TSTP Solution File: SYO500^1.004 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO500^1.004 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:46:26 EDT 2024
% Result : Theorem 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 34
% Syntax : Number of formulae : 358 ( 9 unt; 19 typ; 0 def)
% Number of atoms : 8383 ( 0 equ; 0 cnn)
% Maximal formula atoms : 1277 ( 24 avg)
% Number of connectives : 10961 (2917 ~;3875 |;1257 &;2886 @)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 17 con; 0-1 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
x: $o ).
thf(decl_23,type,
f0: $o > $o ).
thf(decl_24,type,
f1: $o > $o ).
thf(decl_25,type,
f2: $o > $o ).
thf(decl_26,type,
f3: $o > $o ).
thf(decl_27,type,
epred1_0: $o ).
thf(decl_28,type,
epred2_0: $o ).
thf(decl_29,type,
epred3_0: $o ).
thf(decl_30,type,
epred4_0: $o ).
thf(decl_31,type,
epred5_0: $o ).
thf(decl_32,type,
epred6_0: $o ).
thf(decl_33,type,
epred7_0: $o ).
thf(decl_34,type,
epred8_0: $o ).
thf(decl_35,type,
epred9_0: $o ).
thf(decl_36,type,
epred10_0: $o ).
thf(decl_37,type,
epred11_0: $o ).
thf(decl_38,type,
epred12_0: $o ).
thf(decl_39,type,
epred13_0: $o ).
thf(decl_40,type,
epred14_0: $o ).
thf(kaminski4,conjecture,
( ( f0 @ ( f0 @ ( f0 @ ( f1 @ ( f2 @ ( f2 @ ( f2 @ ( f3 @ x ) ) ) ) ) ) ) )
<=> ( f0 @ ( f1 @ ( f1 @ ( f1 @ ( f2 @ ( f3 @ ( f3 @ ( f3 @ x ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kaminski4) ).
thf(c_0_1,plain,
( epred9_0
<=> ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_2,plain,
( epred10_0
<=> ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_3,plain,
( epred8_0
<=> ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_4,plain,
( ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $true )
| ~ epred9_0 )
& ( x
| ~ ( f3 @ $false )
| ( f3 @ $true )
| ~ epred9_0 )
& ( ~ x
| ( f3 @ $true )
| ( f3 @ $false )
| ~ epred9_0 )
& ( x
| ( f3 @ $false )
| ( f3 @ $false )
| ~ epred9_0 )
& ( ~ x
| x
| ~ x
| x
| epred9_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| x
| epred9_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| x
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| x
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ x
| x
| epred9_0 )
& ( ~ x
| x
| ( f3 @ $false )
| x
| epred9_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| x
| epred9_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred9_0 )
& ( ~ ( f3 @ $false )
| ( f3 @ $false )
| x
| epred9_0 )
& ( ~ x
| x
| ~ x
| ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| ( f3 @ $true )
| epred9_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ x
| ( f3 @ $true )
| epred9_0 )
& ( ~ x
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred9_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| ( f3 @ $false )
| ( f3 @ $true )
| epred9_0 )
& ( ~ x
| x
| ~ ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| x
| ~ ( f3 @ $true )
| epred9_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ ( f3 @ $true )
| epred9_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| epred9_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).
thf(c_0_5,plain,
( epred1_0
<=> ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_6,plain,
( epred10_0
<=> ( ( ( ( epred8_0
| ~ ( f3 @ $true ) )
& ( epred9_0
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( epred8_0
| ( f3 @ $true ) )
& ( epred9_0
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_2,c_0_3]),c_0_1]),c_0_3]),c_0_1]) ).
thf(c_0_7,plain,
( x
| ( f3 @ ~ $true )
| ( f3 @ ~ $true )
| ~ epred9_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,plain,
( ( ~ x
| ~ ( f3 @ $true )
| ~ ( f3 @ $true )
| ~ epred8_0 )
& ( x
| ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ epred8_0 )
& ( ~ x
| ( f3 @ $true )
| ~ ( f3 @ $false )
| ~ epred8_0 )
& ( x
| ( f3 @ $false )
| ~ ( f3 @ $false )
| ~ epred8_0 )
& ( ~ x
| x
| ~ x
| x
| epred8_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| x
| epred8_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| x
| epred8_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| x
| epred8_0 )
& ( ( f3 @ $false )
| ~ x
| x
| epred8_0 )
& ( ~ x
| x
| ( f3 @ $false )
| x
| epred8_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| x
| epred8_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred8_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred8_0 )
& ( ( f3 @ $false )
| ( f3 @ $false )
| x
| epred8_0 )
& ( ~ x
| x
| ~ x
| ( f3 @ $true )
| epred8_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| ( f3 @ $true )
| epred8_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred8_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred8_0 )
& ( ( f3 @ $false )
| ~ x
| ( f3 @ $true )
| epred8_0 )
& ( ~ x
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred8_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred8_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred8_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred8_0 )
& ( ( f3 @ $false )
| ( f3 @ $false )
| ( f3 @ $true )
| epred8_0 )
& ( ~ x
| x
| ( f3 @ $true )
| epred8_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $true )
| epred8_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $true )
| epred8_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $true )
| epred8_0 )
& ( ( f3 @ $false )
| ( f3 @ $true )
| epred8_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
thf(c_0_9,plain,
( ( ~ x
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| ~ epred1_0 )
& ( x
| ~ ( f3 @ $false )
| ~ ( f2 @ $true )
| ~ epred1_0 )
& ( ~ x
| ( f3 @ $true )
| ~ ( f2 @ $false )
| ~ epred1_0 )
& ( x
| ( f3 @ $false )
| ~ ( f2 @ $false )
| ~ epred1_0 )
& ( ~ x
| x
| ~ x
| x
| epred1_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| x
| epred1_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| x
| epred1_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| x
| epred1_0 )
& ( ( f2 @ $false )
| ~ x
| x
| epred1_0 )
& ( ~ x
| x
| ( f3 @ $false )
| x
| epred1_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| x
| epred1_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred1_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred1_0 )
& ( ( f2 @ $false )
| ( f3 @ $false )
| x
| epred1_0 )
& ( ~ x
| x
| ~ x
| ( f3 @ $true )
| epred1_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| ( f3 @ $true )
| epred1_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred1_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred1_0 )
& ( ( f2 @ $false )
| ~ x
| ( f3 @ $true )
| epred1_0 )
& ( ~ x
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred1_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred1_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred1_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred1_0 )
& ( ( f2 @ $false )
| ( f3 @ $false )
| ( f3 @ $true )
| epred1_0 )
& ( ~ x
| x
| ( f2 @ $true )
| epred1_0 )
& ( ~ ( f3 @ $false )
| x
| ( f2 @ $true )
| epred1_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f2 @ $true )
| epred1_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f2 @ $true )
| epred1_0 )
& ( ( f2 @ $false )
| ( f2 @ $true )
| epred1_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_10,plain,
( ( epred8_0
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| ~ epred10_0 )
& ( epred9_0
| ~ ( f3 @ $false )
| ~ ( f2 @ $true )
| ~ epred10_0 )
& ( epred8_0
| ( f3 @ $true )
| ~ ( f2 @ $false )
| ~ epred10_0 )
& ( epred9_0
| ( f3 @ $false )
| ~ ( f2 @ $false )
| ~ epred10_0 )
& ( ~ epred9_0
| ~ epred8_0
| ~ epred9_0
| ~ epred8_0
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ~ epred9_0
| ~ epred8_0
| epred10_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ~ epred9_0
| ~ epred8_0
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ epred9_0
| ~ epred8_0
| epred10_0 )
& ( ( f2 @ $false )
| ~ epred9_0
| ~ epred8_0
| epred10_0 )
& ( ~ epred9_0
| ~ epred8_0
| ( f3 @ $false )
| ~ epred8_0
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ( f3 @ $false )
| ~ epred8_0
| epred10_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ~ epred8_0
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ~ epred8_0
| epred10_0 )
& ( ( f2 @ $false )
| ( f3 @ $false )
| ~ epred8_0
| epred10_0 )
& ( ~ epred9_0
| ~ epred8_0
| ~ epred9_0
| ( f3 @ $true )
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ~ epred9_0
| ( f3 @ $true )
| epred10_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ~ epred9_0
| ( f3 @ $true )
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ epred9_0
| ( f3 @ $true )
| epred10_0 )
& ( ( f2 @ $false )
| ~ epred9_0
| ( f3 @ $true )
| epred10_0 )
& ( ~ epred9_0
| ~ epred8_0
| ( f3 @ $false )
| ( f3 @ $true )
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ( f3 @ $false )
| ( f3 @ $true )
| epred10_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred10_0 )
& ( ( f2 @ $false )
| ( f3 @ $false )
| ( f3 @ $true )
| epred10_0 )
& ( ~ epred9_0
| ~ epred8_0
| ( f2 @ $true )
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ( f2 @ $true )
| epred10_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ( f2 @ $true )
| epred10_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f2 @ $true )
| epred10_0 )
& ( ( f2 @ $false )
| ( f2 @ $true )
| epred10_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_11,plain,
( x
| ( f3 @ $true )
| ~ ( f3 @ ~ $true )
| ~ epred9_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_12,plain,
( x
| ( f3 @ ~ $true )
| ~ epred9_0 ),
inference(cn,[status(thm)],[c_0_7]) ).
thf(c_0_13,plain,
( ( f3 @ ~ $true )
| ( f3 @ ~ $true )
| x
| epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
( x
| ( f3 @ $true )
| epred8_0
| ~ ( f3 @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,plain,
( ( f3 @ ~ $true )
| ( f3 @ $true )
| epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,plain,
( x
| ~ ( f3 @ ~ $true )
| ~ ( f2 @ $true )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,plain,
( ( f2 @ $true )
| epred10_0
| ~ epred9_0
| ~ ( f3 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,plain,
( ( f3 @ $true )
| x
| ~ epred9_0 ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_19,plain,
( x
| epred8_0
| ( f3 @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
( ( f2 @ $true )
| epred10_0
| ~ ( f3 @ ~ $true )
| ~ ( f3 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,plain,
( ( f3 @ $true )
| epred8_0
| x ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_22,plain,
( epred2_0
<=> ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_23,plain,
( x
| ~ ( f2 @ $true )
| ~ epred1_0
| ~ epred9_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
thf(c_0_24,plain,
( ( f2 @ $true )
| x
| epred10_0
| ~ epred9_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_25,plain,
( epred9_0
| ~ x
| ~ ( f3 @ $true )
| ~ ( f3 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_26,plain,
( epred8_0
| x
| ~ ( f2 @ $true )
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
thf(c_0_27,plain,
( ( f2 @ $true )
| epred8_0
| x
| epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_21]) ).
