%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM791^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:17:08 AM UTC 2026
% Result : Theorem 0.29s 0.42s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 74 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 860 ( 42 equ; 0 cnn)
% Maximal formula atoms : 171 ( 11 avg)
% Number of connectives : 4348 ( 158 ~; 116 |; 14 &;3941 @)
% ( 0 <=>; 119 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 7 con; 0-3 aty)
% Number of variables : 545 ( 459 ^; 86 !; 0 ?; 545 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_30,type,
power: $i > $i ).
thf(decl_43,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(decl_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_67,type,
d_and: $o > $o > $o ).
thf(decl_68,type,
l_or: $o > $o > $o ).
thf(decl_72,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_75,type,
and3: $o > $o > $o > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_103,type,
esti: $i > $i > $i > $o ).
thf(decl_112,type,
anec: $i > ( $i > $i > $o ) > $i > $o ).
thf(decl_113,type,
ect: $i > ( $i > $i > $o ) > $i ).
thf(decl_116,type,
ecect: $i > ( $i > $i > $o ) > $i > $i ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_163,type,
n_ts: $i > $i > $i ).
thf(decl_177,type,
pair1type: $i > $i ).
thf(decl_190,type,
frac: $i ).
thf(decl_192,type,
num: $i > $i ).
thf(decl_193,type,
den: $i > $i ).
thf(decl_194,type,
n_eq: $i > $i > $o ).
thf(decl_195,type,
moref: $i > $i > $o ).
thf(decl_196,type,
lessf: $i > $i > $o ).
thf(decl_204,type,
inf: $i > $i > $o ).
thf(decl_205,type,
rat: $i ).
thf(decl_206,type,
rt_is: $i > $i > $o ).
thf(decl_213,type,
class: $i > $i ).
thf(decl_216,type,
rt_more: $i > $i > $o ).
thf(decl_218,type,
rt_less: $i > $i > $o ).
thf(decl_221,type,
rt_lessis: $i > $i > $o ).
thf(decl_222,type,
esk1_0: $i ).
thf(decl_223,type,
esk2_0: $i ).
thf(decl_226,type,
esk5_2: $i > $i > $i ).
thf(decl_227,type,
esk6_2: $i > $i > $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_imp) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_is_of) ).
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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_n_eq) ).
thf(def_ect,axiom,
( ect
= ( ^ [X1: $i,X147: $i > $i > $o] : ( d_Sep @ ( power @ X1 ) @ ( anec @ X1 @ X147 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_ect) ).
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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_l_some) ).
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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_rat) ).
thf(def_frac,axiom,
( frac
= ( pair1type @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_frac) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_l_or) ).
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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_class) ).
thf(def_inf,axiom,
( inf
= ( esti @ ( pair1type @ nat ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_inf) ).
thf(def_and3,axiom,
( and3
= ( ^ [X92: $o,X93: $o,X94: $o] : ( d_and @ X92 @ ( d_and @ X93 @ X94 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_and3) ).
thf(def_rt_lessis,axiom,
( rt_lessis
= ( ^ [X1: $i,X665: $i] : ( l_or @ ( rt_less @ X1 @ X665 ) @ ( rt_is @ X1 @ X665 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_rt_is) ).
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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.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/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',def_moref) ).
thf(satz81k,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X680: $i] : ( in @ X680 @ rat )
@ ^ [X681: $i] :
( ( d_not @ ( rt_lessis @ X1 @ X681 ) )
=> ( rt_more @ X1 @ X681 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',satz81k) ).
thf(satz81e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X670: $i] : ( in @ X670 @ rat )
@ ^ [X671: $i] :
( ( d_not @ ( rt_more @ X1 @ X671 ) )
=> ( rt_lessis @ X1 @ X671 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p',satz81e) ).
thf(c_0_20,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_21,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_22,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_23,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
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,
( ect
= ( ^ [Z0: $i,Z1: $i > $i > $o] : ( d_Sep @ ( power @ Z0 ) @ ( anec @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_ect]) ).
thf(c_0_26,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X688: $i] :
( ( in @ X688 @ Z0 )
=> ( non @ Z0 @ Z1 @ X688 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_27,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_28,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_29,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_25]),def_frac]) ).
