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(150,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(151,plain,
( ( ~ ( r @ sK4_SX0 @ sK5_SY57 )
| ( r @ sK4_SX0 @ sK4_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[149]) ).
thf(152,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(153,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(154,plain,
( ( ~ ( r @ sK4_SX0 @ sK5_SY57 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(155,plain,
( ( r @ sK4_SX0 @ sK4_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( r @ SX0 @ SX1 )
| ( r @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( r @ SX0 @ SX1 )
| ~ ( r @ SX1 @ SX2 ) )
| ( r @ SX0 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(158,plain,
( ( r @ sK4_SX0 @ sK5_SY57 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(159,plain,
! [SV6: $i] :
( ( ! [SY58: $i] :
( ~ ( r @ SV6 @ SY58 )
| ( r @ SY58 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(160,plain,
! [SV7: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ~ ( ~ ( r @ SV7 @ SY59 )
| ~ ( r @ SY59 @ SY60 ) )
| ( r @ SV7 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV8: $i,SV6: $i] :
( ( ~ ( r @ SV6 @ SV8 )
| ( r @ SV8 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(162,plain,
! [SV9: $i,SV7: $i] :
( ( ! [SY61: $i] :
( ~ ~ ( ~ ( r @ SV7 @ SV9 )
| ~ ( r @ SV9 @ SY61 ) )
| ( r @ SV7 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(163,plain,
! [SV8: $i,SV6: $i] :
( ( ( ~ ( r @ SV6 @ SV8 ) )
= $true )
| ( ( r @ SV8 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(164,plain,
! [SV10: $i,SV9: $i,SV7: $i] :
( ( ~ ~ ( ~ ( r @ SV7 @ SV9 )
| ~ ( r @ SV9 @ SV10 ) )
| ( r @ SV7 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(165,plain,
! [SV8: $i,SV6: $i] :
( ( ( r @ SV6 @ SV8 )
= $false )
| ( ( r @ SV8 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(166,plain,
! [SV10: $i,SV9: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( r @ SV7 @ SV9 )
| ~ ( r @ SV9 @ SV10 ) ) )
= $true )
| ( ( r @ SV7 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(167,plain,
! [SV10: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( ~ ( r @ SV7 @ SV9 )
| ~ ( r @ SV9 @ SV10 ) ) )
= $false )
| ( ( r @ SV7 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(168,plain,
! [SV10: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( r @ SV7 @ SV9 )
| ~ ( r @ SV9 @ SV10 ) )
= $true )
| ( ( r @ SV7 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(169,plain,
! [SV10: $i,SV9: $i,SV7: $i] :
( ( ( ~ ( r @ SV7 @ SV9 ) )
= $true )
| ( ( ~ ( r @ SV9 @ SV10 ) )
= $true )
| ( ( r @ SV7 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(170,plain,
! [SV10: $i,SV9: $i,SV7: $i] :
( ( ( r @ SV7 @ SV9 )
= $false )
| ( ( ~ ( r @ SV9 @ SV10 ) )
= $true )
| ( ( r @ SV7 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(171,plain,
! [SV7: $i,SV10: $i,SV9: $i] :
( ( ( r @ SV9 @ SV10 )
= $false )
| ( ( r @ SV7 @ SV9 )
= $false )
| ( ( r @ SV7 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(172,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[155,171,165,158]) ).
thf(173,plain,
( ( ~ ( ( ( ! [X: $i] :
( ( ( f @ X )
& ( g @ X ) )
=> ( h @ X ) )
=> ? [X: $i] :
( ( f @ X )
& ~ ( g @ X ) ) )
& ( ! [W: $i] :
( ( f @ W )
=> ( g @ W ) )
| ! [Z: $i] :
( ( f @ Z )
=> ( h @ Z ) ) ) )
=> ( ! [R: $i] :
( ( ( f @ R )
& ( h @ R ) )
=> ( g @ R ) )
=> ? [V: $i] :
( ( f @ V )
& ( g @ V )
& ~ ( h @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(174,plain,
( ( ~ ( ~ ~ ( ~ ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(175,plain,
( ( ~ ~ ( ~ ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(176,plain,
( ( ~ ~ ( ~ ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(177,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(178,plain,
( ( ~ ( ~ ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(179,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(180,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(181,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
| ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( h @ SX0 ) )
| ( g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(183,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ~ ~ ( h @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(184,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(185,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(186,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( f @ SV11 )
| ~ ( h @ SV11 ) )
| ( g @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(187,plain,
! [SV12: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( f @ SV12 )
| ~ ( g @ SV12 ) )
| ~ ~ ( h @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(188,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(189,plain,
( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) )
| ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(190,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( f @ SV11 )
| ~ ( h @ SV11 ) ) )
= $true )
| ( ( g @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(191,plain,
! [SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( f @ SV12 )
| ~ ( g @ SV12 ) )
| ~ ~ ( h @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(192,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(193,plain,
( ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( g @ SX0 ) ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(194,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( f @ SV11 )
| ~ ( h @ SV11 ) ) )
= $false )
| ( ( g @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(195,plain,
! [SV12: $i] :
( ( ~ ~ ( ~ ( f @ SV12 )
| ~ ( g @ SV12 ) )
| ~ ~ ( h @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(196,plain,
( ( ( ! [SX0: $i] :
( ~ ~ ( ~ ( f @ SX0 )
| ~ ( g @ SX0 ) )
| ( h @ SX0 ) ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(197,plain,
! [SV13: $i] :
( ( ( ~ ( f @ SV13 )
| ( g @ SV13 ) )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(198,plain,
! [SV11: $i] :
( ( ( ~ ( f @ SV11 )
| ~ ( h @ SV11 ) )
= $true )
| ( ( g @ SV11 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(199,plain,
! [SV12: $i] :
( ( ( ~ ~ ( ~ ( f @ SV12 )
| ~ ( g @ SV12 ) ) )
= $true )
| ( ( ~ ~ ( h @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(200,plain,
( ( ( ~ ~ ( ~ ( f @ sK6_SX0 )
| ~ ( g @ sK6_SX0 ) )
| ( h @ sK6_SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[196]) ).