thf(c_0_28,plain,
( ( ~ x
| ~ ( f3 @ $true )
| ( f2 @ $true )
| ~ epred2_0 )
& ( x
| ~ ( f3 @ $false )
| ( f2 @ $true )
| ~ epred2_0 )
& ( ~ x
| ( f3 @ $true )
| ( f2 @ $false )
| ~ epred2_0 )
& ( x
| ( f3 @ $false )
| ( f2 @ $false )
| ~ epred2_0 )
& ( ~ x
| x
| ~ x
| x
| epred2_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| x
| epred2_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| x
| epred2_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| x
| epred2_0 )
& ( ~ ( f2 @ $false )
| ~ x
| x
| epred2_0 )
& ( ~ x
| x
| ( f3 @ $false )
| x
| epred2_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| x
| epred2_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred2_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| x
| epred2_0 )
& ( ~ ( f2 @ $false )
| ( f3 @ $false )
| x
| epred2_0 )
& ( ~ x
| x
| ~ x
| ( f3 @ $true )
| epred2_0 )
& ( ~ ( f3 @ $false )
| x
| ~ x
| ( f3 @ $true )
| epred2_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred2_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ x
| ( f3 @ $true )
| epred2_0 )
& ( ~ ( f2 @ $false )
| ~ x
| ( f3 @ $true )
| epred2_0 )
& ( ~ x
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred2_0 )
& ( ~ ( f3 @ $false )
| x
| ( f3 @ $false )
| ( f3 @ $true )
| epred2_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred2_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred2_0 )
& ( ~ ( f2 @ $false )
| ( f3 @ $false )
| ( f3 @ $true )
| epred2_0 )
& ( ~ x
| x
| ~ ( f2 @ $true )
| epred2_0 )
& ( ~ ( f3 @ $false )
| x
| ~ ( f2 @ $true )
| epred2_0 )
& ( ~ x
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| epred2_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| epred2_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| epred2_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
thf(c_0_29,plain,
( epred7_0
<=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ~ ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ~ ( f0 @ $false ) ) )
| ~ ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ( f0 @ $false ) ) )
| ~ ( f0 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ~ ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ~ ( f0 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ( f0 @ $false ) ) )
| ( f0 @ $false ) ) )
| ( f0 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_30,plain,
( epred5_0
<=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ~ ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ~ ( f0 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_31,plain,
( epred6_0
<=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ( f0 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_32,plain,
( ~ x
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_33,plain,
( ( f3 @ $true )
| ~ x
| ~ ( f2 @ ~ $true )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_34,plain,
( epred10_0
| x
| ~ epred1_0
| ~ epred9_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_35,plain,
( ( f2 @ ~ $true )
| ( f2 @ $true )
| epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_36,plain,
( epred9_0
| ~ x
| ~ ( f3 @ $true ) ),
inference(cn,[status(thm)],[c_0_25]) ).
thf(c_0_37,plain,
( ( f2 @ $true )
| epred10_0
| ~ ( f3 @ ~ $true )
| ~ epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_38,plain,
( x
| ( f3 @ ~ $true )
| ~ ( f2 @ ~ $true )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_39,plain,
( epred10_0
| x
| epred8_0
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_40,plain,
( ( f3 @ $true )
| epred9_0
| ~ ( f3 @ ~ $true )
| ~ x ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_41,plain,
( epred9_0
| ~ ( f3 @ ~ $true )
| ~ ( f3 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_42,plain,
( epred4_0
<=> ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_43,plain,
( ( f2 @ $true )
| epred1_0
| ~ x
| ~ ( f3 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_44,plain,
( ( f3 @ $true )
| epred2_0
| ~ ( f2 @ ~ $true )
| ~ x ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_45,plain,
( ( f2 @ ~ $true )
| ( f2 @ $true )
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_46,plain,
( epred11_0
<=> ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_47,plain,
( epred14_0
<=> ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
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introduced(definition) ).
thf(c_0_48,plain,
( epred12_0
<=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
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& ( x
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| ( f3 @ $true ) )
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| ( f3 @ $false ) ) )
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| ( f3 @ $true ) )
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| ( f3 @ $true ) )
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| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
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& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
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| ( f3 @ $false ) ) )
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| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ~ ( f1 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_49,plain,
( epred13_0
<=> ( ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f1 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f3 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f1 @ $false ) ) )
| ( f1 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_50,plain,
( epred7_0
<=> ( ( ( ( epred5_0
| ~ ( f0 @ $true ) )
& ( epred6_0
| ~ ( f0 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( epred5_0
| ( f0 @ $true ) )
& ( epred6_0
| ( f0 @ $false ) ) )
| ( f0 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_30]),c_0_31]) ).
thf(c_0_51,plain,
( ~ x
| ~ ( f3 @ $true )
| ~ ( f3 @ $true )
| ~ epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_52,plain,
( ~ ( f2 @ $true )
| ~ ( f2 @ ~ $true )
| ~ x
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_53,plain,
( ( f2 @ ~ $true )
| ( f3 @ $true )
| epred10_0
| ~ epred9_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_54,plain,
( ( f2 @ $true )
| epred10_0
| ~ epred9_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_34]),c_0_35]) ).
thf(c_0_55,plain,
( epred9_0
| ~ ( f2 @ ~ $true )
| ~ x
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
thf(c_0_56,plain,
( ( f2 @ $true )
| x
| epred10_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_35]) ).
thf(c_0_57,plain,
( epred9_0
| ~ ( f3 @ ~ $true )
| ~ x ),
inference(csr,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_58,plain,
( epred8_0
| x
| epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_19]),c_0_21]) ).
thf(c_0_59,plain,
( epred4_0
<=> ( ( ( ( epred1_0
| ~ ( f2 @ $true ) )
& ( epred2_0
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( epred1_0
| ( f2 @ $true ) )
& ( epred2_0
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_42,c_0_5]),c_0_22]),c_0_5]),c_0_22]) ).
thf(c_0_60,plain,
( x
| ( f2 @ $true )
| epred1_0
| ~ ( f3 @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_61,plain,
( ( f3 @ ~ $true )
| x
| epred2_0
| ~ ( f2 @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_62,plain,
( ( f2 @ $true )
| epred2_0
| epred1_0
| ~ x ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
thf(c_0_63,plain,
( epred11_0
<=> ( ( ( ( epred8_0
| ~ ( f3 @ $true ) )
& ( epred9_0
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( epred8_0
| ( f3 @ $true ) )
& ( epred9_0
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_46,c_0_3]),c_0_1]),c_0_3]),c_0_1]) ).
thf(c_0_64,plain,
( epred14_0
<=> ( ( ( ( epred12_0
| ~ ( f1 @ $true ) )
& ( epred13_0
| ~ ( f1 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( epred12_0
| ( f1 @ $true ) )
& ( epred13_0
| ( f1 @ $false ) ) )
| ( f0 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_48]),c_0_49]) ).
thf(c_0_65,plain,
( ( epred5_0
| ~ ( f0 @ $true )
| ( f0 @ $true )
| ~ epred7_0 )
& ( epred6_0
| ~ ( f0 @ $false )
| ( f0 @ $true )
| ~ epred7_0 )
& ( epred5_0
| ( f0 @ $true )
| ( f0 @ $false )
| ~ epred7_0 )
& ( epred6_0
| ( f0 @ $false )
| ( f0 @ $false )
| ~ epred7_0 )
& ( ~ epred6_0
| ~ epred5_0
| ~ epred6_0
| ~ epred5_0
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred5_0
| ~ epred6_0
| ~ epred5_0
| epred7_0 )
& ( ~ epred6_0
| ~ ( f0 @ $true )
| ~ epred6_0
| ~ epred5_0
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ~ epred6_0
| ~ epred5_0
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred6_0
| ~ epred5_0
| epred7_0 )
& ( ~ epred6_0
| ~ epred5_0
| ( f0 @ $false )
| ~ epred5_0
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred5_0
| ( f0 @ $false )
| ~ epred5_0
| epred7_0 )
& ( ~ epred6_0
| ~ ( f0 @ $true )
| ( f0 @ $false )
| ~ epred5_0
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ( f0 @ $false )
| ~ epred5_0
| epred7_0 )
& ( ~ ( f0 @ $false )
| ( f0 @ $false )
| ~ epred5_0
| epred7_0 )
& ( ~ epred6_0
| ~ epred5_0
| ~ epred6_0
| ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred5_0
| ~ epred6_0
| ( f0 @ $true )
| epred7_0 )
& ( ~ epred6_0
| ~ ( f0 @ $true )
| ~ epred6_0
| ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ~ epred6_0
| ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred6_0
| ( f0 @ $true )
| epred7_0 )
& ( ~ epred6_0
| ~ epred5_0
| ( f0 @ $false )
| ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred5_0
| ( f0 @ $false )
| ( f0 @ $true )
| epred7_0 )
& ( ~ epred6_0
| ~ ( f0 @ $true )
| ( f0 @ $false )
| ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ( f0 @ $false )
| ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ( f0 @ $false )
| ( f0 @ $true )
| epred7_0 )
& ( ~ epred6_0
| ~ epred5_0
| ~ ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ epred5_0
| ~ ( f0 @ $true )
| epred7_0 )
& ( ~ epred6_0
| ~ ( f0 @ $true )
| ~ ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ~ ( f0 @ $true )
| epred7_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| epred7_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
thf(c_0_66,negated_conjecture,
~ ( epred7_0
<=> epred14_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[kaminski4])]),c_0_29]),c_0_47]) ).
