%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM761^4 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:17:03 AM UTC 2026
% Result : Theorem 2.34s 0.71s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 58 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 36 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1059 ( 38 ~; 27 |; 7 &; 944 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 8 con; 0-3 aty)
% Number of variables : 165 ( 134 ^; 31 !; 0 ?; 165 :)
% 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_199,type,
n_pf: $i > $i > $i ).
thf(decl_201,type,
esk1_0: $i ).
thf(decl_202,type,
esk2_0: $i ).
thf(decl_203,type,
esk3_0: $i ).
thf(decl_204,type,
esk4_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.SgZqf5i0hi/E---3.1_3939821.p',def_diffprop) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_imp) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_d_29_ii) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.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.SgZqf5i0hi/E---3.1_3939821.p',def_n_eq) ).
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.SgZqf5i0hi/E---3.1_3939821.p',def_moref) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_n_some) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_iii) ).
thf(def_moreq,axiom,
( moreq
= ( ^ [X1: $i,X465: $i] : ( l_or @ ( moref @ X1 @ X465 ) @ ( n_eq @ X1 @ X465 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_moreq) ).
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.SgZqf5i0hi/E---3.1_3939821.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',def_is_of) ).
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.SgZqf5i0hi/E---3.1_3939821.p',def_lessf) ).
thf(satz65a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X558: $i] : ( in @ X558 @ frac )
@ ^ [X559: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moreq @ X1 @ X559 )
=> ( ( moref @ X4 @ X13 )
=> ( moref @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X559 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',satz65a) ).
thf(satz62g,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X534: $i] : ( in @ X534 @ frac )
@ ^ [X535: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( n_eq @ X1 @ X535 )
=> ( ( moref @ X4 @ X13 )
=> ( moref @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X535 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',satz62g) ).
thf(satz64a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X556: $i] : ( in @ X556 @ frac )
@ ^ [X557: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( lessf @ X1 @ X557 )
=> ( ( lessf @ X4 @ X13 )
=> ( lessf @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X557 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SgZqf5i0hi/E---3.1_3939821.p',satz64a) ).
thf(c_0_17,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_18,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_19,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_20,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_21,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( e_is @ nat @ Z0 @ ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,def_n_is]) ).
thf(c_0_22,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_23,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,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_25,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_26,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_20,c_0_21]),def_n_some]) ).
thf(c_0_27,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_28,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_29,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
thf(c_0_30,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_24,def_n_is]) ).
thf(c_0_31,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_25,c_0_26]) ).
thf(c_0_32,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_33,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
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(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_35,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_27,c_0_21]),def_n_some]) ).
thf(c_0_36,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X558: $i] : ( in @ X558 @ frac )
@ ^ [X559: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moreq @ X1 @ X559 )
=> ( ( moref @ X4 @ X13 )
=> ( moref @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X559 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz65a]) ).
thf(c_0_37,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_28,c_0_29]),c_0_30]),c_0_31]) ).
thf(c_0_38,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_39,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_34,c_0_35]) ).
thf(c_0_40,negated_conjecture,
~ ! [X600: $i] :
( ( in @ X600 @ frac )
=> ! [X599: $i] :
( ( in @ X599 @ frac )
=> ! [X598: $i] :
( ( in @ X598 @ frac )
=> ! [X597: $i] :
( ( in @ X597 @ frac )
=> ( ( ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X600 ) @ ( den @ X599 ) ) @ ( n_pl @ ( n_ts @ ( num @ X599 ) @ ( den @ X600 ) ) @ Z0 ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X600 ) @ ( den @ X599 ) ) @ ( n_ts @ ( num @ X599 ) @ ( den @ X600 ) ) ) )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X598 ) @ ( den @ X597 ) ) @ ( n_pl @ ( n_ts @ ( num @ X597 ) @ ( den @ X598 ) ) @ Z0 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X600 @ X598 ) ) @ ( den @ ( n_pf @ X599 @ X597 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X599 @ X597 ) ) @ ( den @ ( n_pf @ X600 @ X598 ) ) ) @ Z0 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_36]),c_0_37]),c_0_31]),c_0_38]) ).