thf(201,plain,
! [SV13: $i] :
( ( ( ~ ( f @ SV13 ) )
= $true )
| ( ( g @ SV13 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(202,plain,
! [SV11: $i] :
( ( ( ~ ( f @ SV11 ) )
= $true )
| ( ( ~ ( h @ SV11 ) )
= $true )
| ( ( g @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV12: $i] :
( ( ( ~ ( ~ ( f @ SV12 )
| ~ ( g @ SV12 ) ) )
= $false )
| ( ( ~ ~ ( h @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(204,plain,
( ( ( ~ ~ ( ~ ( f @ sK6_SX0 )
| ~ ( g @ sK6_SX0 ) ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(205,plain,
( ( ( h @ sK6_SX0 )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(206,plain,
! [SV13: $i] :
( ( ( f @ SV13 )
= $false )
| ( ( g @ SV13 )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( f @ SX0 )
| ( h @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(207,plain,
! [SV11: $i] :
( ( ( f @ SV11 )
= $false )
| ( ( ~ ( h @ SV11 ) )
= $true )
| ( ( g @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV12: $i] :
( ( ( ~ ( f @ SV12 )
| ~ ( g @ SV12 ) )
= $true )
| ( ( ~ ~ ( h @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(209,plain,
( ( ( ~ ( ~ ( f @ sK6_SX0 )
| ~ ( g @ sK6_SX0 ) ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(210,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $false )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(211,plain,
! [SV13: $i,SV14: $i] :
( ( ( ~ ( f @ SV14 )
| ( h @ SV14 ) )
= $true )
| ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(212,plain,
! [SV11: $i] :
( ( ( h @ SV11 )
= $false )
| ( ( f @ SV11 )
= $false )
| ( ( g @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(213,plain,
! [SV12: $i] :
( ( ( ~ ( f @ SV12 ) )
= $true )
| ( ( ~ ( g @ SV12 ) )
= $true )
| ( ( ~ ~ ( h @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(214,plain,
( ( ( ~ ( f @ sK6_SX0 )
| ~ ( g @ sK6_SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(215,plain,
( ( ( ~ ~ ( ~ ( f @ sK7_SX0 )
| ~ ~ ( g @ sK7_SX0 ) ) )
= $false )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(216,plain,
! [SV13: $i,SV14: $i] :
( ( ( ~ ( f @ SV14 ) )
= $true )
| ( ( h @ SV14 )
= $true )
| ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(217,plain,
! [SV12: $i] :
( ( ( f @ SV12 )
= $false )
| ( ( ~ ( g @ SV12 ) )
= $true )
| ( ( ~ ~ ( h @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(218,plain,
( ( ( ~ ( f @ sK6_SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(219,plain,
( ( ( ~ ( g @ sK6_SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(220,plain,
( ( ( ~ ( ~ ( f @ sK7_SX0 )
| ~ ~ ( g @ sK7_SX0 ) ) )
= $true )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(221,plain,
! [SV13: $i,SV14: $i] :
( ( ( f @ SV14 )
= $false )
| ( ( h @ SV14 )
= $true )
| ( ( g @ SV13 )
= $true )
| ( ( f @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(222,plain,
! [SV12: $i] :
( ( ( g @ SV12 )
= $false )
| ( ( f @ SV12 )
= $false )
| ( ( ~ ~ ( h @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(223,plain,
( ( ( f @ sK6_SX0 )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(224,plain,
( ( ( g @ sK6_SX0 )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(225,plain,
( ( ( ~ ( f @ sK7_SX0 )
| ~ ~ ( g @ sK7_SX0 ) )
= $false )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV12: $i] :
( ( ( ~ ( h @ SV12 ) )
= $false )
| ( ( f @ SV12 )
= $false )
| ( ( g @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(227,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $false )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(228,plain,
( ( ( ! [SX0: $i] :
~ ~ ( ~ ( f @ SX0 )
| ~ ~ ( g @ SX0 ) ) )
= $false )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(229,plain,
( ( ( ~ ( f @ sK7_SX0 ) )
= $false )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(230,plain,
( ( ( ~ ~ ( g @ sK7_SX0 ) )
= $false )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(231,plain,
! [SV12: $i] :
( ( ( h @ SV12 )
= $true )
| ( ( f @ SV12 )
= $false )
| ( ( g @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(232,plain,
( ( ( ~ ~ ( ~ ( f @ sK8_SX0 )
| ~ ~ ( g @ sK8_SX0 ) ) )
= $false )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[227]) ).
thf(233,plain,
( ( ( ~ ~ ( ~ ( f @ sK9_SX0 )
| ~ ~ ( g @ sK9_SX0 ) ) )
= $false )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[228]) ).
