TSTP Solution File: NUM788^4 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM788^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 : Sat May 4 08:57:57 EDT 2024
% Result : Theorem 0.80s 0.73s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 59
% Syntax : Number of formulae : 112 ( 45 unt; 39 typ; 0 def)
% Number of atoms : 800 ( 42 equ; 0 cnn)
% Maximal formula atoms : 117 ( 10 avg)
% Number of connectives : 3934 ( 142 ~; 88 |; 12 &;3573 @)
% ( 0 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 9 con; 0-3 aty)
% Number of variables : 514 ( 425 ^ 89 !; 0 ?; 514 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_29,type,
power: $i > $i ).
thf(decl_42,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_66,type,
d_and: $o > $o > $o ).
thf(decl_67,type,
l_or: $o > $o > $o ).
thf(decl_71,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(decl_72,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_74,type,
and3: $o > $o > $o > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_102,type,
esti: $i > $i > $i > $o ).
thf(decl_111,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(decl_112,type,
ect: $i > ( $i > $i > $o ) > $i ).
thf(decl_115,type,
ecect: $i > ( $i > $i > $o ) > $i > $i ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_148,type,
d_29_ii: $i > $i > $o ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_176,type,
pair1type: $i > $i ).
thf(decl_189,type,
frac: $i ).
thf(decl_191,type,
num: $i > $i ).
thf(decl_192,type,
den: $i > $i ).
thf(decl_193,type,
n_eq: $i > $i > $o ).
thf(decl_194,type,
moref: $i > $i > $o ).
thf(decl_195,type,
lessf: $i > $i > $o ).
thf(decl_203,type,
inf: $i > $i > $o ).
thf(decl_204,type,
rat: $i ).
thf(decl_205,type,
rt_is: $i > $i > $o ).
thf(decl_212,type,
class: $i > $i ).
thf(decl_215,type,
rt_more: $i > $i > $o ).
thf(decl_217,type,
rt_less: $i > $i > $o ).
thf(decl_220,type,
rt_lessis: $i > $i > $o ).
thf(decl_221,type,
esk1_0: $i ).
thf(decl_222,type,
esk2_0: $i ).
thf(decl_223,type,
esk3_0: $i ).
thf(decl_224,type,
esk4_0: $i ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_is_of) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_imp) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_n_eq) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_l_some) ).
thf(def_ect,axiom,
( ect
= ( ^ [X1: $i,X147: $i > $i > $o] : ( d_Sep @ ( power @ X1 ) @ ( anec @ X1 @ X147 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_ect) ).
thf(def_rt_less,axiom,
( rt_less
= ( ^ [X1: $i,X652: $i] :
( l_some @ frac
@ ^ [X4: $i] :
( l_some @ frac
@ ^ [X13: $i] : ( and3 @ ( inf @ X4 @ ( class @ X1 ) ) @ ( inf @ X13 @ ( class @ X652 ) ) @ ( lessf @ X4 @ X13 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_rt_less) ).
thf(def_class,axiom,
( class
= ( ecect @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_class) ).
thf(def_frac,axiom,
( frac
= ( pair1type @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_frac) ).
thf(def_inf,axiom,
( inf
= ( esti @ ( pair1type @ nat ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_inf) ).
thf(def_and3,axiom,
( and3
= ( ^ [X92: $o,X93: $o,X94: $o] : ( d_and @ X92 @ ( d_and @ X93 @ X94 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_and3) ).
thf(def_rat,axiom,
( rat
= ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_rat) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_l_or) ).
thf(def_rt_more,axiom,
( rt_more
= ( ^ [X1: $i,X650: $i] :
( l_some @ frac
@ ^ [X4: $i] :
( l_some @ frac
@ ^ [X13: $i] : ( and3 @ ( inf @ X4 @ ( class @ X1 ) ) @ ( inf @ X13 @ ( class @ X650 ) ) @ ( moref @ X4 @ X13 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_rt_more) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_moref) ).
thf(def_rt_lessis,axiom,
( rt_lessis
= ( ^ [X1: $i,X665: $i] : ( l_or @ ( rt_less @ X1 @ X665 ) @ ( rt_is @ X1 @ X665 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_rt_lessis) ).