thf(c_0_67,plain,
( x
| ~ ( f3 @ ~ $true )
| ~ ( f3 @ $true )
| ~ epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_68,plain,
( ~ x
| ~ epred8_0
| ~ ( f3 @ $true ) ),
inference(cn,[status(thm)],[c_0_51]) ).
thf(c_0_69,plain,
( ~ ( f2 @ $true )
| ~ ( f2 @ ~ $true )
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_38]),c_0_52]) ).
thf(c_0_70,plain,
( ( f2 @ ~ $true )
| epred10_0
| ~ epred1_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_34]),c_0_54]) ).
thf(c_0_71,plain,
( ( f2 @ $true )
| epred10_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_35]),c_0_56]),c_0_54]) ).
thf(c_0_72,plain,
( ( f3 @ $true )
| epred8_0
| epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_15]),c_0_58]) ).
thf(c_0_73,plain,
( ( epred1_0
| ~ ( f2 @ $true )
| ( f2 @ $true )
| ~ epred4_0 )
& ( epred2_0
| ~ ( f2 @ $false )
| ( f2 @ $true )
| ~ epred4_0 )
& ( epred1_0
| ( f2 @ $true )
| ( f2 @ $false )
| ~ epred4_0 )
& ( epred2_0
| ( f2 @ $false )
| ( f2 @ $false )
| ~ epred4_0 )
& ( ~ epred2_0
| ~ epred1_0
| ~ epred2_0
| ~ epred1_0
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ~ epred2_0
| ~ epred1_0
| epred4_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ~ epred2_0
| ~ epred1_0
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ epred2_0
| ~ epred1_0
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred2_0
| ~ epred1_0
| epred4_0 )
& ( ~ epred2_0
| ~ epred1_0
| ( f2 @ $false )
| ~ epred1_0
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ( f2 @ $false )
| ~ epred1_0
| epred4_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ~ epred1_0
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ~ epred1_0
| epred4_0 )
& ( ~ ( f2 @ $false )
| ( f2 @ $false )
| ~ epred1_0
| epred4_0 )
& ( ~ epred2_0
| ~ epred1_0
| ~ epred2_0
| ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ~ epred2_0
| ( f2 @ $true )
| epred4_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ~ epred2_0
| ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ epred2_0
| ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred2_0
| ( f2 @ $true )
| epred4_0 )
& ( ~ epred2_0
| ~ epred1_0
| ( f2 @ $false )
| ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ( f2 @ $false )
| ( f2 @ $true )
| epred4_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ( f2 @ $false )
| ( f2 @ $true )
| epred4_0 )
& ( ~ epred2_0
| ~ epred1_0
| ~ ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ~ ( f2 @ $true )
| epred4_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ~ ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ ( f2 @ $true )
| epred4_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| epred4_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
thf(c_0_74,plain,
( epred2_0
| ~ x
| ~ ( f3 @ $true )
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_75,plain,
( ( f2 @ ~ $true )
| ( f3 @ $true )
| epred1_0
| ~ x ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_76,plain,
( ( f2 @ $true )
| epred2_0
| epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_45]),c_0_62]) ).
thf(c_0_77,plain,
( ( epred8_0
| ~ ( f3 @ $true )
| ( f2 @ $true )
| ~ epred11_0 )
& ( epred9_0
| ~ ( f3 @ $false )
| ( f2 @ $true )
| ~ epred11_0 )
& ( epred8_0
| ( f3 @ $true )
| ( f2 @ $false )
| ~ epred11_0 )
& ( epred9_0
| ( f3 @ $false )
| ( f2 @ $false )
| ~ epred11_0 )
& ( ~ epred9_0
| ~ epred8_0
| ~ epred9_0
| ~ epred8_0
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ~ epred9_0
| ~ epred8_0
| epred11_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ~ epred9_0
| ~ epred8_0
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ epred9_0
| ~ epred8_0
| epred11_0 )
& ( ~ ( f2 @ $false )
| ~ epred9_0
| ~ epred8_0
| epred11_0 )
& ( ~ epred9_0
| ~ epred8_0
| ( f3 @ $false )
| ~ epred8_0
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ( f3 @ $false )
| ~ epred8_0
| epred11_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ~ epred8_0
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ~ epred8_0
| epred11_0 )
& ( ~ ( f2 @ $false )
| ( f3 @ $false )
| ~ epred8_0
| epred11_0 )
& ( ~ epred9_0
| ~ epred8_0
| ~ epred9_0
| ( f3 @ $true )
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ~ epred9_0
| ( f3 @ $true )
| epred11_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ~ epred9_0
| ( f3 @ $true )
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ epred9_0
| ( f3 @ $true )
| epred11_0 )
& ( ~ ( f2 @ $false )
| ~ epred9_0
| ( f3 @ $true )
| epred11_0 )
& ( ~ epred9_0
| ~ epred8_0
| ( f3 @ $false )
| ( f3 @ $true )
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ( f3 @ $false )
| ( f3 @ $true )
| epred11_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ( f3 @ $false )
| ( f3 @ $true )
| epred11_0 )
& ( ~ ( f2 @ $false )
| ( f3 @ $false )
| ( f3 @ $true )
| epred11_0 )
& ( ~ epred9_0
| ~ epred8_0
| ~ ( f2 @ $true )
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ epred8_0
| ~ ( f2 @ $true )
| epred11_0 )
& ( ~ epred9_0
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| epred11_0 )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| epred11_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| epred11_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
thf(c_0_78,plain,
( epred3_0
<=> ( ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ~ ( f2 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f3 @ $true ) )
& ( x
| ~ ( f3 @ $false ) ) )
| ( f2 @ $true ) )
& ( ( ( ~ x
| ( f3 @ $true ) )
& ( x
| ( f3 @ $false ) ) )
| ( f2 @ $false ) ) )
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) ) ),
introduced(definition) ).
thf(c_0_79,plain,
( ( epred12_0
| ~ ( f1 @ $true )
| ( f0 @ $true )
| ~ epred14_0 )
& ( epred13_0
| ~ ( f1 @ $false )
| ( f0 @ $true )
| ~ epred14_0 )
& ( epred12_0
| ( f1 @ $true )
| ( f0 @ $false )
| ~ epred14_0 )
& ( epred13_0
| ( f1 @ $false )
| ( f0 @ $false )
| ~ epred14_0 )
& ( ~ epred13_0
| ~ epred12_0
| ~ epred13_0
| ~ epred12_0
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ epred12_0
| ~ epred13_0
| ~ epred12_0
| epred14_0 )
& ( ~ epred13_0
| ~ ( f1 @ $true )
| ~ epred13_0
| ~ epred12_0
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred13_0
| ~ epred12_0
| epred14_0 )
& ( ~ ( f0 @ $false )
| ~ epred13_0
| ~ epred12_0
| epred14_0 )
& ( ~ epred13_0
| ~ epred12_0
| ( f1 @ $false )
| ~ epred12_0
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ epred12_0
| ( f1 @ $false )
| ~ epred12_0
| epred14_0 )
& ( ~ epred13_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred12_0
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred12_0
| epred14_0 )
& ( ~ ( f0 @ $false )
| ( f1 @ $false )
| ~ epred12_0
| epred14_0 )
& ( ~ epred13_0
| ~ epred12_0
| ~ epred13_0
| ( f1 @ $true )
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ epred12_0
| ~ epred13_0
| ( f1 @ $true )
| epred14_0 )
& ( ~ epred13_0
| ~ ( f1 @ $true )
| ~ epred13_0
| ( f1 @ $true )
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred13_0
| ( f1 @ $true )
| epred14_0 )
& ( ~ ( f0 @ $false )
| ~ epred13_0
| ( f1 @ $true )
| epred14_0 )
& ( ~ epred13_0
| ~ epred12_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ epred12_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred14_0 )
& ( ~ epred13_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred14_0 )
& ( ~ ( f0 @ $false )
| ( f1 @ $false )
| ( f1 @ $true )
| epred14_0 )
& ( ~ epred13_0
| ~ epred12_0
| ~ ( f0 @ $true )
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ epred12_0
| ~ ( f0 @ $true )
| epred14_0 )
& ( ~ epred13_0
| ~ ( f1 @ $true )
| ~ ( f0 @ $true )
| epred14_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ ( f0 @ $true )
| epred14_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| epred14_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])]) ).
thf(c_0_80,plain,
( epred6_0
| ( f0 @ ~ $true )
| ( f0 @ ~ $true )
| ~ epred7_0 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_81,negated_conjecture,
( ( ~ epred7_0
| ~ epred14_0 )
& ( epred7_0
| epred14_0 ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])]) ).
thf(c_0_82,plain,
( ( f3 @ $true )
| ~ x
| ~ ( f3 @ ~ $true )
| ~ epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_83,plain,
( ~ ( f3 @ $true )
| ~ ( f3 @ ~ $true )
| ~ epred8_0 ),
inference(csr,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_84,plain,
( epred10_0
| ~ epred1_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
thf(c_0_85,plain,
( epred8_0
| epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_72]),c_0_58]) ).
thf(c_0_86,plain,
( epred4_0
| ~ epred2_0
| ~ ( f2 @ $true )
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_87,plain,
( epred2_0
| ~ ( f2 @ ~ $true )
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_88,plain,
( ( f2 @ ~ $true )
| epred1_0
| epred2_0
| ~ x ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
thf(c_0_89,plain,
( epred9_0
| ( f3 @ ~ $true )
| ( f2 @ ~ $true )
| ~ epred11_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_90,plain,
( epred8_0
| ( f2 @ $true )
| ~ ( f3 @ $true )
| ~ epred11_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_91,plain,
( epred13_0
<=> ( ( ( ( epred10_0
| ~ ( f1 @ $true ) )
& ( epred11_0
| ~ ( f1 @ $false ) ) )
| ( f1 @ $true ) )
& ( ( ( epred10_0
| ( f1 @ $true ) )
& ( epred11_0
| ( f1 @ $false ) ) )
| ( f1 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_49,c_0_2]),c_0_46]),c_0_2]),c_0_46]) ).