thf(234,plain,
( ( ( f @ sK7_SX0 )
= $true )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(235,plain,
( ( ( ~ ( g @ sK7_SX0 ) )
= $true )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(236,plain,
( ( ( ~ ( ~ ( f @ sK8_SX0 )
| ~ ~ ( g @ sK8_SX0 ) ) )
= $true )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(237,plain,
( ( ( ~ ( ~ ( f @ sK9_SX0 )
| ~ ~ ( g @ sK9_SX0 ) ) )
= $true )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(238,plain,
( ( ( g @ sK7_SX0 )
= $false )
| ( ( h @ sK6_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(239,plain,
( ( ( ~ ( f @ sK8_SX0 )
| ~ ~ ( g @ sK8_SX0 ) )
= $false )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(240,plain,
( ( ( ~ ( f @ sK9_SX0 )
| ~ ~ ( g @ sK9_SX0 ) )
= $false )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(241,plain,
( ( ( ~ ( f @ sK8_SX0 ) )
= $false )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(242,plain,
( ( ( ~ ~ ( g @ sK8_SX0 ) )
= $false )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(243,plain,
( ( ( ~ ( f @ sK9_SX0 ) )
= $false )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(244,plain,
( ( ( ~ ~ ( g @ sK9_SX0 ) )
= $false )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(245,plain,
( ( ( f @ sK8_SX0 )
= $true )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(246,plain,
( ( ( ~ ( g @ sK8_SX0 ) )
= $true )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(247,plain,
( ( ( f @ sK9_SX0 )
= $true )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(248,plain,
( ( ( ~ ( g @ sK9_SX0 ) )
= $true )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(249,plain,
( ( ( g @ sK8_SX0 )
= $false )
| ( ( f @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(250,plain,
( ( ( g @ sK9_SX0 )
= $false )
| ( ( g @ sK6_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(251,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[212,250,249,247,245,238,234,231,221]) ).
thf(252,plain,
( ( ~ ? [X: $i] :
! [Y: $i] :
( ( ( p @ Y )
=> ( q @ X ) )
=> ( ( p @ X )
=> ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(253,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ( p @ SX1 )
| ( q @ SX0 ) )
| ~ ( p @ SX0 )
| ( q @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(254,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ( p @ SX1 )
| ( q @ SX0 ) )
| ~ ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(255,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
( ~ ( ~ ( p @ SX1 )
| ( q @ SX0 ) )
| ~ ( p @ SX0 )
| ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(256,plain,
! [SV15: $i] :
( ( ~ ! [SY62: $i] :
( ~ ( ~ ( p @ SY62 )
| ( q @ SV15 ) )
| ~ ( p @ SV15 )
| ( q @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(257,plain,
! [SV15: $i] :
( ( ! [SY62: $i] :
( ~ ( ~ ( p @ SY62 )
| ( q @ SV15 ) )
| ~ ( p @ SV15 )
| ( q @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(258,plain,
! [SV15: $i] :
( ( ~ ( ~ ( p @ ( sK10_SY62 @ SV15 ) )
| ( q @ SV15 ) )
| ~ ( p @ SV15 )
| ( q @ SV15 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[257]) ).
thf(259,plain,
! [SV15: $i] :
( ( ~ ( ~ ( p @ ( sK10_SY62 @ SV15 ) )
| ( q @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(260,plain,
! [SV15: $i] :
( ( ~ ( p @ SV15 )
| ( q @ SV15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(261,plain,
! [SV15: $i] :
( ( ~ ( p @ ( sK10_SY62 @ SV15 ) )
| ( q @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(262,plain,
! [SV15: $i] :
( ( ~ ( p @ SV15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(263,plain,
! [SV15: $i] :
( ( q @ SV15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(264,plain,
! [SV15: $i] :
( ( ( ~ ( p @ ( sK10_SY62 @ SV15 ) ) )
= $true )
| ( ( q @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(265,plain,
! [SV15: $i] :
( ( p @ SV15 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(266,plain,
! [SV15: $i] :
( ( ( p @ ( sK10_SY62 @ SV15 ) )
= $false )
| ( ( q @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(267,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[263,266,265]) ).
thf(268,plain,
( ( ~ ( ! [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(269,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(270,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(271,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(272,plain,
( ( ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(273,plain,
( ( ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(274,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(275,plain,
! [SV16: $i] :
( ( ~ ( ~ ( p @ SV16 )
| ~ ( q @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(276,plain,
( ( ( ~ ! [SX0: $i] : ( p @ SX0 ) )
= $true )
| ( ( ~ ! [SX0: $i] : ( q @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(277,plain,
! [SV16: $i] :
( ( ~ ( p @ SV16 )
| ~ ( q @ SV16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(278,plain,
( ( ( ! [SX0: $i] : ( p @ SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] : ( q @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(279,plain,
! [SV16: $i] :
( ( ~ ( p @ SV16 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(280,plain,
! [SV16: $i] :
( ( ~ ( q @ SV16 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(281,plain,
( ( ( p @ sK11_SX0 )
= $false )
| ( ( ~ ! [SX0: $i] : ( q @ SX0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[278]) ).