thf(def_rt_is,axiom,
( rt_is
= ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',def_rt_is) ).
thf(satz81d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X668: $i] : ( in @ X668 @ rat )
@ ^ [X669: $i] :
( ( rt_lessis @ X1 @ X669 )
=> ( d_not @ ( rt_more @ X1 @ X669 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',satz81d) ).
thf(satz81g,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X674: $i] : ( in @ X674 @ rat )
@ ^ [X675: $i] :
( ( rt_more @ X1 @ X675 )
=> ( d_not @ ( rt_lessis @ X1 @ X675 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p',satz81g) ).
thf(c_0_20,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_21,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_22,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_23,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_24,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_25,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X682: $i] :
( ( in @ X682 @ Z0 )
=> ( non @ Z0 @ Z1 @ X682 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_26,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,plain,
( ect
= ( ^ [Z0: $i,Z1: $i > $i > $o] : ( d_Sep @ ( power @ Z0 ) @ ( anec @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_ect]) ).
thf(c_0_29,plain,
( rt_less
= ( ^ [Z0: $i,Z1: $i] :
( ! [X686: $i] :
( ( in @ X686 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X685: $i] :
( ( in @ X685 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z3: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z2
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z3
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z1 ) )
@ ( lessf @ Z2 @ Z3 ) ) )
@ X685 ) )
=> ~ $true )
@ X686 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_less]) ).
thf(c_0_30,axiom,
( class
= ( ecect @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_class,c_0_24]),def_frac]) ).
thf(c_0_31,axiom,
( inf
= ( esti @ ( pair1type @ nat ) ) ),
inference(apply_def,[status(thm)],[def_inf,def_frac]) ).
thf(c_0_32,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] : ( d_and @ Z0 @ ( d_and @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_and3]) ).
thf(c_0_33,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X682: $i] :
( ( in @ X682 @ Z0 )
=> ( non @ Z0 @ Z1 @ X682 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_34,axiom,
( rat
= ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_rat,c_0_24]),c_0_28]),def_frac]) ).
thf(c_0_35,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_36,plain,
( rt_more
= ( ^ [Z0: $i,Z1: $i] :
( ! [X684: $i] :
( ( in @ X684 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X683: $i] :
( ( in @ X683 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z3: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z2
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z3
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z1 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) ) ) )
@ X683 ) )
=> ~ $true )
@ X684 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_more]) ).
thf(c_0_37,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] : ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_38,plain,
( rt_lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X687: $i] :
( ( in @ X687 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X688: $i] :
( ( in @ X688 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z3: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z2
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z3
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z1 ) )
@ ( lessf @ Z2 @ Z3 ) ) )
@ X688 ) )
=> ~ $true )
@ X687 ) )
=> ~ $true )
=> ~ $true )
=> ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) ) ) )
@ Z0
@ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_lessis]) ).
thf(c_0_39,plain,
( rt_less
= ( ^ [Z0: $i,Z1: $i] :
( ! [X686: $i] :
( ( in @ X686 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X685: $i] :
( ( in @ X685 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z3: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z2
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z3
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z1 ) )
@ ( lessf @ Z2 @ Z3 ) ) )
@ X685 ) )
=> ~ $true )
@ X686 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,def_frac]),c_0_30]),c_0_31]),c_0_32]),c_0_33]) ).
thf(c_0_40,axiom,
( rt_is
= ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[def_rt_is,c_0_34]) ).
thf(c_0_41,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35,c_0_23]),c_0_27]) ).
thf(c_0_42,plain,
( rt_more
= ( ^ [Z0: $i,Z1: $i] :
( ! [X684: $i] :
( ( in @ X684 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X683: $i] :
( ( in @ X683 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z3: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z2
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z3
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z1 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) ) ) )
@ X683 ) )
=> ~ $true )
@ X684 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_36,def_frac]),c_0_30]),c_0_31]),c_0_37]),c_0_32]),c_0_33]) ).