thf(c_0_30,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_31,plain,
( rt_less
= ( ^ [Z0: $i,Z1: $i] :
( ! [X692: $i] :
( ( in @ X692 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X691: $i] :
( ( in @ X691 @ ( 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 ) ) )
@ X691 ) )
=> ~ $true )
@ X692 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_less]) ).
thf(c_0_32,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_33,axiom,
( inf
= ( esti @ ( pair1type @ nat ) ) ),
inference(apply_def,[status(thm)],[def_inf,def_frac]) ).
thf(c_0_34,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_35,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X688: $i] :
( ( in @ X688 @ Z0 )
=> ( non @ Z0 @ Z1 @ X688 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_36,plain,
( rt_lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X693: $i] :
( ( in @ X693 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X694: $i] :
( ( in @ X694 @ ( 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 ) ) )
@ X694 ) )
=> ~ $true )
@ X693 ) )
=> ~ $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_37,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_29]) ).
thf(c_0_38,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_21]),c_0_27]) ).
thf(c_0_39,plain,
( rt_less
= ( ^ [Z0: $i,Z1: $i] :
( ! [X692: $i] :
( ( in @ X692 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X691: $i] :
( ( in @ X691 @ ( 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 ) ) )
@ X691 ) )
=> ~ $true )
@ X692 ) )
=> ~ $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_31,def_frac]),c_0_32]),c_0_33]),c_0_34]),c_0_35]) ).
thf(c_0_40,plain,
( rt_more
= ( ^ [Z0: $i,Z1: $i] :
( ! [X690: $i] :
( ( in @ X690 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X689: $i] :
( ( in @ X689 @ ( 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 ) ) ) ) )
@ X689 ) )
=> ~ $true )
@ X690 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_more]) ).
thf(c_0_41,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_42,plain,
( rt_lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X693: $i] :
( ( in @ X693 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X694: $i] :
( ( in @ X694 @ ( 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 ) ) )
@ X694 ) )
=> ~ $true )
@ X693 ) )
=> ~ $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_36,c_0_37]),c_0_38]),c_0_39]) ).
thf(c_0_43,plain,
( rt_more
= ( ^ [Z0: $i,Z1: $i] :
( ! [X690: $i] :
( ( in @ X690 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X689: $i] :
( ( in @ X689 @ ( 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 ) ) ) ) )
@ X689 ) )
=> ~ $true )
@ X690 ) )
=> ~ $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_40,def_frac]),c_0_32]),c_0_33]),c_0_41]),c_0_34]),c_0_35]) ).
thf(c_0_44,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X680: $i] : ( in @ X680 @ rat )
@ ^ [X681: $i] :
( ( d_not @ ( rt_lessis @ X1 @ X681 ) )
=> ( rt_more @ X1 @ X681 ) ) ) ),
inference(assume_negation,[status(cth)],[satz81k]) ).
thf(c_0_45,plain,
! [X724: $i] :
( ( in @ X724
@ ( 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 ) ) ) ) ) )
=> ! [X723: $i] :
( ( in @ X723
@ ( 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 ) ) ) ) ) )
=> ( ( ( ! [X719: $i] :
( ( in @ X719 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X720: $i] :
( ( in @ X720 @ ( 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 ) ) )
@ X724 ) )
@ ( 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 ) ) )
@ X723 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X720 ) )
=> ~ $true )
@ X719 ) )
=> ~ $true )
=> ~ $true )
=> ( ( ( ! [X721: $i] :
( ( in @ X721 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X722: $i] :
( ( in @ X722 @ ( 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 ) ) )
@ X724 ) )
@ ( 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 ) ) )
@ X723 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X722 ) )
=> ~ $true )
@ X721 ) )
=> ~ $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 ) ) ) ) )
@ X724
@ X723 ) ) ) ) ),
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)],[satz81e]),c_0_29]),c_0_42]),c_0_27]),c_0_43]),c_0_28]) ).
thf(c_0_46,negated_conjecture,
~ ! [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 ) )
=> ~ $true )
=> ( ! [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 ) ) ) ),
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)],[c_0_44]),c_0_29]),c_0_42]),c_0_27]),c_0_43]),c_0_28]) ).