thf(c_0_92,plain,
( epred5_0
<=> ( ( ( ( epred3_0
| ~ ( f1 @ $true ) )
& ( epred4_0
| ~ ( f1 @ $false ) ) )
| ~ ( f0 @ $true ) )
& ( ( ( epred3_0
| ( f1 @ $true ) )
& ( epred4_0
| ( f1 @ $false ) ) )
| ~ ( f0 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_78]),c_0_42]),c_0_78]),c_0_42]) ).
thf(c_0_93,plain,
( epred6_0
<=> ( ( ( ( epred3_0
| ~ ( f1 @ $true ) )
& ( epred4_0
| ~ ( f1 @ $false ) ) )
| ( f0 @ $true ) )
& ( ( ( epred3_0
| ( f1 @ $true ) )
& ( epred4_0
| ( f1 @ $false ) ) )
| ( f0 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31,c_0_78]),c_0_42]),c_0_78]),c_0_42]) ).
thf(c_0_94,plain,
( epred14_0
| ~ ( f0 @ ~ $true )
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_95,plain,
( epred6_0
| ( f0 @ ~ $true )
| ~ epred7_0 ),
inference(cn,[status(thm)],[c_0_80]) ).
thf(c_0_96,negated_conjecture,
( epred7_0
| epred14_0 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_97,plain,
( epred6_0
| ( f0 @ $true )
| ~ ( f0 @ ~ $true )
| ~ epred7_0 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_98,plain,
( ~ ( f3 @ ~ $true )
| ~ x
| ~ epred8_0 ),
inference(csr,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_99,plain,
( ( f2 @ ~ $true )
| ( f3 @ ~ $true )
| epred10_0
| ~ epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_100,plain,
( epred8_0
| epred10_0
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
thf(c_0_101,plain,
( ( f2 @ $true )
| epred4_0
| ~ ( f2 @ ~ $true )
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_102,plain,
( epred4_0
| ~ epred2_0
| ~ ( f2 @ $true ) ),
inference(cn,[status(thm)],[c_0_86]) ).
thf(c_0_103,plain,
( epred4_0
| ~ epred2_0
| ~ epred1_0
| ~ epred2_0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_104,plain,
( x
| epred2_0
| ~ ( f3 @ ~ $true )
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_105,plain,
( ( f2 @ ~ $true )
| ( f3 @ ~ $true )
| x
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_106,plain,
( epred1_0
| epred2_0
| ~ x ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_76]) ).
thf(c_0_107,plain,
( epred9_0
| ( f2 @ $true )
| ~ ( f3 @ ~ $true )
| ~ epred11_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_108,plain,
( ( f2 @ ~ $true )
| epred9_0
| ~ x
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_89]) ).
thf(c_0_109,plain,
( ( f2 @ $true )
| x
| epred8_0
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_90,c_0_21]) ).
thf(c_0_110,plain,
( epred12_0
<=> ( ( ( ( epred10_0
| ~ ( f1 @ $true ) )
& ( epred11_0
| ~ ( f1 @ $false ) ) )
| ~ ( f1 @ $true ) )
& ( ( ( epred10_0
| ( f1 @ $true ) )
& ( epred11_0
| ( f1 @ $false ) ) )
| ~ ( f1 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_48,c_0_2]),c_0_46]),c_0_2]),c_0_46]) ).
thf(c_0_111,plain,
( ( f3 @ $true )
| epred11_0
| ~ ( f2 @ ~ $true )
| ~ epred9_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_112,plain,
( ( epred10_0
| ~ ( f1 @ $true )
| ( f1 @ $true )
| ~ epred13_0 )
& ( epred11_0
| ~ ( f1 @ $false )
| ( f1 @ $true )
| ~ epred13_0 )
& ( epred10_0
| ( f1 @ $true )
| ( f1 @ $false )
| ~ epred13_0 )
& ( epred11_0
| ( f1 @ $false )
| ( f1 @ $false )
| ~ epred13_0 )
& ( ~ epred11_0
| ~ epred10_0
| ~ epred11_0
| ~ epred10_0
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ~ epred11_0
| ~ epred10_0
| epred13_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ~ epred11_0
| ~ epred10_0
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred11_0
| ~ epred10_0
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred11_0
| ~ epred10_0
| epred13_0 )
& ( ~ epred11_0
| ~ epred10_0
| ( f1 @ $false )
| ~ epred10_0
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ( f1 @ $false )
| ~ epred10_0
| epred13_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred10_0
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred10_0
| epred13_0 )
& ( ~ ( f1 @ $false )
| ( f1 @ $false )
| ~ epred10_0
| epred13_0 )
& ( ~ epred11_0
| ~ epred10_0
| ~ epred11_0
| ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ~ epred11_0
| ( f1 @ $true )
| epred13_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ~ epred11_0
| ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred11_0
| ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred11_0
| ( f1 @ $true )
| epred13_0 )
& ( ~ epred11_0
| ~ epred10_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred13_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ( f1 @ $false )
| ( f1 @ $true )
| epred13_0 )
& ( ~ epred11_0
| ~ epred10_0
| ~ ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ~ ( f1 @ $true )
| epred13_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ~ ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ ( f1 @ $true )
| epred13_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| epred13_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])]) ).
thf(c_0_113,plain,
( ( epred3_0
| ~ ( f1 @ $true )
| ~ ( f0 @ $true )
| ~ epred5_0 )
& ( epred4_0
| ~ ( f1 @ $false )
| ~ ( f0 @ $true )
| ~ epred5_0 )
& ( epred3_0
| ( f1 @ $true )
| ~ ( f0 @ $false )
| ~ epred5_0 )
& ( epred4_0
| ( f1 @ $false )
| ~ ( f0 @ $false )
| ~ epred5_0 )
& ( ~ epred4_0
| ~ epred3_0
| ~ epred4_0
| ~ epred3_0
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ~ epred4_0
| ~ epred3_0
| epred5_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ~ epred4_0
| ~ epred3_0
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred4_0
| ~ epred3_0
| epred5_0 )
& ( ( f0 @ $false )
| ~ epred4_0
| ~ epred3_0
| epred5_0 )
& ( ~ epred4_0
| ~ epred3_0
| ( f1 @ $false )
| ~ epred3_0
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ( f1 @ $false )
| ~ epred3_0
| epred5_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred3_0
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred3_0
| epred5_0 )
& ( ( f0 @ $false )
| ( f1 @ $false )
| ~ epred3_0
| epred5_0 )
& ( ~ epred4_0
| ~ epred3_0
| ~ epred4_0
| ( f1 @ $true )
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ~ epred4_0
| ( f1 @ $true )
| epred5_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ~ epred4_0
| ( f1 @ $true )
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred4_0
| ( f1 @ $true )
| epred5_0 )
& ( ( f0 @ $false )
| ~ epred4_0
| ( f1 @ $true )
| epred5_0 )
& ( ~ epred4_0
| ~ epred3_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred5_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred5_0 )
& ( ( f0 @ $false )
| ( f1 @ $false )
| ( f1 @ $true )
| epred5_0 )
& ( ~ epred4_0
| ~ epred3_0
| ( f0 @ $true )
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ( f0 @ $true )
| epred5_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ( f0 @ $true )
| epred5_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f0 @ $true )
| epred5_0 )
& ( ( f0 @ $false )
| ( f0 @ $true )
| epred5_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])]) ).
thf(c_0_114,plain,
( ( epred3_0
| ~ ( f1 @ $true )
| ( f0 @ $true )
| ~ epred6_0 )
& ( epred4_0
| ~ ( f1 @ $false )
| ( f0 @ $true )
| ~ epred6_0 )
& ( epred3_0
| ( f1 @ $true )
| ( f0 @ $false )
| ~ epred6_0 )
& ( epred4_0
| ( f1 @ $false )
| ( f0 @ $false )
| ~ epred6_0 )
& ( ~ epred4_0
| ~ epred3_0
| ~ epred4_0
| ~ epred3_0
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ~ epred4_0
| ~ epred3_0
| epred6_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ~ epred4_0
| ~ epred3_0
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred4_0
| ~ epred3_0
| epred6_0 )
& ( ~ ( f0 @ $false )
| ~ epred4_0
| ~ epred3_0
| epred6_0 )
& ( ~ epred4_0
| ~ epred3_0
| ( f1 @ $false )
| ~ epred3_0
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ( f1 @ $false )
| ~ epred3_0
| epred6_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred3_0
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred3_0
| epred6_0 )
& ( ~ ( f0 @ $false )
| ( f1 @ $false )
| ~ epred3_0
| epred6_0 )
& ( ~ epred4_0
| ~ epred3_0
| ~ epred4_0
| ( f1 @ $true )
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ~ epred4_0
| ( f1 @ $true )
| epred6_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ~ epred4_0
| ( f1 @ $true )
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred4_0
| ( f1 @ $true )
| epred6_0 )
& ( ~ ( f0 @ $false )
| ~ epred4_0
| ( f1 @ $true )
| epred6_0 )
& ( ~ epred4_0
| ~ epred3_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred6_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred6_0 )
& ( ~ ( f0 @ $false )
| ( f1 @ $false )
| ( f1 @ $true )
| epred6_0 )
& ( ~ epred4_0
| ~ epred3_0
| ~ ( f0 @ $true )
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ epred3_0
| ~ ( f0 @ $true )
| epred6_0 )
& ( ~ epred4_0
| ~ ( f1 @ $true )
| ~ ( f0 @ $true )
| epred6_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ ( f0 @ $true )
| epred6_0 )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| epred6_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])])]) ).
thf(c_0_115,plain,
( epred6_0
| epred14_0
| ~ ( f0 @ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
thf(c_0_116,plain,
( ( f0 @ $true )
| epred6_0
| ~ epred7_0 ),
inference(csr,[status(thm)],[c_0_97,c_0_95]) ).
thf(c_0_117,plain,
( ~ ( f2 @ ~ $true )
| ~ x
| ~ epred8_0
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_33]) ).
thf(c_0_118,plain,
( ( f2 @ ~ $true )
| epred10_0
| ~ x
| ~ epred8_0 ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
thf(c_0_119,plain,
( ( f2 @ ~ $true )
| epred10_0
| x
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_99]),c_0_100]),c_0_71]) ).