thf(282,plain,
! [SV16: $i] :
( ( p @ SV16 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(283,plain,
! [SV16: $i] :
( ( q @ SV16 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(284,plain,
( ( ( ! [SX0: $i] : ( q @ SX0 ) )
= $false )
| ( ( p @ sK11_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(285,plain,
( ( ( q @ sK12_SX0 )
= $false )
| ( ( p @ sK11_SX0 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[284]) ).
thf(286,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[282,285,283]) ).
thf(287,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
& ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
& ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(288,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) )
| ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(289,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) )
| ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(290,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(291,plain,
( ( ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(292,plain,
( ( ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(293,plain,
( ( ~ ( ~ ( p @ sK13_SX0 )
| ~ ( q @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[291]) ).
thf(294,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] : ( q @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(295,plain,
( ( ~ ( p @ sK13_SX0 )
| ~ ( q @ sK13_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(296,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(297,plain,
( ( ~ ! [SX0: $i] : ( q @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(298,plain,
( ( ( ~ ( p @ sK13_SX0 ) )
= $true )
| ( ( ~ ( q @ sK13_SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(299,plain,
( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(300,plain,
( ( ! [SX0: $i] : ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(301,plain,
( ( ( p @ sK13_SX0 )
= $false )
| ( ( ~ ( q @ sK13_SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(302,plain,
! [SV17: $i] :
( ( p @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(303,plain,
! [SV18: $i] :
( ( q @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(304,plain,
( ( ( q @ sK13_SX0 )
= $false )
| ( ( p @ sK13_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(305,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[302,304,303]) ).
thf(306,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
| ! [X: $i] : ( q @ X ) )
=> ! [X: $i] :
( ( p @ X )
| ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(307,plain,
( ( ~ ( ~ ( ! [SX0: $i] : ( p @ SX0 )
| ! [SX0: $i] : ( q @ SX0 ) )
| ! [SX0: $i] :
( ( p @ SX0 )
| ( q @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(308,plain,
( ( ~ ( ! [SX0: $i] : ( p @ SX0 )
| ! [SX0: $i] : ( q @ SX0 ) )
| ! [SX0: $i] :
( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(309,plain,
( ( ~ ( ! [SX0: $i] : ( p @ SX0 )
| ! [SX0: $i] : ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(310,plain,
( ( ! [SX0: $i] :
( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(311,plain,
( ( ! [SX0: $i] : ( p @ SX0 )
| ! [SX0: $i] : ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(312,plain,
( ( ( p @ sK14_SX0 )
| ( q @ sK14_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[310]) ).
thf(313,plain,
( ( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true )
| ( ( ! [SX0: $i] : ( q @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(314,plain,
( ( p @ sK14_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(315,plain,
( ( q @ sK14_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(316,plain,
! [SV19: $i] :
( ( ( p @ SV19 )
= $true )
| ( ( ! [SX0: $i] : ( q @ SX0 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(317,plain,
! [SV19: $i,SV20: $i] :
( ( ( q @ SV20 )
= $true )
| ( ( p @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(318,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[314,317,315]) ).
thf(319,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
| ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(320,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) )
| ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(321,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) )
| ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(322,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(323,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(324,plain,
( ( ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(325,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(326,plain,
( ( ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(327,plain,
( ( ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(328,plain,
( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(329,plain,
( ( ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(330,plain,
( ( ~ ( ( p @ sK15_SX0 )
| ( q @ sK15_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[327]) ).
thf(331,plain,
! [SV21: $i] :
( ( ~ ( p @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(332,plain,
! [SV22: $i] :
( ( ~ ( q @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(333,plain,
( ( ( p @ sK15_SX0 )
| ( q @ sK15_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(334,plain,
! [SV21: $i] :
( ( p @ SV21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(335,plain,
! [SV22: $i] :
( ( q @ SV22 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(336,plain,
( ( ( p @ sK15_SX0 )
= $true )
| ( ( q @ sK15_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(337,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[334,336,335]) ).
thf(338,plain,
( ( ~ ( ( ? [X: $i] : ( p @ X )
| ? [X: $i] : ( q @ X ) )
=> ? [X: $i] :
( ( p @ X )
| ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(339,plain,
( ( ~ ( ~ ( ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(340,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
| ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(341,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(342,plain,
( ( ~ ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(343,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(344,plain,
( ( ! [SX0: $i] :
~ ( ( p @ SX0 )
| ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(345,plain,
( ( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(346,plain,
! [SV23: $i] :
( ( ~ ( ( p @ SV23 )
| ( q @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(347,plain,
( ( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(348,plain,
! [SV23: $i] :
( ( ( p @ SV23 )
| ( q @ SV23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(349,plain,
( ( ( ~ ( p @ sK16_SX0 ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[347]) ).
thf(350,plain,
! [SV23: $i] :
( ( p @ SV23 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(351,plain,
! [SV23: $i] :
( ( q @ SV23 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(352,plain,
( ( ( p @ sK16_SX0 )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(353,plain,
( ( ( ! [SX0: $i] :
~ ( q @ SX0 ) )
= $false )
| ( ( p @ sK16_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(354,plain,
( ( ( ~ ( q @ sK17_SX0 ) )
= $false )
| ( ( p @ sK16_SX0 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[353]) ).
thf(355,plain,
( ( ( q @ sK17_SX0 )
= $true )
| ( ( p @ sK16_SX0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(356,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[350,355,351]) ).