thf(c_0_47,plain,
! [X774: $i,X775: $i] :
( ( ( in @ ( esk6_2 @ X774 @ X775 ) @ ( 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 ) ) ) ) )
@ X774
@ X775 )
| ( in @ ( esk5_2 @ X774 @ X775 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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 ) ) ) ) ) ) )
& ( ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X722: $i] :
( ( in @ X722 @ ( 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 ) ) )
@ X774 ) )
@ ( 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 ) ) )
@ X775 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X722 ) )
=> ~ $true )
@ ( esk6_2 @ X774 @ X775 ) )
| ~ $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 ) ) ) ) )
@ X774
@ X775 )
| ( in @ ( esk5_2 @ X774 @ X775 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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
| ( 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 ) ) ) ) )
@ X774
@ X775 )
| ( in @ ( esk5_2 @ X774 @ X775 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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 @ ( esk6_2 @ X774 @ X775 ) @ ( 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 ) ) ) ) )
@ X774
@ X775 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X720: $i] :
( ( in @ X720 @ ( 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 ) ) )
@ X774 ) )
@ ( 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 ) ) )
@ X775 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X720 ) )
=> ~ $true )
@ ( esk5_2 @ X774 @ X775 ) )
| ~ $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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 ) ) ) ) ) ) )
& ( ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X722: $i] :
( ( in @ X722 @ ( 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 ) ) )
@ X774 ) )
@ ( 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 ) ) )
@ X775 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X722 ) )
=> ~ $true )
@ ( esk6_2 @ X774 @ X775 ) )
| ~ $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 ) ) ) ) )
@ X774
@ X775 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X720: $i] :
( ( in @ X720 @ ( 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 ) ) )
@ X774 ) )
@ ( 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 ) ) )
@ X775 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X720 ) )
=> ~ $true )
@ ( esk5_2 @ X774 @ X775 ) )
| ~ $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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
| ( 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 ) ) ) ) )
@ X774
@ X775 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X720: $i] :
( ( in @ X720 @ ( 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 ) ) )
@ X774 ) )
@ ( 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 ) ) )
@ X775 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X720 ) )
=> ~ $true )
@ ( esk5_2 @ X774 @ X775 ) )
| ~ $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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 @ ( esk6_2 @ X774 @ X775 ) @ ( 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 ) ) ) ) )
@ X774
@ X775 )
| $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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 ) ) ) ) ) ) )
& ( ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X722: $i] :
( ( in @ X722 @ ( 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 ) ) )
@ X774 ) )
@ ( 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 ) ) )
@ X775 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X722 ) )
=> ~ $true )
@ ( esk6_2 @ X774 @ X775 ) )
| ~ $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 ) ) ) ) )
@ X774
@ X775 )
| $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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
| ( 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 ) ) ) ) )
@ X774
@ X775 )
| $true
| ~ ( in @ X775
@ ( 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 @ X774
@ ( 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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])])]) ).
thf(c_0_48,negated_conjecture,
! [X760: $i,X761: $i] :
( ( 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 @ X760 @ ( 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 ) ) )
@ 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 ) ) )
@ X696 ) )
=> ~ $true )
@ X760 )
| ~ $true
| ~ $true )
& ( $true
| ~ $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 ) ) ) ) )
@ esk1_0
@ esk2_0 )
| ~ $true )
& ( ~ ( in @ X761 @ ( 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 ) ) )
@ 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 ) ) ) ) )
@ X698 ) )
=> ~ $true )
@ X761 ) )
& $true ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])])]) ).