thf(c_0_43,plain,
( rt_lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X687: $i] :
( ( in @ X687 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X688: $i] :
( ( in @ X688 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z3: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z2
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z3
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z4: $i,Z5: $i] : ( n_is @ ( n_ts @ ( num @ Z4 ) @ ( den @ Z5 ) ) @ ( n_ts @ ( num @ Z5 ) @ ( den @ Z4 ) ) )
@ Z1 ) )
@ ( lessf @ Z2 @ Z3 ) ) )
@ X688 ) )
=> ~ $true )
@ X687 ) )
=> ~ $true )
=> ~ $true )
=> ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) ) ) )
@ Z0
@ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]) ).
thf(c_0_44,plain,
! [X700: $i] :
( ( in @ X700
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ! [X699: $i] :
( ( in @ X699
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ( ( ( ( ! [X695: $i] :
( ( in @ X695 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X696: $i] :
( ( in @ X696 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X700 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X699 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X696 ) )
=> ~ $true )
@ X695 ) )
=> ~ $true )
=> ~ $true )
=> ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X700
@ X699 ) )
=> ( ( ! [X697: $i] :
( ( in @ X697 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X698: $i] :
( ( in @ X698 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X700 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X699 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X698 ) )
=> ~ $true )
@ X697 ) )
=> ~ $true )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz81d]),c_0_26]),c_0_34]),c_0_42]),c_0_43]),c_0_27]) ).
thf(c_0_45,negated_conjecture,
~ ! [X694: $i] :
( ( in @ X694
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ! [X693: $i] :
( ( in @ X693
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
=> ( ( ! [X689: $i] :
( ( in @ X689 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X690: $i] :
( ( in @ X690 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X694 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X693 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X690 ) )
=> ~ $true )
@ X689 ) )
=> ~ $true )
=> ( ( ( ( ! [X691: $i] :
( ( in @ X691 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X692: $i] :
( ( in @ X692 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X694 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X693 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X692 ) )
=> ~ $true )
@ X691 ) )
=> ~ $true )
=> ~ $true )
=> ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X694
@ X693 ) )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz81g])]),c_0_26]),c_0_34]),c_0_42]),c_0_43]),c_0_27]) ).
thf(c_0_46,plain,
! [X750: $i,X751: $i,X752: $i,X753: $i] :
( ( ~ ( in @ X753 @ ( pair1type @ nat ) )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X698: $i] :
( ( in @ X698 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X750 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X751 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X698 ) )
=> ~ $true )
@ X753 )
| ~ $true
| ~ ( in @ X752 @ ( pair1type @ nat ) )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X696: $i] :
( ( in @ X696 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X750 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X751 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X696 ) )
=> ~ $true )
@ X752 )
| ~ $true
| ~ ( in @ X751
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X750
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) )
& ( $true
| ~ $true
| ~ ( in @ X752 @ ( pair1type @ nat ) )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X696: $i] :
( ( in @ X696 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X750 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X751 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X696 ) )
=> ~ $true )
@ X752 )
| ~ $true
| ~ ( in @ X751
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X750
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) )
& ( ~ ( in @ X753 @ ( pair1type @ nat ) )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X698: $i] :
( ( in @ X698 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X750 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X751 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X698 ) )
=> ~ $true )
@ X753 )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X751
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X750
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X751
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X750
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) )
& ( ~ ( in @ X753 @ ( pair1type @ nat ) )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X698: $i] :
( ( in @ X698 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X750 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X751 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X698 ) )
=> ~ $true )
@ X753 )
| ~ $true
| ~ ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X750
@ X751 )
| ~ ( in @ X751
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X750
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) )
& ( $true
| ~ $true
| ~ ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X750
@ X751 )
| ~ ( in @ X751
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X750
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])]) ).