thf(357,plain,
( ( ~ ? [Y: $i] :
( ( p @ Y )
=> ! [X: $i] : ( p @ X ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(358,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ! [SX1: $i] : ( p @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(359,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ! [SX1: $i] : ( p @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(360,plain,
( ( ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| ! [SX1: $i] : ( p @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(361,plain,
! [SV24: $i] :
( ( ~ ( ~ ( p @ SV24 )
| ! [SX1: $i] : ( p @ SX1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(362,plain,
! [SV24: $i] :
( ( ~ ( p @ SV24 )
| ! [SX1: $i] : ( p @ SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(363,plain,
! [SV24: $i] :
( ( ~ ( p @ SV24 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(364,plain,
( ( ! [SX1: $i] : ( p @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(365,plain,
! [SV24: $i] :
( ( p @ SV24 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(366,plain,
( ( p @ sK18_SX1 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[364]) ).
thf(367,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[365,366]) ).
thf(368,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
& ( q @ X ) )
=> ( ? [X: $i] : ( p @ X )
& ? [X: $i] : ( q @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(369,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(370,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) )
| ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(371,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(372,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(373,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(374,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(375,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ ( q @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(376,plain,
( ( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(377,plain,
( ( ~ ~ ( ~ ( p @ sK19_SX0 )
| ~ ( q @ sK19_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(378,plain,
( ( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false )
| ( ( ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(379,plain,
( ( ~ ( ~ ( p @ sK19_SX0 )
| ~ ( q @ sK19_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(380,plain,
( ( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(381,plain,
( ( ~ ( p @ sK19_SX0 )
| ~ ( q @ sK19_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(382,plain,
! [SV25: $i] :
( ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(383,plain,
( ( ~ ( p @ sK19_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(384,plain,
( ( ~ ( q @ sK19_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(385,plain,
! [SV25: $i] :
( ( ( p @ SV25 )
= $false )
| ( ( ~ ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(386,plain,
( ( p @ sK19_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(387,plain,
( ( q @ sK19_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(388,plain,
! [SV25: $i] :
( ( ( ~ ! [SX0: $i] :
~ ( q @ SX0 ) )
= $false )
| ( ( p @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(389,plain,
! [SV25: $i] :
( ( ( ! [SX0: $i] :
~ ( q @ SX0 ) )
= $true )
| ( ( p @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(390,plain,
! [SV25: $i,SV26: $i] :
( ( ( ~ ( q @ SV26 ) )
= $true )
| ( ( p @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(391,plain,
! [SV25: $i,SV26: $i] :
( ( ( q @ SV26 )
= $false )
| ( ( p @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(392,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[386,391,387]) ).
thf(393,plain,
( ( ~ ! [Y: $i] :
( ! [X: $i] : ( p @ X )
=> ( p @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(394,plain,
( ( ~ ! [SX0: $i] :
( ~ ! [SX1: $i] : ( p @ SX1 )
| ( p @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(395,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] : ( p @ SX1 )
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(396,plain,
( ( ~ ! [SX1: $i] : ( p @ SX1 )
| ( p @ sK20_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[395]) ).
thf(397,plain,
( ( ~ ! [SX1: $i] : ( p @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(398,plain,
( ( p @ sK20_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(399,plain,
( ( ! [SX1: $i] : ( p @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(400,plain,
! [SV27: $i] :
( ( p @ SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(401,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[398,400]) ).
thf(402,plain,
( ( ~ ( ! [X: $i] : ( p @ X )
=> ? [X: $i] : ( p @ X ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(403,plain,
( ( ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(404,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 )
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(405,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(406,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(407,plain,
( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(408,plain,
( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(409,plain,
! [SV28: $i] :
( ( p @ SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(410,plain,
! [SV29: $i] :
( ( ~ ( p @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(411,plain,
! [SV29: $i] :
( ( p @ SV29 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(412,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[409,411]) ).
thf(413,plain,
( ( ~ ( ~ ? [Y: $i] : ( p @ Y )
=> ! [Y: $i] :
( ? [X: $i] : ( p @ X )
=> ( p @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(414,plain,
( ( ~ ( ~ ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( p @ SX1 )
| ( p @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(415,plain,
( ( ~ ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( p @ SX1 )
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(416,plain,
( ( ~ ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(417,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( p @ SX1 )
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(418,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(419,plain,
( ( ~ ~ ! [SX1: $i] :
~ ( p @ SX1 )
| ( p @ sK21_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[417]) ).
thf(420,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(421,plain,
( ( ~ ~ ! [SX1: $i] :
~ ( p @ SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(422,plain,
( ( p @ sK21_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(423,plain,
( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(424,plain,
( ( ~ ! [SX1: $i] :
~ ( p @ SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(425,plain,
! [SV30: $i] :
( ( ~ ( p @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(426,plain,
( ( ! [SX1: $i] :
~ ( p @ SX1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(427,plain,
! [SV30: $i] :
( ( p @ SV30 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(428,plain,
( ( ~ ( p @ sK22_SX1 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[426]) ).
thf(429,plain,
( ( p @ sK22_SX1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(430,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[422,429,427]) ).