thf(c_0_120,plain,
( epred4_0
| ~ ( f2 @ ~ $true )
| ~ epred2_0 ),
inference(csr,[status(thm)],[c_0_101,c_0_102]) ).
thf(c_0_121,plain,
( epred4_0
| ~ epred1_0
| ~ epred2_0 ),
inference(cn,[status(thm)],[c_0_103]) ).
thf(c_0_122,plain,
( ( f2 @ ~ $true )
| epred1_0
| epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_76]),c_0_106]) ).
thf(c_0_123,plain,
( ( f3 @ $true )
| ( f3 @ ~ $true )
| ~ x
| ~ epred9_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_124,plain,
( ( f2 @ ~ $true )
| ( f2 @ $true )
| epred9_0
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_107,c_0_89]) ).
thf(c_0_125,plain,
( epred9_0
| ~ x
| ~ epred1_0
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_55,c_0_108]) ).
thf(c_0_126,plain,
( x
| epred8_0
| ~ epred1_0
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_109]) ).
thf(c_0_127,plain,
( epred8_0
| ( f3 @ $true )
| ( f2 @ ~ $true )
| ~ epred11_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_128,plain,
( epred7_0
| ~ epred6_0
| ~ ( f0 @ $true )
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_129,plain,
( ( epred10_0
| ~ ( f1 @ $true )
| ~ ( f1 @ $true )
| ~ epred12_0 )
& ( epred11_0
| ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred12_0 )
& ( epred10_0
| ( f1 @ $true )
| ~ ( f1 @ $false )
| ~ epred12_0 )
& ( epred11_0
| ( f1 @ $false )
| ~ ( f1 @ $false )
| ~ epred12_0 )
& ( ~ epred11_0
| ~ epred10_0
| ~ epred11_0
| ~ epred10_0
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ~ epred11_0
| ~ epred10_0
| epred12_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ~ epred11_0
| ~ epred10_0
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred11_0
| ~ epred10_0
| epred12_0 )
& ( ( f1 @ $false )
| ~ epred11_0
| ~ epred10_0
| epred12_0 )
& ( ~ epred11_0
| ~ epred10_0
| ( f1 @ $false )
| ~ epred10_0
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ( f1 @ $false )
| ~ epred10_0
| epred12_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred10_0
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ~ epred10_0
| epred12_0 )
& ( ( f1 @ $false )
| ( f1 @ $false )
| ~ epred10_0
| epred12_0 )
& ( ~ epred11_0
| ~ epred10_0
| ~ epred11_0
| ( f1 @ $true )
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ~ epred11_0
| ( f1 @ $true )
| epred12_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ~ epred11_0
| ( f1 @ $true )
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ epred11_0
| ( f1 @ $true )
| epred12_0 )
& ( ( f1 @ $false )
| ~ epred11_0
| ( f1 @ $true )
| epred12_0 )
& ( ~ epred11_0
| ~ epred10_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ( f1 @ $false )
| ( f1 @ $true )
| epred12_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $false )
| ( f1 @ $true )
| epred12_0 )
& ( ( f1 @ $false )
| ( f1 @ $false )
| ( f1 @ $true )
| epred12_0 )
& ( ~ epred11_0
| ~ epred10_0
| ( f1 @ $true )
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ epred10_0
| ( f1 @ $true )
| epred12_0 )
& ( ~ epred11_0
| ~ ( f1 @ $true )
| ( f1 @ $true )
| epred12_0 )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ( f1 @ $true )
| epred12_0 )
& ( ( f1 @ $false )
| ( f1 @ $true )
| epred12_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])])]) ).
thf(c_0_130,plain,
( epred3_0
<=> ( ( ( ( epred1_0
| ~ ( f2 @ $true ) )
& ( epred2_0
| ~ ( f2 @ $false ) ) )
| ~ ( f2 @ $true ) )
& ( ( ( epred1_0
| ( f2 @ $true ) )
& ( epred2_0
| ( f2 @ $false ) ) )
| ~ ( f2 @ $false ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_78,c_0_5]),c_0_22]),c_0_5]),c_0_22]) ).
thf(c_0_131,plain,
( epred11_0
| ~ epred9_0
| ~ ( f3 @ $true )
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_132,plain,
( x
| ( f2 @ $true )
| ~ ( f3 @ ~ $true )
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_133,plain,
( ( f2 @ $true )
| ~ x
| ~ ( f3 @ $true )
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_134,plain,
( ( f3 @ $true )
| ( f2 @ ~ $true )
| ~ x
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_135,plain,
( epred9_0
| ( f3 @ ~ $true )
| ~ ( f2 @ ~ $true )
| ~ epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_136,plain,
( ( f2 @ $true )
| epred11_0
| epred10_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_111]),c_0_35]) ).
thf(c_0_137,plain,
( epred9_0
| ~ ( f3 @ ~ $true )
| ~ ( f2 @ $true )
| ~ epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_138,plain,
( epred8_0
| ~ ( f3 @ $true )
| ~ ( f2 @ $true )
| ~ epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_139,plain,
( epred8_0
| ( f3 @ $true )
| ~ ( f2 @ ~ $true )
| ~ epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_140,plain,
( epred11_0
| ( f1 @ ~ $true )
| ( f1 @ ~ $true )
| ~ epred13_0 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_141,plain,
( epred4_0
| ~ ( f1 @ ~ $true )
| ~ ( f0 @ $true )
| ~ epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_142,plain,
( epred13_0
| ( f0 @ $true )
| ~ ( f1 @ ~ $true )
| ~ epred14_0 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_143,plain,
( epred4_0
| ( f0 @ $true )
| ~ ( f1 @ ~ $true )
| ~ epred6_0 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_144,plain,
( epred14_0
| ~ ( f1 @ ~ $true )
| ~ ( f1 @ $true )
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_145,plain,
( epred14_0
| epred6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_96]) ).
thf(c_0_146,plain,
( epred10_0
| ~ x
| ~ epred8_0
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
thf(c_0_147,plain,
( x
| epred10_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_119]),c_0_71]) ).
thf(c_0_148,plain,
( epred4_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_45]),c_0_121]),c_0_102]) ).
thf(c_0_149,plain,
( epred1_0
| epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_122]),c_0_76]) ).
thf(c_0_150,plain,
( ( f3 @ ~ $true )
| ( f3 @ $true )
| ~ epred9_0 ),
inference(csr,[status(thm)],[c_0_123,c_0_18]) ).
thf(c_0_151,plain,
( ( f2 @ $true )
| epred9_0
| ~ epred11_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_38]),c_0_124]),c_0_125]) ).
thf(c_0_152,plain,
( epred8_0
| ~ ( f2 @ ~ $true )
| ~ epred11_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_33]),c_0_126]),c_0_69]) ).
thf(c_0_153,plain,
( ( f2 @ ~ $true )
| ( f2 @ $true )
| epred8_0
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_90,c_0_127]) ).
thf(c_0_154,plain,
( ( f0 @ $true )
| epred7_0
| ~ ( f0 @ ~ $true )
| ~ epred6_0 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_155,plain,
( epred7_0
| ~ epred6_0
| ~ ( f0 @ $true ) ),
inference(cn,[status(thm)],[c_0_128]) ).
thf(c_0_156,plain,
( epred7_0
| ~ epred6_0
| ~ epred5_0
| ~ epred6_0
| ~ epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
thf(c_0_157,plain,
( ( f1 @ ~ $true )
| ( f1 @ ~ $true )
| epred12_0
| ~ epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_158,plain,
( ( epred1_0
| ~ ( f2 @ $true )
| ~ ( f2 @ $true )
| ~ epred3_0 )
& ( epred2_0
| ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ epred3_0 )
& ( epred1_0
| ( f2 @ $true )
| ~ ( f2 @ $false )
| ~ epred3_0 )
& ( epred2_0
| ( f2 @ $false )
| ~ ( f2 @ $false )
| ~ epred3_0 )
& ( ~ epred2_0
| ~ epred1_0
| ~ epred2_0
| ~ epred1_0
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ~ epred2_0
| ~ epred1_0
| epred3_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ~ epred2_0
| ~ epred1_0
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ epred2_0
| ~ epred1_0
| epred3_0 )
& ( ( f2 @ $false )
| ~ epred2_0
| ~ epred1_0
| epred3_0 )
& ( ~ epred2_0
| ~ epred1_0
| ( f2 @ $false )
| ~ epred1_0
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ( f2 @ $false )
| ~ epred1_0
| epred3_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ~ epred1_0
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ~ epred1_0
| epred3_0 )
& ( ( f2 @ $false )
| ( f2 @ $false )
| ~ epred1_0
| epred3_0 )
& ( ~ epred2_0
| ~ epred1_0
| ~ epred2_0
| ( f2 @ $true )
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ~ epred2_0
| ( f2 @ $true )
| epred3_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ~ epred2_0
| ( f2 @ $true )
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ epred2_0
| ( f2 @ $true )
| epred3_0 )
& ( ( f2 @ $false )
| ~ epred2_0
| ( f2 @ $true )
| epred3_0 )
& ( ~ epred2_0
| ~ epred1_0
| ( f2 @ $false )
| ( f2 @ $true )
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ( f2 @ $false )
| ( f2 @ $true )
| epred3_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ( f2 @ $true )
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ( f2 @ $false )
| ( f2 @ $true )
| epred3_0 )
& ( ( f2 @ $false )
| ( f2 @ $false )
| ( f2 @ $true )
| epred3_0 )
& ( ~ epred2_0
| ~ epred1_0
| ( f2 @ $true )
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ epred1_0
| ( f2 @ $true )
| epred3_0 )
& ( ~ epred2_0
| ~ ( f2 @ $true )
| ( f2 @ $true )
| epred3_0 )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ( f2 @ $true )
| epred3_0 )
& ( ( f2 @ $false )
| ( f2 @ $true )
| epred3_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_130])])]) ).
thf(c_0_159,plain,
( x
| epred11_0
| ~ ( f2 @ $true )
| ~ epred9_0 ),
inference(spm,[status(thm)],[c_0_131,c_0_18]) ).