thf(c_0_49,plain,
! [X5: $i,X4: $i] :
( ( 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 ) ) ) ) )
@ X4
@ X5 )
| ( in @ ( esk5_2 @ X4 @ X5 ) @ ( pair1type @ nat ) )
| ~ ( 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 ) ) )
@ X4 ) )
@ ( 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 ) ) )
@ X5 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X815 ) )
=> ~ $true )
@ ( esk6_2 @ X4 @ X5 ) )
| ~ $true
| ~ $true
| ~ ( 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 ) ) ) ) ) )
| ~ ( 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 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( 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 )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_51,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 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_52,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk6_2 @ X1 @ X4 ) @ ( 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 ) ) ) ) )
@ X1
@ X4 )
| ( in @ ( esk5_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ $true
| ~ ( 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 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_53,plain,
! [X5: $i,X4: $i] :
( ( 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 ) ) ) ) )
@ X4
@ X5 )
| ~ ( 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 ) ) )
@ X4 ) )
@ ( 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 ) ) )
@ X5 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X817 ) )
=> ~ $true )
@ ( esk6_2 @ X4 @ X5 ) )
| ~ $true
| ~ ( 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 ) ) )
@ X4 ) )
@ ( 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 ) ) )
@ X5 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X818 ) )
=> ~ $true )
@ ( esk5_2 @ X4 @ X5 ) )
| ~ $true
| ~ ( 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 ) ) ) ) ) )
| ~ ( 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 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_54,plain,
! [X4: $i,X5: $i] :
( ( in @ ( esk5_2 @ X4 @ X5 ) @ ( 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 ) ) ) ) )
@ X4
@ X5 )
| ~ ( 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 ) ) ) ) ) )
| ~ ( 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 ) ) ) ) ) )
| ~ ( 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 ) ) )
@ X4 ) )
@ ( 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 ) ) )
@ X5 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X819 ) )
=> ~ $true )
@ ( esk6_2 @ X4 @ X5 ) ) ),
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( 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 ) )
=> ~ $true )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_50]) ).
thf(c_0_56,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)],[c_0_51]) ).
thf(c_0_57,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk5_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ( in @ ( esk6_2 @ X1 @ X4 ) @ ( 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 ) ) ) ) )
@ 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 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_52]) ).
thf(c_0_58,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_48]) ).
thf(c_0_59,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_48]) ).
thf(c_0_60,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk6_2 @ X1 @ X4 ) @ ( 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 ) ) ) ) )
@ X1
@ X4 )
| ~ $true
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X821: $i] :
( ( in @ X821 @ ( 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 ) ) ) ) )
@ X821 ) )
=> ~ $true )
@ ( esk5_2 @ X1 @ X4 ) )
| ~ $true
| ~ ( 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 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_61,plain,
! [X4: $i,X5: $i] :
( ( 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 ) ) ) ) )
@ X4
@ X5 )
| ~ ( 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 ) ) ) ) ) )
| ~ ( 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 ) ) ) ) ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X822: $i] :
( ( in @ X822 @ ( 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 ) ) )
@ X4 ) )
@ ( 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 ) ) )
@ X5 ) )
@ ( lessf @ Z0 @ Z1 ) ) )
@ X822 ) )
=> ~ $true )
@ ( esk6_2 @ X4 @ X5 ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X823: $i] :
( ( in @ X823 @ ( 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 ) ) )
@ X4 ) )
@ ( 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 ) ) )
@ X5 ) )
@ ( d_29_ii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X823 ) )
=> ~ $true )
@ ( esk5_2 @ X4 @ X5 ) ) ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X824: $i] :
( ( in @ X824 @ ( 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 ) ) ) ) )
@ X824 ) )
=> ~ $true )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_63,plain,
! [X4: $i,X1: $i] :
( ( 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 @ ( esk5_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X825: $i] :
( ( in @ X825 @ ( 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 ) ) )
@ X825 ) )
@ ( esk6_2 @ 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 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_54]) ).
thf(c_0_64,negated_conjecture,
! [X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X826: $i] :
( ( in @ X826 @ ( 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 ) ) )
@ X826 ) )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_55]) ).
thf(c_0_65,negated_conjecture,
( ( in @ ( esk5_2 @ esk1_0 @ esk2_0 ) @ ( pair1type @ nat ) )
| ( in @ ( esk6_2 @ esk1_0 @ esk2_0 ) @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59])]) ).
thf(c_0_66,plain,
! [X1: $i,X4: $i] :
( ( in @ ( esk6_2 @ X1 @ X4 ) @ ( 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 ) ) ) ) )
@ 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 ) ) ) ) ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X827: $i] :
( ( in @ X827 @ ( 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 ) ) ) ) )
@ X827 ) )
=> ~ $true )
@ ( esk5_2 @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_60]) ).
