%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM743^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:16:59 AM UTC 2026
% Result : Theorem 8.82s 1.64s
% Output : CNFRefutation 8.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 79 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 394 ( 39 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1833 ( 89 ~; 84 |; 11 &;1592 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 7 con; 0-3 aty)
% Number of variables : 210 ( 165 ^; 45 !; 0 ?; 210 :)
% 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_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_68,type,
l_or: $o > $o > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_150,type,
iii: $i > $i > $o ).
thf(decl_163,type,
n_ts: $i > $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_197,type,
moreq: $i > $i > $o ).
thf(decl_198,type,
lesseq: $i > $i > $o ).
thf(decl_200,type,
esk1_0: $i ).
thf(decl_201,type,
esk2_0: $i ).
thf(decl_202,type,
esk3_0: $i ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_diffprop) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_imp) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_iii) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_l_or) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_n_eq) ).
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/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_lessf) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_n_some) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_d_29_ii) ).
thf(def_lesseq,axiom,
( lesseq
= ( ^ [X1: $i,X466: $i] : ( l_or @ ( lessf @ X1 @ X466 ) @ ( n_eq @ X1 @ X466 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_lesseq) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_is_of) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_moref) ).
thf(satz51b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X495: $i] : ( in @ X495 @ frac )
@ ^ [X496: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lessf @ X1 @ X496 )
=> ( ( lesseq @ X496 @ X4 )
=> ( lessf @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',satz51b) ).
thf(satz51a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X493: $i] : ( in @ X493 @ frac )
@ ^ [X494: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lesseq @ X1 @ X494 )
=> ( ( lessf @ X494 @ X4 )
=> ( lessf @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',satz51a) ).
thf(def_moreq,axiom,
( moreq
= ( ^ [X1: $i,X465: $i] : ( l_or @ ( moref @ X1 @ X465 ) @ ( n_eq @ X1 @ X465 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',def_moreq) ).
thf(satz41e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X471: $i] : ( in @ X471 @ frac )
@ ^ [X472: $i] :
( ( d_not @ ( moref @ X1 @ X472 ) )
=> ( lesseq @ X1 @ X472 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',satz41e) ).
thf(satz41c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X467: $i] : ( in @ X467 @ frac )
@ ^ [X468: $i] :
( ( moreq @ X1 @ X468 )
=> ( d_not @ ( lessf @ X1 @ X468 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',satz41c) ).
thf(satz38,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X437: $i] : ( in @ X437 @ frac )
@ ^ [X438: $i] :
( ( n_eq @ X1 @ X438 )
=> ( n_eq @ X438 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p',satz38) ).
thf(c_0_20,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_21,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_22,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_23,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z1 @ ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_24,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_20,def_n_is]) ).
thf(c_0_25,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_26,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_27,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_28,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_29,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z1 @ ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_24]),def_n_some]) ).
thf(c_0_30,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_31,plain,
( lesseq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lesseq]) ).
thf(c_0_32,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
thf(c_0_33,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_27,def_n_is]) ).
thf(c_0_34,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_35,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_36,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_37,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_38,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_24]),def_n_some]) ).
thf(c_0_39,plain,
( lesseq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( 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)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
thf(c_0_40,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_41,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_42,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X495: $i] : ( in @ X495 @ frac )
@ ^ [X496: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lessf @ X1 @ X496 )
=> ( ( lesseq @ X496 @ X4 )
=> ( lessf @ X1 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz51b]) ).
thf(c_0_43,plain,
! [X558: $i] :
( ( in @ X558 @ frac )
=> ! [X557: $i] :
( ( in @ X557 @ frac )
=> ! [X556: $i] :
( ( in @ X556 @ frac )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X557 ) @ ( den @ X558 ) ) @ ( n_pl @ ( n_ts @ ( num @ X558 ) @ ( den @ X557 ) ) @ Z0 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X558 ) @ ( den @ X557 ) ) @ ( n_ts @ ( num @ X557 ) @ ( den @ X558 ) ) ) )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X556 ) @ ( den @ X557 ) ) @ ( n_pl @ ( n_ts @ ( num @ X557 ) @ ( den @ X556 ) ) @ Z0 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X556 ) @ ( den @ X558 ) ) @ ( n_pl @ ( n_ts @ ( num @ X558 ) @ ( den @ X556 ) ) @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz51a]),c_0_39]),c_0_34]),c_0_40]) ).