thf(c_0_160,plain,
( ( f2 @ $true )
| x
| ~ epred2_0
| ~ epred9_0 ),
inference(spm,[status(thm)],[c_0_132,c_0_12]) ).
thf(c_0_161,plain,
( x
| ( f3 @ ~ $true )
| ( f2 @ ~ $true )
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_162,plain,
( ( f2 @ ~ $true )
| ( f2 @ $true )
| ~ x
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
thf(c_0_163,plain,
( epred9_0
| ~ ( f2 @ ~ $true )
| ~ x
| ~ epred10_0 ),
inference(spm,[status(thm)],[c_0_57,c_0_135]) ).
thf(c_0_164,plain,
( ( f2 @ ~ $true )
| ~ x
| ~ epred8_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_68,c_0_134]) ).
thf(c_0_165,plain,
( epred11_0
| ~ ( f2 @ ~ $true )
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_166,plain,
( ( f2 @ ~ $true )
| epred10_0
| epred11_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_53]),c_0_136]) ).
thf(c_0_167,plain,
( epred10_0
| ~ ( f1 @ $true )
| ~ ( f1 @ $true )
| ~ epred12_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_168,plain,
( epred13_0
| ~ epred11_0
| ~ ( f1 @ $true )
| ~ ( f1 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_169,plain,
( epred9_0
| ~ ( f2 @ $true )
| ~ ( f2 @ ~ $true )
| ~ epred10_0 ),
inference(spm,[status(thm)],[c_0_137,c_0_135]) ).
thf(c_0_170,plain,
( epred8_0
| ~ ( f2 @ $true )
| ~ ( f2 @ ~ $true )
| ~ epred10_0 ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
thf(c_0_171,plain,
( epred11_0
| ( f1 @ $true )
| ~ ( f1 @ ~ $true )
| ~ epred13_0 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_172,plain,
( epred11_0
| ( f1 @ ~ $true )
| ~ epred13_0 ),
inference(cn,[status(thm)],[c_0_140]) ).
thf(c_0_173,plain,
( epred4_0
| ( f1 @ ~ $true )
| ~ ( f0 @ ~ $true )
| ~ epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_174,plain,
( epred13_0
| ( f1 @ ~ $true )
| ( f0 @ ~ $true )
| ~ epred14_0 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_175,plain,
( epred13_0
| epred4_0
| ~ ( f1 @ ~ $true )
| ~ epred5_0
| ~ epred14_0 ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
thf(c_0_176,plain,
( epred4_0
| ( f1 @ ~ $true )
| ( f0 @ ~ $true )
| ~ epred6_0 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_177,plain,
( epred4_0
| ~ ( f1 @ ~ $true )
| ~ epred5_0
| ~ epred6_0 ),
inference(spm,[status(thm)],[c_0_141,c_0_143]) ).
thf(c_0_178,plain,
( epred12_0
| ( f0 @ $true )
| ~ ( f1 @ $true )
| ~ epred14_0 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_179,plain,
( epred4_0
| epred14_0
| ~ ( f1 @ $true )
| ~ ( f1 @ ~ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_143]),c_0_145]) ).
thf(c_0_180,plain,
( epred10_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_100]) ).
thf(c_0_181,plain,
( epred1_0
| epred4_0 ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
thf(c_0_182,plain,
( ( f3 @ $true )
| ~ epred8_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_150]),c_0_18]) ).
thf(c_0_183,plain,
( x
| ~ epred8_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_12]),c_0_18]) ).
thf(c_0_184,plain,
( ( f2 @ ~ $true )
| epred9_0
| ~ epred1_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_89]),c_0_151]),c_0_125]) ).
thf(c_0_185,plain,
( ( f2 @ $true )
| epred8_0
| ~ epred11_0
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
thf(c_0_186,plain,
( epred7_0
| ~ ( f0 @ ~ $true )
| ~ epred6_0 ),
inference(csr,[status(thm)],[c_0_154,c_0_155]) ).
thf(c_0_187,plain,
( ( f0 @ ~ $true )
| ( f0 @ $true )
| epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_188,plain,
( epred7_0
| ~ epred5_0
| ~ epred6_0 ),
inference(cn,[status(thm)],[c_0_156]) ).
thf(c_0_189,plain,
( epred14_0
| ~ ( f1 @ ~ $true )
| ~ epred12_0
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_190,plain,
( ( f0 @ $true )
| epred5_0
| ~ ( f1 @ ~ $true )
| ~ epred3_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_191,plain,
( ( f0 @ $true )
| epred5_0
| ~ ( f1 @ ~ $true )
| ~ ( f1 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_192,plain,
( ( f1 @ $true )
| epred12_0
| ~ ( f1 @ ~ $true )
| ~ epred10_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_193,plain,
( epred12_0
| ( f1 @ ~ $true )
| ~ epred10_0 ),
inference(cn,[status(thm)],[c_0_157]) ).
thf(c_0_194,plain,
( epred6_0
| ~ ( f1 @ ~ $true )
| ~ ( f1 @ $true )
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_195,plain,
( epred1_0
| ~ ( f2 @ $true )
| ~ ( f2 @ $true )
| ~ epred3_0 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_196,plain,
( ( f2 @ ~ $true )
| ( f2 @ ~ $true )
| epred3_0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_197,plain,
( epred11_0
| x
| ~ epred9_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
thf(c_0_198,plain,
( ( f2 @ ~ $true )
| ( f2 @ $true )
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_161]),c_0_162]) ).
thf(c_0_199,plain,
( epred9_0
| ~ x
| ~ epred10_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_85]) ).
thf(c_0_200,plain,
( epred11_0
| ~ ( f3 @ ~ $true )
| ~ epred8_0
| ~ ( f2 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_201,plain,
( epred10_0
| epred11_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_136]) ).
thf(c_0_202,plain,
( epred10_0
| ( f1 @ $true )
| ~ ( f1 @ ~ $true )
| ~ epred12_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_203,plain,
( epred10_0
| ~ epred12_0
| ~ ( f1 @ $true ) ),
inference(cn,[status(thm)],[c_0_167]) ).
thf(c_0_204,plain,
( ( f1 @ $true )
| epred13_0
| ~ ( f1 @ ~ $true )
| ~ epred11_0 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_205,plain,
( epred13_0
| ~ epred11_0
| ~ ( f1 @ $true ) ),
inference(cn,[status(thm)],[c_0_168]) ).
thf(c_0_206,plain,
( ( f1 @ ~ $true )
| ( f1 @ $true )
| epred6_0
| ~ ( f0 @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_207,plain,
( epred9_0
| ~ ( f2 @ ~ $true )
| ~ epred11_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_135]),c_0_169]) ).
thf(c_0_208,plain,
( epred8_0
| ~ ( f2 @ ~ $true )
| ~ epred11_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_139]),c_0_170]) ).
thf(c_0_209,plain,
( epred11_0
| ~ ( f1 @ ~ $true )
| ~ ( f1 @ $true )
| ~ epred12_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_210,plain,
( ( f1 @ $true )
| epred11_0
| ~ epred13_0 ),
inference(csr,[status(thm)],[c_0_171,c_0_172]) ).
thf(c_0_211,plain,
( epred13_0
| epred4_0
| ~ epred5_0
| ~ epred14_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).
thf(c_0_212,plain,
( epred4_0
| ~ epred5_0
| ~ epred6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_176]),c_0_177]) ).
thf(c_0_213,plain,
( epred12_0
| epred4_0
| ~ ( f1 @ ~ $true )
| ~ ( f1 @ $true )
| ~ epred5_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_178]),c_0_179]) ).
thf(c_0_214,plain,
( epred4_0
| epred10_0 ),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
thf(c_0_215,plain,
( ~ epred8_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_182]),c_0_183]) ).
thf(c_0_216,plain,
( epred9_0
| ~ epred1_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_184]),c_0_151]) ).
thf(c_0_217,plain,
( epred8_0
| ~ epred1_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_127]),c_0_126]),c_0_185]),c_0_152]) ).
thf(c_0_218,negated_conjecture,
( ~ epred7_0
| ~ epred14_0 ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
thf(c_0_219,plain,
( epred7_0
| ~ epred6_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188]),c_0_155]) ).
thf(c_0_220,plain,
( ( f1 @ ~ $true )
| epred14_0
| ~ ( f0 @ ~ $true )
| ~ epred12_0 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_221,plain,
( ( f0 @ ~ $true )
| ( f1 @ ~ $true )
| epred5_0
| ~ epred3_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_222,plain,
( epred5_0
| epred14_0
| ~ ( f1 @ ~ $true )
| ~ epred12_0
| ~ epred3_0 ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
thf(c_0_223,plain,
( epred5_0
| epred14_0
| ~ ( f1 @ $true )
| ~ ( f1 @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_144,c_0_191]) ).
thf(c_0_224,plain,
( ( f1 @ $true )
| epred12_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[c_0_192,c_0_193]) ).
thf(c_0_225,plain,
( epred12_0
| epred6_0
| ~ ( f1 @ $true )
| ~ ( f1 @ ~ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_178]),c_0_145]) ).
thf(c_0_226,plain,
( epred1_0
| ( f2 @ $true )
| ~ ( f2 @ ~ $true )
| ~ epred3_0 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_227,plain,
( epred1_0
| ~ epred3_0
| ~ ( f2 @ $true ) ),
inference(cn,[status(thm)],[c_0_195]) ).
thf(c_0_228,plain,
( epred6_0
| ~ ( f1 @ ~ $true )
| ~ epred3_0
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_229,plain,
( ( f2 @ $true )
| epred3_0
| ~ ( f2 @ ~ $true )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_230,plain,
( epred3_0
| ( f2 @ ~ $true )
| ~ epred1_0 ),
inference(cn,[status(thm)],[c_0_196]) ).
thf(c_0_231,plain,
( epred3_0
| ~ epred2_0
| ~ epred1_0
| ~ epred2_0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
thf(c_0_232,plain,
( ( f2 @ $true )
| epred11_0
| ~ epred2_0
| ~ epred9_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_111]),c_0_197]),c_0_198]) ).
