%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM790^4 : 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 : n013.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 08:17:07 AM UTC 2026
% Result : Theorem 0.90s 0.53s
% Output : CNFRefutation 0.90s
% 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_150,type,
iii: $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_220,type,
rt_moreis: $i > $i > $o ).
thf(decl_222,type,
esk1_0: $i ).
thf(decl_223,type,
esk2_0: $i ).
thf(decl_224,type,
esk3_2: $i > $i > $i ).
thf(decl_225,type,
esk4_2: $i > $i > $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.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.52UbL4RjQX/E---3.1_2064333.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.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.52UbL4RjQX/E---3.1_2064333.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.52UbL4RjQX/E---3.1_2064333.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.52UbL4RjQX/E---3.1_2064333.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.52UbL4RjQX/E---3.1_2064333.p',def_rat) ).
thf(def_frac,axiom,
( frac
= ( pair1type @ nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',def_frac) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.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/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',def_rt_more) ).
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.52UbL4RjQX/E---3.1_2064333.p',def_class) ).
thf(def_inf,axiom,
( inf
= ( esti @ ( pair1type @ nat ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.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.52UbL4RjQX/E---3.1_2064333.p',def_and3) ).
thf(def_rt_moreis,axiom,
( rt_moreis
= ( ^ [X1: $i,X664: $i] : ( l_or @ ( rt_more @ X1 @ X664 ) @ ( rt_is @ X1 @ X664 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',def_rt_moreis) ).
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.52UbL4RjQX/E---3.1_2064333.p',def_rt_is) ).
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.52UbL4RjQX/E---3.1_2064333.p',def_rt_less) ).
thf(def_lessf,axiom,
( lessf
= ( ^ [X1: $i,X450: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X450 ) ) @ ( n_ts @ ( num @ X450 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',def_lessf) ).
thf(satz81j,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X678: $i] : ( in @ X678 @ rat )
@ ^ [X679: $i] :
( ( d_not @ ( rt_moreis @ X1 @ X679 ) )
=> ( rt_less @ X1 @ X679 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',satz81j) ).
thf(satz81f,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X672: $i] : ( in @ X672 @ rat )
@ ^ [X673: $i] :
( ( d_not @ ( rt_less @ X1 @ X673 ) )
=> ( rt_moreis @ X1 @ X673 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.52UbL4RjQX/E---3.1_2064333.p',satz81f) ).
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] :
( ! [X686: $i] :
( ( in @ X686 @ Z0 )
=> ( non @ Z0 @ Z1 @ X686 ) )
=> ~ $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_more
= ( ^ [Z0: $i,Z1: $i] :
( ! [X688: $i] :
( ( in @ X688 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X687: $i] :
( ( in @ X687 @ ( 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 ) )
@ ( moref @ Z2 @ Z3 ) ) )
@ X687 ) )
=> ~ $true )
@ X688 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_more]) ).
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] :
( ! [X686: $i] :
( ( in @ X686 @ Z0 )
=> ( non @ Z0 @ Z1 @ X686 ) )
=> ~ $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_moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X691: $i] :
( ( in @ X691 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X692: $i] :
( ( in @ X692 @ ( 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 ) )
@ ( moref @ Z2 @ Z3 ) ) )
@ X692 ) )
=> ~ $true )
@ X691 ) )
=> ~ $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_moreis]) ).