thf(c_0_47,negated_conjecture,
( ( in @ esk1_0
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
& ( in @ esk2_0
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
& ( ( in @ esk3_0 @ ( pair1type @ nat ) )
| ~ $true )
& ( ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X690: $i] :
( ( in @ X690 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X690 ) )
=> ~ $true )
@ esk3_0 )
| ~ $true )
& ( ( in @ esk4_0 @ ( pair1type @ nat ) )
| ~ $true
| ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 ) )
& ( ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X692: $i] :
( ( in @ X692 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X692 ) )
=> ~ $true )
@ esk4_0 )
| ~ $true
| ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 ) )
& ( $true
| ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 ) )
& $true ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
thf(c_0_48,plain,
! [X1: $i,X8: $i,X6: $i,X5: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X799: $i] :
( ( in @ X799 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X5 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X6 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X799 ) )
=> ~ $true )
@ X1 )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X800: $i] :
( ( in @ X800 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X5 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X6 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X800 ) )
=> ~ $true )
@ X8 )
| ~ ( in @ X1 @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X8 @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X6
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X5
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_49,negated_conjecture,
( ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X801: $i] :
( ( in @ X801 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X801 ) )
=> ~ $true )
@ esk3_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_50,plain,
! [X1: $i,X6: $i,X5: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X802: $i] :
( ( in @ X802 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X5 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X6 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X802 ) )
=> ~ $true )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) )
| ~ $true
| ~ ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X5
@ X6 )
| ~ ( in @ X6
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X5
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_51,plain,
! [X1: $i,X8: $i,X6: $i,X5: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X803: $i] :
( ( in @ X803 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X5 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X6 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X803 ) )
=> ~ $true )
@ X8 )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X804: $i] :
( ( in @ X804 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X5 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X6 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X804 ) )
=> ~ $true )
@ X1 )
| ~ ( in @ X8 @ ( pair1type @ nat ) )
| ~ ( in @ X1 @ ( pair1type @ nat ) )
| ~ ( in @ X6
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X5
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_52,negated_conjecture,
~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X805: $i] :
( ( in @ X805 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X805 ) )
=> ~ $true )
@ esk3_0 ),
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_53,plain,
! [X1: $i,X5: $i,X6: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X806: $i] :
( ( in @ X806 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X5 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X6 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X806 ) )
=> ~ $true )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) )
| ~ ( in @ X6
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X5
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X5
@ X6 ) ),
inference(cn,[status(thm)],[c_0_50]) ).
thf(c_0_54,negated_conjecture,
( ( in @ esk3_0 @ ( pair1type @ nat ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_55,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X807: $i] :
( ( in @ X807 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X1 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X4 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X807 ) )
@ X5 )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X808: $i] :
( ( in @ X808 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X1 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X4 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X808 ) )
@ X6 )
| ~ ( in @ X4
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X1
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X6 @ ( pair1type @ nat ) )
| ~ ( in @ X5 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_51]) ).
thf(c_0_56,negated_conjecture,
( in @ esk2_0
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_57,negated_conjecture,
( ( in @ esk4_0 @ ( pair1type @ nat ) )
| ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_58,negated_conjecture,
~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X809: $i] :
( ( in @ X809 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X809 ) )
@ esk3_0 ),
inference(cn,[status(thm)],[c_0_52]) ).
thf(c_0_59,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X810: $i] :
( ( in @ X810 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X1 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X4 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X810 ) )
@ X5 )
| ~ ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X1
@ X4 )
| ~ ( in @ X4
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X1
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X5 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_60,negated_conjecture,
( in @ esk1_0
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_61,negated_conjecture,
in @ esk3_0 @ ( pair1type @ nat ),
inference(cn,[status(thm)],[c_0_54]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i,X5: $i,X4: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X811: $i] :
( ( in @ X811 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X1 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X811 ) )
@ X4 )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X812: $i] :
( ( in @ X812 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ X1 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X812 ) )
@ X5 )
| ~ ( in @ X1
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) )
| ~ ( in @ X5 @ ( pair1type @ nat ) )
| ~ ( in @ X4 @ ( pair1type @ nat ) ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_63,negated_conjecture,
( ( in @ esk4_0 @ ( pair1type @ nat ) )
| ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 ) ),
inference(cn,[status(thm)],[c_0_57]) ).
thf(c_0_64,negated_conjecture,
~ ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_56]),c_0_60]),c_0_61])]) ).
thf(c_0_65,negated_conjecture,
( ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X813: $i] :
( ( in @ X813 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X813 ) )
=> ~ $true )
@ esk4_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_66,negated_conjecture,
! [X4: $i,X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X814: $i] :
( ( in @ X814 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X814 ) )
@ X1 )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X815: $i] :
( ( in @ X815 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X815 ) )
@ X4 )
| ~ ( in @ X4 @ ( pair1type @ nat ) )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(spm,[status(thm)],[c_0_62,c_0_60]) ).