thf(431,plain,
( ( ~ ( ! [X: $i] :
( ( p @ X )
| c )
=> ( ! [X: $i] : ( p @ X )
| c ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(432,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( p @ SX0 )
| c )
| ! [SX0: $i] : ( p @ SX0 )
| c ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(433,plain,
( ( ~ ! [SX0: $i] :
( ( p @ SX0 )
| c )
| ! [SX0: $i] : ( p @ SX0 )
| c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(434,plain,
( ( ~ ! [SX0: $i] :
( ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(435,plain,
( ( ! [SX0: $i] : ( p @ SX0 )
| c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(436,plain,
( ( ! [SX0: $i] :
( ( p @ SX0 )
| c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(437,plain,
( ( ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(438,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(439,plain,
! [SV31: $i] :
( ( ( p @ SV31 )
| c )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(440,plain,
( ( p @ sK23_SX0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[437]) ).
thf(441,plain,
! [SV31: $i] :
( ( ( p @ SV31 )
= $true )
| ( c = $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(442,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[438,441,440]) ).
thf(443,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
| c )
=> ! [X: $i] :
( ( p @ X )
| c ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(444,plain,
( ( ~ ( ~ ( ! [SX0: $i] : ( p @ SX0 )
| c )
| ! [SX0: $i] :
( ( p @ SX0 )
| c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(445,plain,
( ( ~ ( ! [SX0: $i] : ( p @ SX0 )
| c )
| ! [SX0: $i] :
( ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(446,plain,
( ( ~ ( ! [SX0: $i] : ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(447,plain,
( ( ! [SX0: $i] :
( ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(448,plain,
( ( ! [SX0: $i] : ( p @ SX0 )
| c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(449,plain,
( ( ( p @ sK24_SX0 )
| c )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[447]) ).
thf(450,plain,
( ( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(451,plain,
( ( p @ sK24_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(452,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(453,plain,
! [SV32: $i] :
( ( ( p @ SV32 )
= $true )
| ( c = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(454,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[451,453,452]) ).
thf(455,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
& c )
=> ( ? [X: $i] : ( p @ X )
& c ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(456,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c )
| ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(457,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c )
| ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(458,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(459,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(460,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(461,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(462,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(463,plain,
( ( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( ( ~ c ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(464,plain,
( ( ~ ~ ( ~ ( p @ sK25_SX0 )
| ~ c ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[462]) ).
thf(465,plain,
( ( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false )
| ( ( ~ c ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(466,plain,
( ( ~ ( ~ ( p @ sK25_SX0 )
| ~ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(467,plain,
( ( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( ( ~ c ) = $true ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(468,plain,
( ( ~ ( p @ sK25_SX0 )
| ~ c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(469,plain,
! [SV33: $i] :
( ( ( ~ ( p @ SV33 ) )
= $true )
| ( ( ~ c ) = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(470,plain,
( ( ~ ( p @ sK25_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(471,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(472,plain,
! [SV33: $i] :
( ( ( p @ SV33 )
= $false )
| ( ( ~ c ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(473,plain,
( ( p @ sK25_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(474,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(475,plain,
! [SV33: $i] :
( ( c = $false )
| ( ( p @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(476,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[473,475,474]) ).
thf(477,plain,
( ( ~ ( ( ? [X: $i] : ( p @ X )
& c )
=> ? [X: $i] :
( ( p @ X )
& c ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(478,plain,
( ( ~ ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(479,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(480,plain,
( ( ~ ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(481,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(482,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(483,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( p @ SX0 )
| ~ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(484,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| ~ c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(485,plain,
! [SV34: $i] :
( ( ~ ~ ( ~ ( p @ SV34 )
| ~ c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(486,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(487,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(488,plain,
! [SV34: $i] :
( ( ~ ( ~ ( p @ SV34 )
| ~ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(489,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(490,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(491,plain,
! [SV34: $i] :
( ( ~ ( p @ SV34 )
| ~ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(492,plain,
( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(493,plain,
! [SV34: $i] :
( ( ( ~ ( p @ SV34 ) )
= $true )
| ( ( ~ c ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(494,plain,
( ( ~ ( p @ sK26_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[492]) ).
thf(495,plain,
! [SV34: $i] :
( ( ( p @ SV34 )
= $false )
| ( ( ~ c ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(496,plain,
( ( p @ sK26_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(497,plain,
! [SV34: $i] :
( ( c = $false )
| ( ( p @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(498,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[490,497,496]) ).
thf(499,plain,
( ( ~ ( ? [X: $i] : c
=> c ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(500,plain,
( ( ~ ( ~ ~ ! [SX0: $i] : ~ c
| c ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(501,plain,
( ( ~ ~ ! [SX0: $i] : ~ c
| c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(502,plain,
( ( ~ ~ ! [SX0: $i] : ~ c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(503,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(504,plain,
( ( ~ ! [SX0: $i] : ~ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(505,plain,
( ( ! [SX0: $i] : ~ c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(506,plain,
( ( ~ c ) = $false ),
inference(extcnf_forall_neg,[status(esa)],[505]) ).
thf(507,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(508,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[503,507]) ).
thf(509,plain,
( ( ~ ( c
=> ? [X: $i] : c ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(510,plain,
( ( ~ ( ~ c
| ~ ! [SX0: $i] : ~ c ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(511,plain,
( ( ~ c
| ~ ! [SX0: $i] : ~ c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(512,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(513,plain,
( ( ~ ! [SX0: $i] : ~ c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(514,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(515,plain,
( ( ! [SX0: $i] : ~ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(516,plain,
( ( ~ c ) = $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(517,plain,
c = $false,
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(518,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[514,517]) ).