thf(c_0_44,plain,
( moreq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreq]) ).
thf(c_0_45,plain,
! [X547: $i] :
( ( in @ X547 @ frac )
=> ! [X546: $i] :
( ( in @ X546 @ frac )
=> ( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X547 ) @ ( den @ X546 ) ) @ ( n_pl @ ( n_ts @ ( num @ X546 ) @ ( den @ X547 ) ) @ Z0 ) ) )
=> ~ $true )
=> ( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X546 ) @ ( den @ X547 ) ) @ ( n_pl @ ( n_ts @ ( num @ X547 ) @ ( den @ X546 ) ) @ Z0 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X547 ) @ ( den @ X546 ) ) @ ( n_ts @ ( num @ X546 ) @ ( den @ X547 ) ) ) ) ) ) ),
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)],[satz41e]),c_0_26]),c_0_41]),c_0_39]),c_0_40]) ).
thf(c_0_46,negated_conjecture,
~ ! [X536: $i] :
( ( in @ X536 @ frac )
=> ! [X535: $i] :
( ( in @ X535 @ frac )
=> ! [X534: $i] :
( ( in @ X534 @ frac )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X535 ) @ ( den @ X536 ) ) @ ( n_pl @ ( n_ts @ ( num @ X536 ) @ ( den @ X535 ) ) @ Z0 ) ) )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X534 ) @ ( den @ X535 ) ) @ ( n_pl @ ( n_ts @ ( num @ X535 ) @ ( den @ X534 ) ) @ Z0 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X535 ) @ ( den @ X534 ) ) @ ( n_ts @ ( num @ X534 ) @ ( den @ X535 ) ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X534 ) @ ( den @ X536 ) ) @ ( n_pl @ ( n_ts @ ( num @ X536 ) @ ( den @ X534 ) ) @ Z0 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_42]),c_0_39]),c_0_34]),c_0_40]) ).
thf(c_0_47,plain,
! [X927: $i,X928: $i,X929: $i] :
( ( ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X928 ) @ ( den @ X927 ) ) @ ( n_pl @ ( n_ts @ ( num @ X927 ) @ ( den @ X928 ) ) @ Z0 ) ) )
| ~ $true
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X929 ) @ ( den @ X928 ) ) @ ( n_pl @ ( n_ts @ ( num @ X928 ) @ ( den @ X929 ) ) @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X929 ) @ ( den @ X927 ) ) @ ( n_pl @ ( n_ts @ ( num @ X927 ) @ ( den @ X929 ) ) @ Z0 ) ) )
| ~ ( in @ X929 @ frac )
| ~ ( in @ X928 @ frac )
| ~ ( in @ X927 @ frac ) )
& ( ~ ( e_is @ nat @ ( n_ts @ ( num @ X927 ) @ ( den @ X928 ) ) @ ( n_ts @ ( num @ X928 ) @ ( den @ X927 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X929 ) @ ( den @ X928 ) ) @ ( n_pl @ ( n_ts @ ( num @ X928 ) @ ( den @ X929 ) ) @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X929 ) @ ( den @ X927 ) ) @ ( n_pl @ ( n_ts @ ( num @ X927 ) @ ( den @ X929 ) ) @ Z0 ) ) )
| ~ ( in @ X929 @ frac )
| ~ ( in @ X928 @ frac )
| ~ ( in @ X927 @ frac ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])]) ).
thf(c_0_48,plain,
( moreq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat
@ ^ [Z2: $i] : ( e_is @ nat @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( 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)],[c_0_44,c_0_32]),c_0_41]),c_0_33]) ).