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_more
= ( ^ [Z0: $i,Z1: $i] :
( ! [X688: $i] :
( ( in @ X688 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X687: $i] :
( ( in @ X687 @ ( 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 ) )
@ ( moref @ Z2 @ Z3 ) ) )
@ X687 ) )
=> ~ $true )
@ X688 ) )
=> ~ $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_less
= ( ^ [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 ) )
@ ( iii @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) ) ) )
@ X689 ) )
=> ~ $true )
@ X690 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_less]) ).
thf(c_0_41,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] : ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_42,plain,
( rt_moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X691: $i] :
( ( in @ X691 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z2: $i] :
( ! [X692: $i] :
( ( in @ X692 @ ( 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 ) )
@ ( moref @ Z2 @ Z3 ) ) )
@ X692 ) )
=> ~ $true )
@ X691 ) )
=> ~ $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_less
= ( ^ [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 ) )
@ ( iii @ ( 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
@ ^ [X678: $i] : ( in @ X678 @ rat )
@ ^ [X679: $i] :
( ( d_not @ ( rt_moreis @ X1 @ X679 ) )
=> ( rt_less @ X1 @ X679 ) ) ) ),
inference(assume_negation,[status(cth)],[satz81j]) ).
thf(c_0_45,plain,
! [X710: $i] :
( ( in @ X710
@ ( 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 ) ) ) ) ) )
=> ! [X709: $i] :
( ( in @ X709
@ ( 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 ) ) ) ) ) )
=> ( ( ( ! [X705: $i] :
( ( in @ X705 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X706: $i] :
( ( in @ X706 @ ( 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 ) ) )
@ X710 ) )
@ ( 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 ) ) )
@ X709 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X706 ) )
=> ~ $true )
@ X705 ) )
=> ~ $true )
=> ~ $true )
=> ( ( ( ! [X707: $i] :
( ( in @ X707 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X708: $i] :
( ( in @ X708 @ ( 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 ) ) )
@ X710 ) )
@ ( 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 ) ) )
@ X709 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X708 ) )
=> ~ $true )
@ X707 ) )
=> ~ $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 ) ) ) ) )
@ X710
@ X709 ) ) ) ) ),
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)],[satz81f]),c_0_29]),c_0_42]),c_0_27]),c_0_43]),c_0_28]) ).
thf(c_0_46,negated_conjecture,
~ ! [X698: $i] :
( ( in @ X698
@ ( 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 ) ) ) ) ) )
=> ! [X697: $i] :
( ( in @ X697
@ ( 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 @ ( pair1type @ nat ) )
=> ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X694: $i] :
( ( in @ X694 @ ( 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 ) ) )
@ X698 ) )
@ ( 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 ) ) )
@ X697 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X694 ) )
=> ~ $true )
@ X693 ) )
=> ~ $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 ) ) ) ) )
@ X698
@ X697 ) )
=> ~ $true )
=> ( ! [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 ) ) )
@ X698 ) )
@ ( 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 ) ) )
@ X697 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X696 ) )
=> ~ $true )
@ X695 ) )
=> ~ $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,
! [X797: $i,X798: $i] :
( ( ( in @ ( esk4_2 @ X797 @ X798 ) @ ( 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 ) ) ) ) )
@ X797
@ X798 )
| ( in @ ( esk3_2 @ X797 @ X798 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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] :
( ! [X708: $i] :
( ( in @ X708 @ ( 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 ) ) )
@ X797 ) )
@ ( 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 ) ) )
@ X798 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X708 ) )
=> ~ $true )
@ ( esk4_2 @ X797 @ X798 ) )
| ~ $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 ) ) ) ) )
@ X797
@ X798 )
| ( in @ ( esk3_2 @ X797 @ X798 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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 ) ) ) ) )
@ X797
@ X798 )
| ( in @ ( esk3_2 @ X797 @ X798 ) @ ( pair1type @ nat ) )
| ~ $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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 @ ( esk4_2 @ X797 @ X798 ) @ ( 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 ) ) ) ) )
@ X797
@ X798 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X706: $i] :
( ( in @ X706 @ ( 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 ) ) )
@ X797 ) )
@ ( 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 ) ) )
@ X798 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X706 ) )
=> ~ $true )
@ ( esk3_2 @ X797 @ X798 ) )
| ~ $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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] :
( ! [X708: $i] :
( ( in @ X708 @ ( 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 ) ) )
@ X797 ) )
@ ( 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 ) ) )
@ X798 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X708 ) )
=> ~ $true )
@ ( esk4_2 @ X797 @ X798 ) )
| ~ $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 ) ) ) ) )
@ X797
@ X798 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X706: $i] :
( ( in @ X706 @ ( 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 ) ) )
@ X797 ) )