thf(519,plain,
( ( ~ ( ! [X: $i] : c
=> c ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(520,plain,
( ( ~ ( ~ ! [SX0: $i] : c
| c ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(521,plain,
( ( ~ ! [SX0: $i] : c
| c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(522,plain,
( ( ~ ! [SX0: $i] : c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(523,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[521]) ).
thf(524,plain,
( ( ! [SX0: $i] : c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(525,plain,
c = $true,
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(526,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[523,525]) ).
thf(527,plain,
( ( ~ ( c
=> ! [X: $i] : c ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(528,plain,
( ( ~ ( ~ c
| ! [SX0: $i] : c ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(529,plain,
( ( ~ c
| ! [SX0: $i] : c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(530,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(531,plain,
( ( ! [SX0: $i] : c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(532,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(533,plain,
c = $false,
inference(extcnf_forall_neg,[status(esa)],[531]) ).
thf(534,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[532,533]) ).
thf(535,plain,
( ( ~ ( ? [X: $i] :
( c
=> ( p @ X ) )
=> ( c
=> ? [X: $i] : ( p @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(536,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) )
| ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(537,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) )
| ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(538,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(539,plain,
( ( ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(540,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(541,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(542,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(543,plain,
( ( ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(544,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(545,plain,
( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(546,plain,
( ( ~ ( ~ c
| ( p @ sK29_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[543]) ).
thf(547,plain,
! [SV37: $i] :
( ( ~ ( p @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(548,plain,
( ( ~ c
| ( p @ sK29_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(549,plain,
! [SV37: $i] :
( ( p @ SV37 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(550,plain,
( ( ( ~ c ) = $true )
| ( ( p @ sK29_SX0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(551,plain,
( ( c = $false )
| ( ( p @ sK29_SX0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(552,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[544,551,549]) ).
thf(553,plain,
( ( ~ ( ( c
=> ? [X: $i] : ( p @ X ) )
=> ? [X: $i] :
( c
=> ( p @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(554,plain,
( ( ~ ( ~ ( ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
| ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(555,plain,
( ( ~ ( ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
| ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(556,plain,
( ( ~ ( ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(557,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(558,plain,
( ( ~ c
| ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(559,plain,
( ( ! [SX0: $i] :
~ ( ~ c
| ( p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(560,plain,
( ( ( ~ c ) = $true )
| ( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(561,plain,
! [SV38: $i] :
( ( ~ ( ~ c
| ( p @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(562,plain,
( ( c = $false )
| ( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(563,plain,
! [SV38: $i] :
( ( ~ c
| ( p @ SV38 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(564,plain,
( ( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false )
| ( c = $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(565,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(566,plain,
! [SV38: $i] :
( ( p @ SV38 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(567,plain,
( ( ( ~ ( p @ sK30_SX0 ) )
= $false )
| ( c = $false ) ),
inference(extcnf_forall_neg,[status(esa)],[564]) ).
thf(568,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(569,plain,
( ( ( p @ sK30_SX0 )
= $true )
| ( c = $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(570,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[566,569,568]) ).
thf(571,plain,
( ( ~ ( ? [X: $i] :
( ( p @ X )
=> c )
=> ( ! [X: $i] : ( p @ X )
=> c ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(572,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c )
| ~ ! [SX0: $i] : ( p @ SX0 )
| c ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(573,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c )
| ~ ! [SX0: $i] : ( p @ SX0 )
| c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(574,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(575,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 )
| c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(576,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(577,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(578,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[575]) ).
thf(579,plain,
( ( ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(580,plain,
( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(581,plain,
( ( ~ ( ~ ( p @ sK31_SX0 )
| c ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[579]) ).
thf(582,plain,
! [SV39: $i] :
( ( p @ SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(583,plain,
( ( ~ ( p @ sK31_SX0 )
| c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(584,plain,
( ( ( ~ ( p @ sK31_SX0 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(585,plain,
( ( ( p @ sK31_SX0 )
= $false )
| ( c = $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(586,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[578,585,582]) ).
thf(587,plain,
( ( ~ ( ( ! [X: $i] : ( p @ X )
=> c )
=> ? [X: $i] :
( ( p @ X )
=> c ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(588,plain,
( ( ~ ( ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| c )
| ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(589,plain,
( ( ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| c )
| ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(590,plain,
( ( ~ ( ~ ! [SX0: $i] : ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(591,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(592,plain,
( ( ~ ! [SX0: $i] : ( p @ SX0 )
| c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(593,plain,
( ( ! [SX0: $i] :
~ ( ~ ( p @ SX0 )
| c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(594,plain,
( ( ( ~ ! [SX0: $i] : ( p @ SX0 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(595,plain,
! [SV40: $i] :
( ( ~ ( ~ ( p @ SV40 )
| c ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(596,plain,
( ( ( ! [SX0: $i] : ( p @ SX0 ) )
= $false )
| ( c = $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(597,plain,
! [SV40: $i] :
( ( ~ ( p @ SV40 )
| c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(598,plain,
( ( ( p @ sK32_SX0 )
= $false )
| ( c = $true ) ),
inference(extcnf_forall_neg,[status(esa)],[596]) ).
thf(599,plain,
! [SV40: $i] :
( ( ~ ( p @ SV40 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(600,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(601,plain,
! [SV40: $i] :
( ( p @ SV40 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(602,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[598,601,600]) ).