thf(c_0_49,plain,
! [X917: $i,X918: $i] :
( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) @ ( n_pl @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ ( n_pl @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) @ Z0 ) ) )
| ~ ( in @ X918 @ frac )
| ~ ( in @ X917 @ frac ) )
& ( $true
| ( e_is @ nat @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ ( n_pl @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) @ Z0 ) ) )
| ~ ( in @ X918 @ frac )
| ~ ( in @ X917 @ frac ) )
& ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) @ ( n_pl @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) )
| $true
| ~ ( in @ X918 @ frac )
| ~ ( in @ X917 @ frac ) )
& ( $true
| ( e_is @ nat @ ( n_ts @ ( num @ X917 ) @ ( den @ X918 ) ) @ ( n_ts @ ( num @ X918 ) @ ( den @ X917 ) ) )
| $true
| ~ ( in @ X918 @ frac )
| ~ ( in @ X917 @ frac ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
thf(c_0_50,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) )
& ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) ) )
& ( $true
| ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) ) )
& ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])]) ).
thf(c_0_51,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X4 ) ) @ ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ Z0 ) ) )
| ~ $true
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_52,plain,
! [X871: $i] :
( ( in @ X871 @ frac )
=> ! [X870: $i] :
( ( in @ X870 @ frac )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X871 ) @ ( den @ X870 ) ) @ ( n_pl @ ( n_ts @ ( num @ X870 ) @ ( den @ X871 ) ) @ Z0 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X871 ) @ ( den @ X870 ) ) @ ( n_ts @ ( num @ X870 ) @ ( den @ X871 ) ) ) )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X870 ) @ ( den @ X871 ) ) @ ( n_pl @ ( n_ts @ ( num @ X871 ) @ ( den @ X870 ) ) @ Z0 ) ) )
=> ~ $true ) ) ) ),
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)],[satz41c]),c_0_26]),c_0_48]),c_0_34]),c_0_40]) ).
thf(c_0_53,plain,
! [X1: $i,X4: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_54,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_55,plain,
! [X638: $i] :
( ( in @ X638 @ frac )
=> ! [X637: $i] :
( ( in @ X637 @ frac )
=> ( ( e_is @ nat @ ( n_ts @ ( num @ X638 ) @ ( den @ X637 ) ) @ ( n_ts @ ( num @ X637 ) @ ( den @ X638 ) ) )
=> ( e_is @ nat @ ( n_ts @ ( num @ X637 ) @ ( den @ X638 ) ) @ ( n_ts @ ( num @ X638 ) @ ( den @ X637 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz38]),c_0_33]),c_0_40]) ).
thf(c_0_56,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X4 ) ) @ ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ Z0 ) ) ) ),
inference(cn,[status(thm)],[c_0_51]) ).
thf(c_0_57,negated_conjecture,
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_58,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_59,plain,
! [X1268: $i,X1269: $i] :
( ( ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1268 ) @ ( den @ X1269 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1269 ) @ ( den @ X1268 ) ) @ Z0 ) ) )
| ~ $true
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1269 ) @ ( den @ X1268 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1268 ) @ ( den @ X1269 ) ) @ Z0 ) ) )
| ~ $true
| ~ ( in @ X1269 @ frac )
| ~ ( in @ X1268 @ frac ) )
& ( ~ ( e_is @ nat @ ( n_ts @ ( num @ X1268 ) @ ( den @ X1269 ) ) @ ( n_ts @ ( num @ X1269 ) @ ( den @ X1268 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1269 ) @ ( den @ X1268 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1268 ) @ ( den @ X1269 ) ) @ Z0 ) ) )
| ~ $true
| ~ ( in @ X1269 @ frac )
| ~ ( in @ X1268 @ frac ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])]) ).
thf(c_0_60,negated_conjecture,
( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_61,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_62,negated_conjecture,
! [X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ esk3_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ X1 ) ) @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ esk3_0 ) ) )
| ~ ( in @ X1 @ frac ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_63,negated_conjecture,
~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_64,plain,
! [X1015: $i,X1016: $i] :
( ~ ( in @ X1015 @ frac )
| ~ ( in @ X1016 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1015 ) @ ( den @ X1016 ) ) @ ( n_ts @ ( num @ X1016 ) @ ( den @ X1015 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ X1016 ) @ ( den @ X1015 ) ) @ ( n_ts @ ( num @ X1015 ) @ ( den @ X1016 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
thf(c_0_65,negated_conjecture,
! [X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_54]),c_0_58])]) ).