thf(c_0_233,plain,
( ( f2 @ ~ $true )
| epred9_0
| ~ epred10_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_161]),c_0_198]),c_0_199]) ).
thf(c_0_234,plain,
( ( f2 @ ~ $true )
| epred10_0
| epred11_0
| ~ epred8_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_99]),c_0_35]) ).
thf(c_0_235,plain,
( epred8_0
| epred11_0
| epred10_0 ),
inference(spm,[status(thm)],[c_0_201,c_0_85]) ).
thf(c_0_236,plain,
( ( f3 @ ~ $true )
| epred11_0
| ~ ( f2 @ ~ $true )
| ~ epred8_0 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_237,plain,
( epred2_0
| ( f2 @ ~ $true )
| ( f2 @ ~ $true )
| ~ epred4_0 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_238,plain,
( ~ ( f2 @ ~ $true )
| ~ x
| ~ epred2_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_33]),c_0_69]) ).
thf(c_0_239,plain,
( epred10_0
| ~ ( f1 @ ~ $true )
| ~ epred12_0 ),
inference(csr,[status(thm)],[c_0_202,c_0_203]) ).
thf(c_0_240,plain,
( epred10_0
| ( f1 @ $true )
| ( f1 @ ~ $true )
| ~ epred13_0 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
thf(c_0_241,plain,
( epred13_0
| ~ ( f1 @ ~ $true )
| ~ epred11_0 ),
inference(csr,[status(thm)],[c_0_204,c_0_205]) ).
thf(c_0_242,plain,
( ( f1 @ ~ $true )
| ( f1 @ $true )
| epred13_0
| epred6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_174]),c_0_145]) ).
thf(c_0_243,plain,
( epred9_0
| ~ epred10_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_89]),c_0_124]),c_0_207]) ).
thf(c_0_244,plain,
( epred8_0
| ~ epred10_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_153]),c_0_208]) ).
thf(c_0_245,plain,
( epred6_0
| ~ epred4_0
| ~ ( f1 @ $true )
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_246,plain,
( epred11_0
| ~ epred12_0
| ~ epred13_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_172]),c_0_210]) ).
thf(c_0_247,plain,
( epred4_0
| epred13_0
| ~ epred5_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_145]),c_0_212]) ).
thf(c_0_248,plain,
( epred4_0
| epred12_0
| ~ ( f1 @ $true )
| ~ epred5_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_193]),c_0_214]) ).
thf(c_0_249,plain,
( ~ epred1_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]) ).
thf(c_0_250,negated_conjecture,
( ~ epred14_0
| ~ epred6_0 ),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
thf(c_0_251,plain,
( epred5_0
| epred14_0
| ~ epred12_0
| ~ epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_222]) ).
thf(c_0_252,plain,
( epred12_0
| epred14_0
| epred5_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_193]),c_0_224]) ).
thf(c_0_253,plain,
( epred6_0
| epred12_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_193]),c_0_224]) ).
thf(c_0_254,plain,
( epred1_0
| ~ epred3_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_226,c_0_45]),c_0_227]) ).
thf(c_0_255,plain,
( ( f1 @ ~ $true )
| epred6_0
| ~ ( f0 @ ~ $true )
| ~ epred3_0 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_256,plain,
( epred5_0
| epred6_0
| ~ ( f1 @ ~ $true )
| ~ epred3_0 ),
inference(spm,[status(thm)],[c_0_228,c_0_190]) ).
thf(c_0_257,plain,
( ( f2 @ $true )
| epred3_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[c_0_229,c_0_230]) ).
thf(c_0_258,plain,
( epred3_0
| ~ epred1_0
| ~ epred2_0 ),
inference(cn,[status(thm)],[c_0_231]) ).
thf(c_0_259,plain,
( ( f2 @ ~ $true )
| epred11_0
| ~ epred9_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_134]),c_0_197]),c_0_232]) ).
thf(c_0_260,plain,
( epred9_0
| ~ ( f2 @ $true )
| ~ epred10_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_169,c_0_233]) ).
thf(c_0_261,plain,
( ( f2 @ $true )
| x
| ~ epred2_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_135]),c_0_198]),c_0_160]) ).
thf(c_0_262,plain,
( epred10_0
| epred11_0
| ~ ( f2 @ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_234]),c_0_235]) ).
thf(c_0_263,plain,
( ( f2 @ $true )
| epred11_0
| epred10_0
| ~ epred8_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_236]),c_0_35]) ).
thf(c_0_264,plain,
( epred2_0
| ( f2 @ $true )
| ~ ( f2 @ ~ $true )
| ~ epred4_0 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_265,plain,
( epred2_0
| ( f2 @ ~ $true )
| ~ epred4_0 ),
inference(cn,[status(thm)],[c_0_237]) ).
thf(c_0_266,plain,
( ~ ( f2 @ ~ $true )
| ~ epred2_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_38]),c_0_238]),c_0_69]) ).
thf(c_0_267,plain,
( x
| epred8_0
| ~ ( f2 @ $true )
| ~ epred10_0 ),
inference(spm,[status(thm)],[c_0_138,c_0_21]) ).
thf(c_0_268,plain,
( ( f2 @ $true )
| epred8_0
| x
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_132,c_0_19]) ).
thf(c_0_269,plain,
( epred14_0
| ~ epred13_0
| ~ ( f1 @ $true )
| ~ ( f0 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_270,plain,
( ( f0 @ $true )
| epred5_0
| ~ epred4_0
| ~ ( f1 @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_271,plain,
( epred10_0
| ~ epred12_0
| ~ epred13_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_203]) ).
thf(c_0_272,plain,
( epred6_0
| epred13_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_205]) ).
thf(c_0_273,plain,
( ~ epred10_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_243]),c_0_244]) ).
thf(c_0_274,plain,
( ( f1 @ $true )
| epred6_0
| ~ ( f0 @ ~ $true )
| ~ epred4_0 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_275,plain,
( epred12_0
| ( f1 @ $true )
| ( f0 @ ~ $true )
| ~ epred14_0 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_276,plain,
( epred12_0
| epred6_0
| ~ ( f1 @ $true )
| ~ epred4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_178]),c_0_145]) ).
thf(c_0_277,plain,
( epred4_0
| epred11_0
| ~ epred12_0
| ~ epred5_0 ),
inference(spm,[status(thm)],[c_0_246,c_0_247]) ).
thf(c_0_278,plain,
( epred12_0
| epred4_0
| ~ epred5_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_224]),c_0_214]) ).
thf(c_0_279,plain,
( epred4_0
| ~ epred11_0 ),
inference(spm,[status(thm)],[c_0_249,c_0_181]) ).
thf(c_0_280,negated_conjecture,
( epred5_0
| ~ epred6_0
| ~ epred12_0
| ~ epred3_0 ),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
thf(c_0_281,negated_conjecture,
( epred5_0
| epred12_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_252]),c_0_253]) ).
thf(c_0_282,plain,
( epred10_0
| ~ epred3_0 ),
inference(spm,[status(thm)],[c_0_180,c_0_254]) ).
thf(c_0_283,plain,
( epred5_0
| epred6_0
| ~ epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_221]),c_0_256]) ).
thf(c_0_284,plain,
( epred3_0
| ~ epred1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_230]),c_0_257]),c_0_258]) ).
thf(c_0_285,plain,
( epred11_0
| ~ epred9_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_259]),c_0_232]) ).
thf(c_0_286,plain,
( epred9_0
| ~ epred10_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_199]) ).
thf(c_0_287,plain,
( epred11_0
| epred10_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_263]),c_0_235]) ).
thf(c_0_288,plain,
( ( f2 @ $true )
| epred2_0
| ~ epred4_0 ),
inference(csr,[status(thm)],[c_0_264,c_0_265]) ).
thf(c_0_289,plain,
( ( f2 @ $true )
| ~ epred2_0
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_266,c_0_198]) ).
thf(c_0_290,plain,
( ~ x
| ~ epred1_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_134]),c_0_162]),c_0_266]) ).
thf(c_0_291,plain,
( epred8_0
| x
| ~ epred10_0
| ~ epred2_0 ),
inference(spm,[status(thm)],[c_0_267,c_0_268]) ).
thf(c_0_292,plain,
( ( f1 @ $true )
| epred14_0
| ~ ( f0 @ ~ $true )
| ~ epred13_0 ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_293,plain,
( ( f0 @ ~ $true )
| ( f1 @ $true )
| epred5_0
| ~ epred4_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_294,plain,
( epred5_0
| epred14_0
| ~ ( f1 @ $true )
| ~ epred13_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_269,c_0_270]) ).
thf(c_0_295,plain,
( epred6_0
| ~ epred12_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_272]),c_0_273]) ).
thf(c_0_296,plain,
( epred12_0
| epred6_0
| ~ epred4_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_145]),c_0_276]) ).
thf(c_0_297,plain,
( epred4_0
| ~ epred5_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_278]),c_0_279]) ).
thf(c_0_298,negated_conjecture,
( epred5_0
| ~ epred3_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_280,c_0_281]),c_0_282]),c_0_283]) ).
thf(c_0_299,plain,
( epred4_0
| epred3_0 ),
inference(spm,[status(thm)],[c_0_284,c_0_181]) ).
thf(c_0_300,plain,
( epred11_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_286]),c_0_287]) ).
thf(c_0_301,plain,
( epred2_0
| ~ epred4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_265]),c_0_288]) ).
thf(c_0_302,plain,
( ~ epred1_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_161]),c_0_289]),c_0_290]),c_0_266]) ).
thf(c_0_303,plain,
( ( f2 @ $true )
| epred8_0
| ~ epred2_0
| ~ epred10_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_139]),c_0_291]),c_0_198]) ).
thf(c_0_304,plain,
( epred5_0
| epred14_0
| ~ epred13_0
| ~ epred4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_293]),c_0_294]) ).
thf(c_0_305,plain,
( ( f1 @ ~ $true )
| ( f1 @ $true )
| epred12_0 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
thf(c_0_306,plain,
( epred3_0
| ~ ( f1 @ $true )
| ~ ( f0 @ $true )
| ~ epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_307,plain,
( epred3_0
| ( f0 @ $true )
| ~ ( f1 @ $true )
| ~ epred6_0 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_308,plain,
( epred6_0
| ~ epred11_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_295,c_0_296]) ).