@ ( 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 ) ) )
@ X798 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X706 ) )
=> ~ $true )
@ ( esk3_2 @ X797 @ X798 ) )
| ~ $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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 ) ) ) ) )
@ X797
@ X798 )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X706: $i] :
( ( in @ X706 @ ( 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 ) ) )
@ X797 ) )
@ ( 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 ) ) )
@ X798 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X706 ) )
=> ~ $true )
@ ( esk3_2 @ X797 @ X798 ) )
| ~ $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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 @ ( esk4_2 @ X797 @ X798 ) @ ( 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 ) ) ) ) )
@ X797
@ X798 )
| $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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] :
( ! [X708: $i] :
( ( in @ X708 @ ( 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 ) ) )
@ X797 ) )
@ ( 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 ) ) )
@ X798 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X708 ) )
=> ~ $true )
@ ( esk4_2 @ X797 @ X798 ) )
| ~ $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 ) ) ) ) )
@ X797
@ X798 )
| $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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 ) ) ) ) )
@ X797
@ X798 )
| $true
| ~ ( in @ X798
@ ( 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 @ X797
@ ( 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,
! [X791: $i,X792: $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 @ X791 @ ( pair1type @ nat ) )
| ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X694: $i] :
( ( in @ X694 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X694 ) )
=> ~ $true )
@ X791 )
| ~ $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 @ X792 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X696 ) )
=> ~ $true )
@ X792 ) )
& $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 @ ( esk3_2 @ X4 @ X5 ) @ ( pair1type @ nat ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X879: $i] :
( ( in @ X879 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X879 ) )
=> ~ $true )
@ ( esk4_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] :
( ! [X880: $i] :
( ( in @ X880 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X880 ) )
=> ~ $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 @ ( esk4_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 @ ( esk3_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] :
( ! [X881: $i] :
( ( in @ X881 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X881 ) )
=> ~ $true )
@ ( esk4_2 @ X4 @ X5 ) )
| ~ $true
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X882: $i] :
( ( in @ X882 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X882 ) )
=> ~ $true )
@ ( esk3_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 @ ( esk3_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] :
( ! [X883: $i] :
( ( in @ X883 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X883 ) )
=> ~ $true )
@ ( esk4_2 @ X4 @ X5 ) ) ),
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X884: $i] :
( ( in @ X884 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X884 ) )
=> ~ $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 @ ( esk3_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ( in @ ( esk4_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 @ ( esk4_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] :
( ! [X885: $i] :
( ( in @ X885 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X885 ) )
=> ~ $true )
@ ( esk3_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] :
( ! [X886: $i] :
( ( in @ X886 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X886 ) )
=> ~ $true )
@ ( esk4_2 @ X4 @ X5 ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X887: $i] :
( ( in @ X887 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X887 ) )
=> ~ $true )
@ ( esk3_2 @ X4 @ X5 ) ) ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i] :
( ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
( ! [X888: $i] :
( ( in @ X888 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X888 ) )
=> ~ $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 @ ( esk3_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X889: $i] :
( ( in @ X889 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X889 ) )
@ ( esk4_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] :
~ ! [X890: $i] :
( ( in @ X890 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X890 ) )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_55]) ).
thf(c_0_65,negated_conjecture,
( ( in @ ( esk3_2 @ esk1_0 @ esk2_0 ) @ ( pair1type @ nat ) )
| ( in @ ( esk4_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 @ ( esk4_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] :
( ! [X891: $i] :
( ( in @ X891 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X891 ) )
=> ~ $true )
@ ( esk3_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] :
~ ! [X892: $i] :
( ( in @ X892 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X892 ) )
@ ( esk3_2 @ X1 @ X4 ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X893: $i] :
( ( in @ X893 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X893 ) )
@ ( esk4_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] :
~ ! [X894: $i] :
( ( in @ X894 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X894 ) )
@ X1 )
| ~ ( in @ X1 @ ( pair1type @ nat ) ) ),
inference(cn,[status(thm)],[c_0_62]) ).