thf(c_0_67,plain,
! [X4: $i,X1: $i] :
( ( 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 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X828: $i] :
( ( in @ X828 @ ( 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 ) ) ) ) )
@ X828 ) )
@ ( esk5_2 @ X1 @ X4 ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X829: $i] :
( ( in @ X829 @ ( 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 ) ) )
@ X829 ) )
@ ( esk6_2 @ 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 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_61]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X830: $i] :
( ( in @ X830 @ ( 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 ) ) ) ) )
@ X830 ) )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_62]) ).
thf(c_0_69,negated_conjecture,
in @ ( esk5_2 @ esk1_0 @ esk2_0 ) @ ( pair1type @ nat ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_58]),c_0_59])]),c_0_56]),c_0_65]) ).
thf(c_0_70,plain,
! [X4: $i,X1: $i] :
( ( 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 @ ( esk6_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X831: $i] :
( ( in @ X831 @ ( 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 ) ) ) ) )
@ X831 ) )
@ ( esk5_2 @ 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 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_66]) ).
thf(c_0_71,negated_conjecture,
~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X832: $i] :
( ( in @ X832 @ ( 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 ) ) )
@ X832 ) )
@ ( esk6_2 @ esk1_0 @ esk2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_58]),c_0_59]),c_0_69])]),c_0_56]) ).
thf(c_0_72,negated_conjecture,
in @ ( esk6_2 @ esk1_0 @ esk2_0 ) @ ( pair1type @ nat ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_58]),c_0_59]),c_0_69])]),c_0_56]) ).
thf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_64]),c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM791^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.19 % Computer : n009.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 12:58:19 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.24 Running higher-order theorem proving
% 0.23/0.32 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/tmp/tmp.49T22wwOzQ/E---3.1_3944968.p
% 0.29/0.42 % Version: 3.5.1-ho
% 0.29/0.42 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.29/0.42 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.42 % Starting pre_casc_4 with 1200s (4) cores
% 0.29/0.42 % Starting full_lambda_6 with 300s (1) cores
% 0.29/0.42 % Starting sh10 with 300s (1) cores
% 0.29/0.42 % Starting post_as_ho9 with 300s (1) cores
% 0.29/0.42 % Starting post_as_ho8 with 300s (1) cores
% 0.29/0.42 % post_as_ho9 with pid 3944985 completed with status 0
% 0.29/0.42 % Result found by post_as_ho9
% 0.29/0.42 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.29/0.42 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.42 % Starting pre_casc_4 with 1200s (4) cores
% 0.29/0.42 % Starting full_lambda_6 with 300s (1) cores
% 0.29/0.42 % Starting sh10 with 300s (1) cores
% 0.29/0.42 % Starting post_as_ho9 with 300s (1) cores
% 0.29/0.42 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.29/0.42 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.29/0.42 % Search class: HGHNF-FFLS31-DHSMMFBN
% 0.29/0.42 % partial match(5): HGHSM-FSLS31-SHSMMSBN
% 0.29/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.42 % SubtermCWHack with pid 3944987 completed with status 0
% 0.29/0.42 % Result found by SubtermCWHack
% 0.29/0.42 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.29/0.42 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.42 % Starting pre_casc_4 with 1200s (4) cores
% 0.29/0.42 % Starting full_lambda_6 with 300s (1) cores
% 0.29/0.42 % Starting sh10 with 300s (1) cores
% 0.29/0.42 % Starting post_as_ho9 with 300s (1) cores
% 0.29/0.42 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.29/0.42 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.29/0.42 % Search class: HGHNF-FFLS31-DHSMMFBN
% 0.29/0.42 % partial match(5): HGHSM-FSLS31-SHSMMSBN
% 0.29/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.42 % Preprocessing time : 0.003 s
% 0.29/0.42
% 0.29/0.42 % Proof found!