thf(c_0_309,negated_conjecture,
epred4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_298]),c_0_299]) ).
thf(c_0_310,plain,
( epred11_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_300,c_0_301]) ).
thf(c_0_311,plain,
( ~ epred1_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_302,c_0_301]) ).
thf(c_0_312,plain,
( ( f2 @ ~ $true )
| epred8_0
| ~ epred10_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_134]),c_0_291]),c_0_303]) ).
thf(c_0_313,negated_conjecture,
( epred5_0
| ~ epred6_0
| ~ epred13_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_250,c_0_304]) ).
thf(c_0_314,plain,
( epred12_0
| epred13_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_305]),c_0_205]) ).
thf(c_0_315,plain,
( epred3_0
| ( f1 @ $true )
| ~ ( f0 @ ~ $true )
| ~ epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
thf(c_0_316,plain,
( epred3_0
| ( f1 @ $true )
| ( f0 @ ~ $true )
| ~ epred6_0 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
thf(c_0_317,plain,
( epred3_0
| ~ ( f1 @ $true )
| ~ epred5_0
| ~ epred6_0 ),
inference(spm,[status(thm)],[c_0_306,c_0_307]) ).
thf(c_0_318,plain,
( epred6_0
| ~ epred11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_308,c_0_309])]) ).
thf(c_0_319,plain,
epred11_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_310,c_0_309])]) ).
thf(c_0_320,plain,
( ~ epred4_0
| ~ epred3_0 ),
inference(spm,[status(thm)],[c_0_311,c_0_254]) ).
thf(c_0_321,plain,
( epred8_0
| ~ epred10_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_312]),c_0_303]) ).
thf(c_0_322,negated_conjecture,
( epred12_0
| epred5_0
| ~ epred4_0
| ~ epred11_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_314]),c_0_296]) ).
thf(c_0_323,plain,
( epred3_0
| ~ epred5_0
| ~ epred6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_316]),c_0_317]) ).
thf(c_0_324,plain,
epred6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_318,c_0_319])]) ).
thf(c_0_325,plain,
~ epred3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_320,c_0_309])]) ).
thf(c_0_326,plain,
( ~ epred10_0
| ~ epred2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_286]),c_0_321]) ).
thf(c_0_327,negated_conjecture,
( epred5_0
| epred12_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_322,c_0_309])]),c_0_319])]) ).
thf(c_0_328,plain,
~ epred5_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_323,c_0_324])]),c_0_325]) ).
thf(c_0_329,plain,
( ~ epred10_0
| ~ epred4_0 ),
inference(spm,[status(thm)],[c_0_326,c_0_301]) ).
thf(c_0_330,negated_conjecture,
epred12_0,
inference(sr,[status(thm)],[c_0_327,c_0_328]) ).
thf(c_0_331,plain,
~ epred10_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_329,c_0_309])]) ).
thf(c_0_332,plain,
( ( f0 @ ~ $true )
| ( f1 @ $true ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_316,c_0_324])]),c_0_325]) ).
thf(c_0_333,plain,
~ ( f1 @ $true ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_330])]),c_0_331]) ).
thf(c_0_334,plain,
( ( f1 @ ~ $true )
| ( f1 @ $true )
| epred14_0
| ~ ( f0 @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_335,plain,
f0 @ ~ $true,
inference(sr,[status(thm)],[c_0_332,c_0_333]) ).
thf(c_0_336,plain,
~ ( f1 @ ~ $true ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_239,c_0_330])]),c_0_331]) ).
thf(c_0_337,negated_conjecture,
~ epred14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_324])]) ).
thf(c_0_338,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_334,c_0_335])]),c_0_333]),c_0_336]),c_0_337]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO500^1.004 : TPTP v8.2.0. Released v4.1.0.
% 0.00/0.09 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n011.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon May 20 10:03:08 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.13/0.38 Running higher-order theorem proving
% 0.13/0.38 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.50 # Version: 3.1.0-ho
% 0.13/0.50 # Preprocessing class: HSSSSMSSSSSNFFN.
% 0.13/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.13/0.50 # Starting ho_unfolding_6 with 300s (1) cores
% 0.13/0.50 # Starting sh4l with 300s (1) cores
% 0.13/0.50 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.13/0.50 # new_ho_10 with pid 21182 completed with status 0
% 0.13/0.50 # Result found by new_ho_10
% 0.13/0.50 # Preprocessing class: HSSSSMSSSSSNFFN.
% 0.13/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.13/0.50 # No SInE strategy applied
% 0.13/0.50 # Search class: HGHNF-FSMM00-SFFFFFNN
% 0.13/0.50 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.50 # Starting sh3 with 811s (1) cores
% 0.13/0.50 # Starting new_ho_10 with 151s (1) cores
% 0.13/0.50 # Starting new_bool_1 with 136s (1) cores
% 0.13/0.50 # Starting new_bool_9 with 136s (1) cores
% 0.13/0.50 # Starting ehoh_best8_lambda with 136s (1) cores
% 0.13/0.50 # new_ho_10 with pid 21190 completed with status 0
% 0.13/0.50 # Result found by new_ho_10
% 0.13/0.50 # Preprocessing class: HSSSSMSSSSSNFFN.
% 0.13/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.13/0.50 # No SInE strategy applied
% 0.13/0.50 # Search class: HGHNF-FSMM00-SFFFFFNN
% 0.13/0.50 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.50 # Starting sh3 with 811s (1) cores
% 0.13/0.50 # Starting new_ho_10 with 151s (1) cores
% 0.13/0.50 # Preprocessing time : 0.003 s
% 0.13/0.50 # Presaturation interreduction done
% 0.13/0.50
% 0.13/0.50 # Proof found!
% 0.13/0.50 # SZS status Theorem
% 0.13/0.50 # SZS output start CNFRefutation
% See solution above
% 0.13/0.50 # Parsed axioms : 6
% 0.13/0.50 # Removed by relevancy pruning/SinE : 0
% 0.13/0.50 # Initial clauses : 413
% 0.13/0.50 # Removed in clause preprocessing : 168
% 0.13/0.50 # Initial clauses in saturation : 245
% 0.13/0.50 # Processed clauses : 1133
% 0.13/0.50 # ...of these trivial : 4
% 0.13/0.50 # ...subsumed : 514
% 0.13/0.50 # ...remaining for further processing : 615
% 0.13/0.50 # Other redundant clauses eliminated : 0
% 0.13/0.50 # Clauses deleted for lack of memory : 0
% 0.13/0.50 # Backward-subsumed : 297
% 0.13/0.50 # Backward-rewritten : 122
% 0.13/0.50 # Generated clauses : 2509
% 0.13/0.50 # ...of the previous two non-redundant : 1503
% 0.13/0.50 # ...aggressively subsumed : 0
% 0.13/0.50 # Contextual simplify-reflections : 241
% 0.13/0.50 # Paramodulations : 2493
% 0.13/0.50 # Factorizations : 0
% 0.13/0.50 # NegExts : 0
% 0.13/0.50 # Equation resolutions : 0
% 0.13/0.50 # Disequality decompositions : 0
% 0.13/0.50 # Total rewrite steps : 129
% 0.13/0.50 # ...of those cached : 122
% 0.13/0.50 # Propositional unsat checks : 0
% 0.13/0.50 # Propositional check models : 0
% 0.13/0.50 # Propositional check unsatisfiable : 0
% 0.13/0.50 # Propositional clauses : 0
% 0.13/0.50 # Propositional clauses after purity: 0
% 0.13/0.50 # Propositional unsat core size : 0
% 0.13/0.50 # Propositional preprocessing time : 0.000
% 0.13/0.50 # Propositional encoding time : 0.000
% 0.13/0.50 # Propositional solver time : 0.000
% 0.13/0.50 # Success case prop preproc time : 0.000
% 0.13/0.50 # Success case prop encoding time : 0.000
% 0.13/0.50 # Success case prop solver time : 0.000
% 0.13/0.50 # Current number of processed clauses : 53
% 0.13/0.50 # Positive orientable unit clauses : 7
% 0.13/0.50 # Positive unorientable unit clauses: 0
% 0.13/0.50 # Negative unit clauses : 8
% 0.13/0.50 # Non-unit-clauses : 38
% 0.13/0.50 # Current number of unprocessed clauses: 634
% 0.13/0.50 # ...number of literals in the above : 3191
% 0.13/0.50 # Current number of archived formulas : 0
% 0.13/0.50 # Current number of archived clauses : 562
% 0.13/0.50 # Clause-clause subsumption calls (NU) : 58112
% 0.13/0.50 # Rec. Clause-clause subsumption calls : 21427
% 0.13/0.50 # Non-unit clause-clause subsumptions : 981
% 0.13/0.50 # Unit Clause-clause subsumption calls : 998
% 0.13/0.50 # Rewrite failures with RHS unbound : 0
% 0.13/0.50 # BW rewrite match attempts : 7
% 0.13/0.50 # BW rewrite match successes : 7
% 0.13/0.50 # Condensation attempts : 1133
% 0.13/0.50 # Condensation successes : 0
% 0.13/0.50 # Termbank termtop insertions : 43097
% 0.13/0.50 # Search garbage collected termcells : 2459
% 0.13/0.50
% 0.13/0.50 # -------------------------------------------------
% 0.13/0.50 # User time : 0.106 s
% 0.13/0.50 # System time : 0.003 s
% 0.13/0.50 # Total time : 0.109 s
% 0.13/0.50 # Maximum resident set size: 2388 pages
% 0.13/0.50
% 0.13/0.50 # -------------------------------------------------
% 0.13/0.50 # User time : 0.485 s
% 0.13/0.50 # System time : 0.016 s
% 0.13/0.50 # Total time : 0.500 s
% 0.13/0.50 # Maximum resident set size: 1748 pages
% 0.13/0.50 % E---3.1 exiting
% 0.13/0.50 % E exiting
%------------------------------------------------------------------------------