thf(c_0_69,negated_conjecture,
in @ ( esk3_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 @ ( esk4_2 @ X1 @ X4 ) @ ( pair1type @ nat ) )
| ~ ( non @ ( pair1type @ nat )
@ ^ [Z0: $i] :
~ ! [X895: $i] :
( ( in @ X895 @ ( 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 ) )
@ ( iii @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) )
@ X895 ) )
@ ( esk3_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] :
~ ! [X896: $i] :
( ( in @ X896 @ ( 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 ) )
@ ( moref @ Z0 @ Z1 ) ) )
@ X896 ) )
@ ( esk4_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 @ ( esk4_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
% 0.00/0.02 % Problem : NUM790^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:56:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.21/0.30 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.52UbL4RjQX/E---3.1_2064333.p
% 0.90/0.53 % Version: 3.5.1-ho
% 0.90/0.53 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.90/0.53 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.53 % Starting pre_casc_4 with 1200s (4) cores
% 0.90/0.53 % Starting full_lambda_6 with 300s (1) cores
% 0.90/0.53 % Starting sh10 with 300s (1) cores
% 0.90/0.53 % Starting post_as_ho9 with 300s (1) cores
% 0.90/0.53 % Starting post_as_ho8 with 300s (1) cores
% 0.90/0.53 % post_as_ho9 with pid 2064349 completed with status 0
% 0.90/0.53 % Result found by post_as_ho9
% 0.90/0.53 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.90/0.53 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.53 % Starting pre_casc_4 with 1200s (4) cores
% 0.90/0.53 % Starting full_lambda_6 with 300s (1) cores
% 0.90/0.53 % Starting sh10 with 300s (1) cores
% 0.90/0.53 % Starting post_as_ho9 with 300s (1) cores
% 0.90/0.53 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.90/0.53 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.90/0.53 % Search class: HGHNF-FFLS31-DHSMMFBN
% 0.90/0.53 % partial match(5): HGHSM-FSLS31-SHSMMSBN
% 0.90/0.53 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.90/0.53 % Starting SubtermCWHack with 28s (1) cores
% 0.90/0.53 % SubtermCWHack with pid 2064351 completed with status 0
% 0.90/0.53 % Result found by SubtermCWHack
% 0.90/0.53 % Preprocessing class: HSLMSMSMLLLCHSA.
% 0.90/0.53 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.53 % Starting pre_casc_4 with 1200s (4) cores
% 0.90/0.53 % Starting full_lambda_6 with 300s (1) cores
% 0.90/0.53 % Starting sh10 with 300s (1) cores
% 0.90/0.53 % Starting post_as_ho9 with 300s (1) cores
% 0.90/0.53 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.90/0.53 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.90/0.53 % Search class: HGHNF-FFLS31-DHSMMFBN
% 0.90/0.53 % partial match(5): HGHSM-FSLS31-SHSMMSBN
% 0.90/0.53 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.90/0.53 % Starting SubtermCWHack with 28s (1) cores
% 0.90/0.53 % Preprocessing time : 0.005 s
% 0.90/0.53
% 0.90/0.53 % Proof found!