thf(c_0_66,plain,
! [X4: $i,X1: $i] :
( ~ ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ Z0 ) ) )
| ~ $true
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ esk1_0 ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_60]),c_0_58]),c_0_61])]) ).
thf(c_0_68,negated_conjecture,
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_63]) ).
thf(c_0_69,plain,
! [X4: $i,X1: $i] :
( ( e_is @ nat @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_70,negated_conjecture,
e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_60]),c_0_61])]),c_0_63]) ).
thf(c_0_71,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X4 ) ) @ ( n_pl @ ( n_ts @ ( num @ X4 ) @ ( den @ X5 ) ) @ Z0 ) ) )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_72,plain,
! [X1: $i,X4: $i] :
( ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ Z0 ) ) ) ),
inference(cn,[status(thm)],[c_0_66]) ).
thf(c_0_73,negated_conjecture,
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_54])]) ).
thf(c_0_74,negated_conjecture,
e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_54]),c_0_58])]) ).
thf(c_0_75,negated_conjecture,
! [X1: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ X1 ) ) )
| ~ ( in @ X1 @ frac ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_60]),c_0_58]),c_0_61])]) ).
thf(c_0_76,negated_conjecture,
e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_58]),c_0_54])]) ).
thf(c_0_77,negated_conjecture,
( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk3_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk2_0 ) ) @ Z0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_54])]) ).
thf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_77]),c_0_74]),c_0_58]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM743^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:49:01 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.23/0.28 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.BKpGnnHkjg/E---3.1_708140.p
% 8.82/1.64 % Version: 3.5.1-ho
% 8.82/1.64 % Preprocessing class: HSLMSMSMLLLCHSA.
% 8.82/1.64 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 8.82/1.64 % Starting pre_casc_4 with 1200s (4) cores
% 8.82/1.64 % Starting full_lambda_6 with 300s (1) cores
% 8.82/1.64 % Starting sh10 with 300s (1) cores
% 8.82/1.64 % Starting post_as_ho9 with 300s (1) cores
% 8.82/1.64 % Starting post_as_ho8 with 300s (1) cores
% 8.82/1.64 % pre_casc_4 with pid 708153 completed with status 0
% 8.82/1.64 % Result found by pre_casc_4
% 8.82/1.64 % Preprocessing class: HSLMSMSMLLLCHSA.
% 8.82/1.64 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 8.82/1.64 % Starting pre_casc_4 with 1200s (4) cores
% 8.82/1.64 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 8.82/1.64 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 8.82/1.64 % Search class: HGHSM-FSLM31-DHSMMFBN
% 8.82/1.64 % partial match(2): HGHSM-FSLM31-DHSFFFBN
% 8.82/1.64 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 8.82/1.64 % Starting SubtermCWHack with 109s (1) cores
% 8.82/1.64 % Starting pre_casc_4 with 121s (1) cores
% 8.82/1.64 % Starting full_lambda_10 with 211s (1) cores
% 8.82/1.64 % Starting new_bool_8 with 210s (1) cores
% 8.82/1.64 % full_lambda_10 with pid 708160 completed with status 0
% 8.82/1.64 % Result found by full_lambda_10
% 8.82/1.64 % Preprocessing class: HSLMSMSMLLLCHSA.
% 8.82/1.64 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 8.82/1.64 % Starting pre_casc_4 with 1200s (4) cores
% 8.82/1.64 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 8.82/1.64 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 8.82/1.64 % Search class: HGHSM-FSLM31-DHSMMFBN
% 8.82/1.64 % partial match(2): HGHSM-FSLM31-DHSFFFBN
% 8.82/1.64 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 8.82/1.64 % Starting SubtermCWHack with 109s (1) cores
% 8.82/1.64 % Starting pre_casc_4 with 121s (1) cores
% 8.82/1.64 % Starting full_lambda_10 with 211s (1) cores
% 8.82/1.64 % Preprocessing time : 0.012 s
% 8.82/1.64 % Presaturation interreduction done
% 8.82/1.64
% 8.82/1.64 % Proof found!