thf(603,plain,
( ( ~ ( ! [X: $i] :
( c
=> ( p @ X ) )
=> ( c
=> ! [X: $i] : ( p @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(604,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) )
| ~ c
| ! [SX0: $i] : ( p @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(605,plain,
( ( ~ ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) )
| ~ c
| ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(606,plain,
( ( ~ ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(607,plain,
( ( ~ c
| ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[605]) ).
thf(608,plain,
( ( ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(609,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[607]) ).
thf(610,plain,
( ( ! [SX0: $i] : ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[607]) ).
thf(611,plain,
! [SV41: $i] :
( ( ~ c
| ( p @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(612,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(613,plain,
( ( p @ sK33_SX0 )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[610]) ).
thf(614,plain,
! [SV41: $i] :
( ( ( ~ c ) = $true )
| ( ( p @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(615,plain,
! [SV41: $i] :
( ( c = $false )
| ( ( p @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(616,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[612,615,613]) ).
thf(617,plain,
( ( ~ ( ( c
=> ! [X: $i] : ( p @ X ) )
=> ! [X: $i] :
( c
=> ( p @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(618,plain,
( ( ~ ( ~ ( ~ c
| ! [SX0: $i] : ( p @ SX0 ) )
| ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(619,plain,
( ( ~ ( ~ c
| ! [SX0: $i] : ( p @ SX0 ) )
| ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(620,plain,
( ( ~ ( ~ c
| ! [SX0: $i] : ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(621,plain,
( ( ! [SX0: $i] :
( ~ c
| ( p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(622,plain,
( ( ~ c
| ! [SX0: $i] : ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(623,plain,
( ( ~ c
| ( p @ sK34_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[621]) ).
thf(624,plain,
( ( ( ~ c ) = $true )
| ( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(625,plain,
( ( ~ c ) = $false ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(626,plain,
( ( p @ sK34_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(627,plain,
( ( c = $false )
| ( ( ! [SX0: $i] : ( p @ SX0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(628,plain,
c = $true,
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(629,plain,
! [SV42: $i] :
( ( ( p @ SV42 )
= $true )
| ( c = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(630,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[626,629,628]) ).
thf(631,plain,
( ( ~ ( ! [X: $i] :
( ( p @ X )
=> c )
=> ( ? [X: $i] : ( p @ X )
=> c ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(632,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( p @ SX0 )
| c )
| ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(633,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ SX0 )
| c )
| ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(634,plain,
( ( ~ ! [SX0: $i] :
( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(635,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(636,plain,
( ( ! [SX0: $i] :
( ~ ( p @ SX0 )
| c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(637,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(638,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(639,plain,
! [SV43: $i] :
( ( ~ ( p @ SV43 )
| c )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(640,plain,
( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(641,plain,
! [SV43: $i] :
( ( ( ~ ( p @ SV43 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(642,plain,
( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(643,plain,
! [SV43: $i] :
( ( ( p @ SV43 )
= $false )
| ( c = $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(644,plain,
( ( ~ ( p @ sK35_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[642]) ).
thf(645,plain,
( ( p @ sK35_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(646,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[638,645,643]) ).
thf(647,plain,
( ( ~ ( ( ? [X: $i] : ( p @ X )
=> c )
=> ! [X: $i] :
( ( p @ X )
=> c ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(648,plain,
( ( ~ ( ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c )
| ! [SX0: $i] :
( ~ ( p @ SX0 )
| c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(649,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c )
| ! [SX0: $i] :
( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(650,plain,
( ( ~ ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(651,plain,
( ( ! [SX0: $i] :
( ~ ( p @ SX0 )
| c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[649]) ).
thf(652,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 )
| c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(653,plain,
( ( ~ ( p @ sK36_SX0 )
| c )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[651]) ).
thf(654,plain,
( ( ( ~ ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(655,plain,
( ( ~ ( p @ sK36_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(656,plain,
c = $false,
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(657,plain,
( ( ( ~ ! [SX0: $i] :
~ ( p @ SX0 ) )
= $false )
| ( c = $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(658,plain,
( ( p @ sK36_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(659,plain,
( ( ( ! [SX0: $i] :
~ ( p @ SX0 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(660,plain,
! [SV44: $i] :
( ( ( ~ ( p @ SV44 ) )
= $true )
| ( c = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(661,plain,
! [SV44: $i] :
( ( ( p @ SV44 )
= $false )
| ( c = $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(662,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[656,661,658]) ).
thf(663,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[662,142,172,251,267,286,305,318,337,356,367,392,401,412,430,442,454,476,498,508,518,526,534,552,570,586,602,616,630,646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN917+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 17:25:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.28/0.57
% 2.28/0.57 No.of.Axioms: 0
% 2.28/0.57
% 2.28/0.57 Length.of.Defs: 0
% 2.28/0.57
% 2.28/0.57 Contains.Choice.Funs: false
% 2.28/0.57 ...........
% 2.28/0.57
% 2.28/0.57 ********************************
% 2.28/0.57 * All subproblems solved! *
% 2.28/0.57 ********************************
% 2.28/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:662,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.28/0.57
% 2.28/0.57 %**** Beginning of derivation protocol ****
% 2.28/0.57 % SZS output start CNFRefutation
% See solution above
% 2.28/0.58
% 2.28/0.58 %**** End of derivation protocol ****
% 2.28/0.58 %**** no. of clauses in derivation: 663 ****
% 2.28/0.58 %**** clause counter: 662 ****
% 2.28/0.58
% 2.28/0.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,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:662,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------