% 0.90/0.53 % SZS status Theorem
% 0.90/0.53 % SZS output start CNFRefutation
% See solution above
% 0.90/0.53 % Parsed axioms : 699
% 0.90/0.53 % Removed by relevancy pruning/SinE : 645
% 0.90/0.53 % Initial clauses : 67
% 0.90/0.53 % Removed in clause preprocessing : 19
% 0.90/0.53 % Initial clauses in saturation : 48
% 0.90/0.53 % Processed clauses : 333
% 0.90/0.53 % ...of these trivial : 0
% 0.90/0.53 % ...subsumed : 172
% 0.90/0.53 % ...remaining for further processing : 161
% 0.90/0.53 % Other redundant clauses eliminated : 0
% 0.90/0.53 % Clauses deleted for lack of memory : 0
% 0.90/0.53 % Backward-subsumed : 2
% 0.90/0.53 % Backward-rewritten : 1
% 0.90/0.53 % Generated clauses : 1254
% 0.90/0.53 % ...of the previous two non-redundant : 1241
% 0.90/0.53 % ...aggressively subsumed : 0
% 0.90/0.53 % Contextual simplify-reflections : 1
% 0.90/0.53 % Paramodulations : 1254
% 0.90/0.53 % Factorizations : 0
% 0.90/0.53 % NegExts : 0
% 0.90/0.53 % Equation resolutions : 0
% 0.90/0.53 % Disequality decompositions : 0
% 0.90/0.53 % Total rewrite steps : 19
% 0.90/0.53 % ...of those cached : 15
% 0.90/0.53 % Propositional unsat checks : 0
% 0.90/0.53 % Propositional check models : 0
% 0.90/0.53 % Propositional check unsatisfiable : 0
% 0.90/0.53 % Propositional clauses : 0
% 0.90/0.53 % Propositional clauses after purity: 0
% 0.90/0.53 % Propositional unsat core size : 0
% 0.90/0.53 % Propositional preprocessing time : 0.000
% 0.90/0.53 % Propositional encoding time : 0.000
% 0.90/0.53 % Propositional solver time : 0.000
% 0.90/0.53 % Success case prop preproc time : 0.000
% 0.90/0.53 % Success case prop encoding time : 0.000
% 0.90/0.53 % Success case prop solver time : 0.000
% 0.90/0.53 % Current number of processed clauses : 158
% 0.90/0.53 % Positive orientable unit clauses : 6
% 0.90/0.53 % Positive unorientable unit clauses: 0
% 0.90/0.53 % Negative unit clauses : 2
% 0.90/0.53 % Non-unit-clauses : 150
% 0.90/0.53 % Current number of unprocessed clauses: 955
% 0.90/0.53 % ...number of literals in the above : 11460
% 0.90/0.53 % Current number of archived formulas : 0
% 0.90/0.53 % Current number of archived clauses : 3
% 0.90/0.53 % Clause-clause subsumption calls (NU) : 27420
% 0.90/0.53 % Rec. Clause-clause subsumption calls : 3104
% 0.90/0.53 % Non-unit clause-clause subsumptions : 175
% 0.90/0.53 % Unit Clause-clause subsumption calls : 21
% 0.90/0.53 % Rewrite failures with RHS unbound : 0
% 0.90/0.53 % BW rewrite match attempts : 1
% 0.90/0.53 % BW rewrite match successes : 1
% 0.90/0.53 % Condensation attempts : 0
% 0.90/0.53 % Condensation successes : 0
% 0.90/0.53 % Termbank termtop insertions : 132351
% 0.90/0.53 % Search garbage collected termcells : 12547
% 0.90/0.53
% 0.90/0.53 % -------------------------------------------------
% 0.90/0.53 % User time : 0.174 s
% 0.90/0.53 % System time : 0.012 s
% 0.90/0.53 % Total time : 0.186 s
% 0.90/0.53 % Maximum resident set size: 6296 pages
% 0.90/0.53
% 0.90/0.53 % -------------------------------------------------
% 0.90/0.53 % User time : 0.193 s
% 0.90/0.53 % System time : 0.023 s
% 0.90/0.53 % Total time : 0.216 s
% 0.90/0.53 % Maximum resident set size: 6400 pages
% 0.90/0.53 % E exiting
%------------------------------------------------------------------------------