% 8.82/1.64 % SZS status Theorem
% 8.82/1.64 % SZS output start CNFRefutation
% See solution above
% 8.82/1.64 % Parsed axioms : 566
% 8.82/1.64 % Removed by relevancy pruning/SinE : 379
% 8.82/1.64 % Initial clauses : 318
% 8.82/1.64 % Removed in clause preprocessing : 87
% 8.82/1.64 % Initial clauses in saturation : 231
% 8.82/1.64 % Processed clauses : 1414
% 8.82/1.64 % ...of these trivial : 25
% 8.82/1.64 % ...subsumed : 297
% 8.82/1.64 % ...remaining for further processing : 1092
% 8.82/1.64 % Other redundant clauses eliminated : 15
% 8.82/1.64 % Clauses deleted for lack of memory : 0
% 8.82/1.64 % Backward-subsumed : 22
% 8.82/1.64 % Backward-rewritten : 44
% 8.82/1.64 % Generated clauses : 13406
% 8.82/1.64 % ...of the previous two non-redundant : 13042
% 8.82/1.64 % ...aggressively subsumed : 0
% 8.82/1.64 % Contextual simplify-reflections : 21
% 8.82/1.64 % Paramodulations : 9560
% 8.82/1.64 % Factorizations : 0
% 8.82/1.64 % NegExts : 272
% 8.82/1.64 % Equation resolutions : 70
% 8.82/1.64 % Disequality decompositions : 0
% 8.82/1.64 % Total rewrite steps : 2378
% 8.82/1.64 % ...of those cached : 2308
% 8.82/1.64 % Propositional unsat checks : 0
% 8.82/1.64 % Propositional check models : 0
% 8.82/1.64 % Propositional check unsatisfiable : 0
% 8.82/1.64 % Propositional clauses : 0
% 8.82/1.64 % Propositional clauses after purity: 0
% 8.82/1.64 % Propositional unsat core size : 0
% 8.82/1.64 % Propositional preprocessing time : 0.000
% 8.82/1.64 % Propositional encoding time : 0.000
% 8.82/1.64 % Propositional solver time : 0.000
% 8.82/1.64 % Success case prop preproc time : 0.000
% 8.82/1.64 % Success case prop encoding time : 0.000
% 8.82/1.64 % Success case prop solver time : 0.000
% 8.82/1.64 % Current number of processed clauses : 794
% 8.82/1.64 % Positive orientable unit clauses : 62
% 8.82/1.64 % Positive unorientable unit clauses: 8
% 8.82/1.64 % Negative unit clauses : 14
% 8.82/1.64 % Non-unit-clauses : 710
% 8.82/1.64 % Current number of unprocessed clauses: 11922
% 8.82/1.64 % ...number of literals in the above : 88968
% 8.82/1.64 % Current number of archived formulas : 0
% 8.82/1.64 % Current number of archived clauses : 298
% 8.82/1.64 % Clause-clause subsumption calls (NU) : 247131
% 8.82/1.64 % Rec. Clause-clause subsumption calls : 21870
% 8.82/1.64 % Non-unit clause-clause subsumptions : 289
% 8.82/1.64 % Unit Clause-clause subsumption calls : 856
% 8.82/1.64 % Rewrite failures with RHS unbound : 0
% 8.82/1.64 % BW rewrite match attempts : 643
% 8.82/1.64 % BW rewrite match successes : 144
% 8.82/1.64 % Condensation attempts : 1414
% 8.82/1.64 % Condensation successes : 5
% 8.82/1.64 % Termbank termtop insertions : 3506296
% 8.82/1.64 % Search garbage collected termcells : 29207
% 8.82/1.64
% 8.82/1.64 % -------------------------------------------------
% 8.82/1.64 % User time : 1.191 s
% 8.82/1.64 % System time : 0.033 s
% 8.82/1.64 % Total time : 1.224 s
% 8.82/1.64 % Maximum resident set size: 8760 pages
% 8.82/1.64
% 8.82/1.64 % -------------------------------------------------
% 8.82/1.64 % User time : 4.839 s
% 8.82/1.64 % System time : 0.133 s
% 8.82/1.64 % Total time : 4.972 s
% 8.82/1.64 % Maximum resident set size: 5888 pages
% 8.82/1.64 % E exiting
%------------------------------------------------------------------------------