thf(c_0_67,negated_conjecture,
in @ esk4_0 @ ( pair1type @ nat ),
inference(sr,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_68,negated_conjecture,
( ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X816: $i] :
( ( in @ X816 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X816 ) )
=> ~ $true )
@ esk4_0 ) ),
inference(cn,[status(thm)],[c_0_65]) ).
thf(c_0_69,negated_conjecture,
! [X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X817: $i] :
( ( in @ X817 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X817 ) )
@ X1 )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X818: $i] :
( ( in @ X818 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X818 ) )
@ esk4_0 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_70,negated_conjecture,
( ( e_is
@ ( d_Sep @ ( power @ ( pair1type @ nat ) )
@ ( anec @ ( pair1type @ nat )
@ ^ [Z0: $i,Z1: $i] : ( n_is @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ esk1_0
@ esk2_0 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X819: $i] :
( ( in @ X819 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X819 ) )
@ esk4_0 ) ),
inference(cn,[status(thm)],[c_0_68]) ).
thf(c_0_71,negated_conjecture,
( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X820: $i] :
( ( in @ X820 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z1: $i] :
( d_and
@ ( esti @ ( pair1type @ nat ) @ Z0
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk1_0 ) )
@ ( d_and
@ ( esti @ ( pair1type @ nat ) @ Z1
@ ( ecect @ ( pair1type @ nat )
@ ^ [Z2: $i,Z3: $i] : ( n_is @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) )
@ esk2_0 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X820 ) )
@ esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_69]),c_0_61])]) ).
thf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : NUM788^4 : TPTP v8.1.2. Released v7.1.0.
% 0.08/0.16 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 09:57:45 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.20/0.51 Running higher-order theorem proving
% 0.20/0.51 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.NBYexqKPxm/E---3.1_19418.p
% 0.80/0.73 # Version: 3.1.0-ho
% 0.80/0.73 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.80/0.73 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.73 # Starting pre_casc_4 with 1200s (4) cores
% 0.80/0.73 # Starting full_lambda_6 with 300s (1) cores
% 0.80/0.73 # Starting sh10 with 300s (1) cores
% 0.80/0.73 # Starting post_as_ho9 with 300s (1) cores
% 0.80/0.73 # Starting post_as_ho8 with 300s (1) cores
% 0.80/0.73 # post_as_ho9 with pid 19500 completed with status 0
% 0.80/0.73 # Result found by post_as_ho9
% 0.80/0.73 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.80/0.73 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.73 # Starting pre_casc_4 with 1200s (4) cores
% 0.80/0.73 # Starting full_lambda_6 with 300s (1) cores
% 0.80/0.73 # Starting sh10 with 300s (1) cores
% 0.80/0.73 # Starting post_as_ho9 with 300s (1) cores
% 0.80/0.73 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.80/0.73 # Search class: HGHNF-FFLS31-DHSMMFBN
% 0.80/0.73 # partial match(5): HGHSM-FSLS31-SHSMMSBN
% 0.80/0.73 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.80/0.73 # Starting new_ho_10 with 163s (1) cores
% 0.80/0.73 # new_ho_10 with pid 19503 completed with status 0
% 0.80/0.73 # Result found by new_ho_10
% 0.80/0.73 # Preprocessing class: HSLMSMSMLLLCHSA.
% 0.80/0.73 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.73 # Starting pre_casc_4 with 1200s (4) cores
% 0.80/0.73 # Starting full_lambda_6 with 300s (1) cores
% 0.80/0.73 # Starting sh10 with 300s (1) cores
% 0.80/0.73 # Starting post_as_ho9 with 300s (1) cores
% 0.80/0.73 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.80/0.73 # Search class: HGHNF-FFLS31-DHSMMFBN
% 0.80/0.73 # partial match(5): HGHSM-FSLS31-SHSMMSBN
% 0.80/0.73 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.80/0.73 # Starting new_ho_10 with 163s (1) cores
% 0.80/0.73 # Preprocessing time : 0.003 s
% 0.80/0.73 # Presaturation interreduction done
% 0.80/0.73
% 0.80/0.73 # Proof found!