thf(c_0_41,plain,
! [X620: $i] :
( ( in @ X620 @ frac )
=> ! [X619: $i] :
( ( in @ X619 @ frac )
=> ! [X618: $i] :
( ( in @ X618 @ frac )
=> ! [X617: $i] :
( ( in @ X617 @ frac )
=> ( ( e_is @ nat @ ( n_ts @ ( num @ X620 ) @ ( den @ X619 ) ) @ ( n_ts @ ( num @ X619 ) @ ( den @ X620 ) ) )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X618 ) @ ( den @ X617 ) ) @ ( n_pl @ ( n_ts @ ( num @ X617 ) @ ( den @ X618 ) ) @ Z0 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X620 @ X618 ) ) @ ( den @ ( n_pf @ X619 @ X617 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X619 @ X617 ) ) @ ( den @ ( n_pf @ X620 @ X618 ) ) ) @ Z0 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz62g]),c_0_30]),c_0_31]),c_0_38]) ).
thf(c_0_42,plain,
! [X792: $i] :
( ( in @ X792 @ frac )
=> ! [X791: $i] :
( ( in @ X791 @ frac )
=> ! [X790: $i] :
( ( in @ X790 @ frac )
=> ! [X789: $i] :
( ( in @ X789 @ frac )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X791 ) @ ( den @ X792 ) ) @ ( n_pl @ ( n_ts @ ( num @ X792 ) @ ( den @ X791 ) ) @ Z0 ) ) )
=> ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X789 ) @ ( den @ X790 ) ) @ ( n_pl @ ( n_ts @ ( num @ X790 ) @ ( den @ X789 ) ) @ Z0 ) ) )
=> ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X791 @ X789 ) ) @ ( den @ ( n_pf @ X792 @ X790 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X792 @ X790 ) ) @ ( den @ ( n_pf @ X791 @ X789 ) ) ) @ Z0 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz64a]),c_0_39]),c_0_38]) ).
thf(c_0_43,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( in @ esk4_0 @ frac )
& ( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
& ( $true
| ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
& ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) )
& ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ 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_40])])])])]) ).
thf(c_0_44,plain,
! [X1092: $i,X1093: $i,X1094: $i,X1095: $i] :
( ~ ( in @ X1092 @ frac )
| ~ ( in @ X1093 @ frac )
| ~ ( in @ X1094 @ frac )
| ~ ( in @ X1095 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1092 ) @ ( den @ X1093 ) ) @ ( n_ts @ ( num @ X1093 ) @ ( den @ X1092 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1094 ) @ ( den @ X1095 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1095 ) @ ( den @ X1094 ) ) @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X1092 @ X1094 ) ) @ ( den @ ( n_pf @ X1093 @ X1095 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X1093 @ X1095 ) ) @ ( den @ ( n_pf @ X1092 @ X1094 ) ) ) @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
thf(c_0_45,plain,
! [X1269: $i,X1270: $i,X1271: $i,X1272: $i] :
( ~ ( in @ X1269 @ frac )
| ~ ( in @ X1270 @ frac )
| ~ ( in @ X1271 @ frac )
| ~ ( in @ X1272 @ frac )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1270 ) @ ( den @ X1269 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1269 ) @ ( den @ X1270 ) ) @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X1272 ) @ ( den @ X1271 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1271 ) @ ( den @ X1272 ) ) @ Z0 ) ) )
| ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X1270 @ X1272 ) ) @ ( den @ ( n_pf @ X1269 @ X1271 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X1269 @ X1271 ) ) @ ( den @ ( n_pf @ X1270 @ X1272 ) ) ) @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
thf(c_0_46,negated_conjecture,
~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_47,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X6 @ 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 @ X5 ) @ ( den @ X6 ) ) @ ( n_pl @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_48,negated_conjecture,
( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_49,negated_conjecture,
in @ esk4_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_51,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_52,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_53,plain,
! [X1: $i,X4: $i,X5: $i,X6: $i] :
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) @ ( n_pl @ ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) ) @ Z0 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X6 @ frac )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_pl @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ Z0 ) ) )
| ~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) @ ( n_pl @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_54,negated_conjecture,
( ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ Z0 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_55,negated_conjecture,
~ ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]),c_0_50]),c_0_51]),c_0_52])]) ).
thf(c_0_56,negated_conjecture,
~ ( l_some @ nat
@ ^ [Z0: $i] : ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_pl @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ Z0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_53]),c_0_48]),c_0_50]),c_0_49]),c_0_52]),c_0_51])]) ).
thf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_54,c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM761^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n009.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 12:53:30 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.21/0.27 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.SgZqf5i0hi/E---3.1_3939821.p
% 2.34/0.71 % Version: 3.5.1-ho
% 2.34/0.71 % Preprocessing class: HSLMSMSMLLLCHSA.