% 0.29/0.42 % SZS status Theorem
% 0.29/0.42 % SZS output start CNFRefutation
% See solution above
% 0.29/0.42 % Parsed axioms : 700
% 0.29/0.42 % Removed by relevancy pruning/SinE : 657
% 0.29/0.42 % Initial clauses : 56
% 0.29/0.42 % Removed in clause preprocessing : 19
% 0.29/0.42 % Initial clauses in saturation : 37
% 0.29/0.42 % Processed clauses : 144
% 0.29/0.42 % ...of these trivial : 0
% 0.29/0.42 % ...subsumed : 46
% 0.29/0.42 % ...remaining for further processing : 98
% 0.29/0.42 % Other redundant clauses eliminated : 0
% 0.29/0.42 % Clauses deleted for lack of memory : 0
% 0.29/0.42 % Backward-subsumed : 3
% 0.29/0.42 % Backward-rewritten : 5
% 0.29/0.42 % Generated clauses : 276
% 0.29/0.42 % ...of the previous two non-redundant : 255
% 0.29/0.42 % ...aggressively subsumed : 0
% 0.29/0.42 % Contextual simplify-reflections : 6
% 0.29/0.42 % Paramodulations : 276
% 0.29/0.42 % Factorizations : 0
% 0.29/0.42 % NegExts : 0
% 0.29/0.42 % Equation resolutions : 0
% 0.29/0.42 % Disequality decompositions : 0
% 0.29/0.42 % Total rewrite steps : 137
% 0.29/0.42 % ...of those cached : 131
% 0.29/0.42 % Propositional unsat checks : 0
% 0.29/0.42 % Propositional check models : 0
% 0.29/0.42 % Propositional check unsatisfiable : 0
% 0.29/0.42 % Propositional clauses : 0
% 0.29/0.42 % Propositional clauses after purity: 0
% 0.29/0.42 % Propositional unsat core size : 0
% 0.29/0.42 % Propositional preprocessing time : 0.000
% 0.29/0.42 % Propositional encoding time : 0.000
% 0.29/0.42 % Propositional solver time : 0.000
% 0.29/0.42 % Success case prop preproc time : 0.000
% 0.29/0.42 % Success case prop encoding time : 0.000
% 0.29/0.42 % Success case prop solver time : 0.000
% 0.29/0.42 % Current number of processed clauses : 90
% 0.29/0.42 % Positive orientable unit clauses : 8
% 0.29/0.42 % Positive unorientable unit clauses: 0
% 0.29/0.42 % Negative unit clauses : 2
% 0.29/0.42 % Non-unit-clauses : 80
% 0.29/0.42 % Current number of unprocessed clauses: 141
% 0.29/0.42 % ...number of literals in the above : 1151
% 0.29/0.42 % Current number of archived formulas : 0
% 0.29/0.42 % Current number of archived clauses : 8
% 0.29/0.42 % Clause-clause subsumption calls (NU) : 8138
% 0.29/0.42 % Rec. Clause-clause subsumption calls : 1299
% 0.29/0.42 % Non-unit clause-clause subsumptions : 54
% 0.29/0.42 % Unit Clause-clause subsumption calls : 170
% 0.29/0.42 % Rewrite failures with RHS unbound : 0
% 0.29/0.42 % BW rewrite match attempts : 3
% 0.29/0.42 % BW rewrite match successes : 3
% 0.29/0.42 % Condensation attempts : 0
% 0.29/0.42 % Condensation successes : 0
% 0.29/0.42 % Termbank termtop insertions : 90572
% 0.29/0.42 % Search garbage collected termcells : 10905
% 0.29/0.42
% 0.29/0.42 % -------------------------------------------------
% 0.29/0.42 % User time : 0.049 s
% 0.29/0.42 % System time : 0.009 s
% 0.29/0.42 % Total time : 0.058 s
% 0.29/0.42 % Maximum resident set size: 6248 pages
% 0.29/0.42
% 0.29/0.42 % -------------------------------------------------
% 0.29/0.42 % User time : 0.069 s
% 0.29/0.42 % System time : 0.018 s
% 0.29/0.42 % Total time : 0.087 s
% 0.29/0.42 % Maximum resident set size: 6144 pages
% 0.29/0.42 % E exiting
%------------------------------------------------------------------------------