% 0.80/0.73 # SZS status Theorem
% 0.80/0.73 # SZS output start CNFRefutation
% See solution above
% 0.80/0.73 # Parsed axioms : 697
% 0.80/0.73 # Removed by relevancy pruning/SinE : 655
% 0.80/0.73 # Initial clauses : 51
% 0.80/0.73 # Removed in clause preprocessing : 15
% 0.80/0.73 # Initial clauses in saturation : 36
% 0.80/0.73 # Processed clauses : 277
% 0.80/0.73 # ...of these trivial : 0
% 0.80/0.73 # ...subsumed : 59
% 0.80/0.73 # ...remaining for further processing : 218
% 0.80/0.73 # Other redundant clauses eliminated : 0
% 0.80/0.73 # Clauses deleted for lack of memory : 0
% 0.80/0.73 # Backward-subsumed : 1
% 0.80/0.73 # Backward-rewritten : 4
% 0.80/0.73 # Generated clauses : 893
% 0.80/0.73 # ...of the previous two non-redundant : 846
% 0.80/0.73 # ...aggressively subsumed : 0
% 0.80/0.73 # Contextual simplify-reflections : 13
% 0.80/0.73 # Paramodulations : 891
% 0.80/0.73 # Factorizations : 0
% 0.80/0.73 # NegExts : 0
% 0.80/0.73 # Equation resolutions : 0
% 0.80/0.73 # Disequality decompositions : 0
% 0.80/0.73 # Total rewrite steps : 251
% 0.80/0.73 # ...of those cached : 242
% 0.80/0.73 # Propositional unsat checks : 0
% 0.80/0.73 # Propositional check models : 0
% 0.80/0.73 # Propositional check unsatisfiable : 0
% 0.80/0.73 # Propositional clauses : 0
% 0.80/0.73 # Propositional clauses after purity: 0
% 0.80/0.73 # Propositional unsat core size : 0
% 0.80/0.73 # Propositional preprocessing time : 0.000
% 0.80/0.73 # Propositional encoding time : 0.000
% 0.80/0.73 # Propositional solver time : 0.000
% 0.80/0.73 # Success case prop preproc time : 0.000
% 0.80/0.73 # Success case prop encoding time : 0.000
% 0.80/0.73 # Success case prop solver time : 0.000
% 0.80/0.73 # Current number of processed clauses : 175
% 0.80/0.73 # Positive orientable unit clauses : 11
% 0.80/0.73 # Positive unorientable unit clauses: 0
% 0.80/0.73 # Negative unit clauses : 3
% 0.80/0.73 # Non-unit-clauses : 161
% 0.80/0.73 # Current number of unprocessed clauses: 636
% 0.80/0.73 # ...number of literals in the above : 4715
% 0.80/0.73 # Current number of archived formulas : 0
% 0.80/0.73 # Current number of archived clauses : 43
% 0.80/0.73 # Clause-clause subsumption calls (NU) : 21296
% 0.80/0.73 # Rec. Clause-clause subsumption calls : 3841
% 0.80/0.73 # Non-unit clause-clause subsumptions : 72
% 0.80/0.73 # Unit Clause-clause subsumption calls : 144
% 0.80/0.73 # Rewrite failures with RHS unbound : 0
% 0.80/0.73 # BW rewrite match attempts : 38
% 0.80/0.73 # BW rewrite match successes : 4
% 0.80/0.73 # Condensation attempts : 277
% 0.80/0.73 # Condensation successes : 0
% 0.80/0.73 # Termbank termtop insertions : 213082
% 0.80/0.73 # Search garbage collected termcells : 10344
% 0.80/0.73
% 0.80/0.73 # -------------------------------------------------
% 0.80/0.73 # User time : 0.170 s
% 0.80/0.73 # System time : 0.011 s
% 0.80/0.73 # Total time : 0.181 s
% 0.80/0.73 # Maximum resident set size: 4108 pages
% 0.80/0.73
% 0.80/0.73 # -------------------------------------------------
% 0.80/0.73 # User time : 0.189 s
% 0.80/0.73 # System time : 0.015 s
% 0.80/0.73 # Total time : 0.204 s
% 0.80/0.73 # Maximum resident set size: 3124 pages
% 0.80/0.73 % E---3.1 exiting
% 0.80/0.73 % E exiting
%------------------------------------------------------------------------------