% 2.34/0.71 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 2.34/0.71 % Starting pre_casc_4 with 1200s (4) cores
% 2.34/0.71 % Starting full_lambda_6 with 300s (1) cores
% 2.34/0.71 % Starting sh10 with 300s (1) cores
% 2.34/0.71 % Starting post_as_ho9 with 300s (1) cores
% 2.34/0.71 % Starting post_as_ho8 with 300s (1) cores
% 2.34/0.71 % pre_casc_4 with pid 3939834 completed with status 0
% 2.34/0.71 % Result found by pre_casc_4
% 2.34/0.71 % Preprocessing class: HSLMSMSMLLLCHSA.
% 2.34/0.71 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 2.34/0.71 % Starting pre_casc_4 with 1200s (4) cores
% 2.34/0.71 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 2.34/0.71 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 2.34/0.71 % Search class: HGHSM-FSLM31-DHSMMFBN
% 2.34/0.71 % partial match(2): HGHSM-FSLM31-DHSFFFBN
% 2.34/0.71 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 2.34/0.71 % Starting SubtermCWHack with 109s (1) cores
% 2.34/0.71 % Starting pre_casc_4 with 121s (1) cores
% 2.34/0.71 % Starting full_lambda_10 with 211s (1) cores
% 2.34/0.71 % Starting new_bool_8 with 210s (1) cores
% 2.34/0.71 % pre_casc_4 with pid 3939840 completed with status 0
% 2.34/0.71 % Result found by pre_casc_4
% 2.34/0.71 % Preprocessing class: HSLMSMSMLLLCHSA.
% 2.34/0.71 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 2.34/0.71 % Starting pre_casc_4 with 1200s (4) cores
% 2.34/0.71 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 2.34/0.71 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 2.34/0.71 % Search class: HGHSM-FSLM31-DHSMMFBN
% 2.34/0.71 % partial match(2): HGHSM-FSLM31-DHSFFFBN
% 2.34/0.71 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 2.34/0.71 % Starting SubtermCWHack with 109s (1) cores
% 2.34/0.71 % Starting pre_casc_4 with 121s (1) cores
% 2.34/0.71 % Preprocessing time : 0.011 s
% 2.34/0.71 % Presaturation interreduction done
% 2.34/0.71
% 2.34/0.71 % Proof found!
% 2.34/0.71 % SZS status Theorem
% 2.34/0.71 % SZS output start CNFRefutation
% See solution above
% 2.34/0.71 % Parsed axioms : 600
% 2.34/0.71 % Removed by relevancy pruning/SinE : 376
% 2.34/0.71 % Initial clauses : 366
% 2.34/0.71 % Removed in clause preprocessing : 91
% 2.34/0.71 % Initial clauses in saturation : 275
% 2.34/0.71 % Processed clauses : 589
% 2.34/0.71 % ...of these trivial : 3
% 2.34/0.71 % ...subsumed : 130
% 2.34/0.71 % ...remaining for further processing : 455
% 2.34/0.71 % Other redundant clauses eliminated : 15
% 2.34/0.71 % Clauses deleted for lack of memory : 0
% 2.34/0.71 % Backward-subsumed : 5
% 2.34/0.71 % Backward-rewritten : 6
% 2.34/0.71 % Generated clauses : 6482
% 2.34/0.71 % ...of the previous two non-redundant : 6392
% 2.34/0.71 % ...aggressively subsumed : 0
% 2.34/0.71 % Contextual simplify-reflections : 8
% 2.34/0.71 % Paramodulations : 1450
% 2.34/0.71 % Factorizations : 0
% 2.34/0.71 % NegExts : 6
% 2.34/0.71 % Equation resolutions : 17
% 2.34/0.71 % Disequality decompositions : 0
% 2.34/0.71 % Total rewrite steps : 391
% 2.34/0.71 % ...of those cached : 339
% 2.34/0.71 % Propositional unsat checks : 0
% 2.34/0.71 % Propositional check models : 0
% 2.34/0.71 % Propositional check unsatisfiable : 0
% 2.34/0.71 % Propositional clauses : 0
% 2.34/0.71 % Propositional clauses after purity: 0
% 2.34/0.71 % Propositional unsat core size : 0
% 2.34/0.71 % Propositional preprocessing time : 0.000
% 2.34/0.71 % Propositional encoding time : 0.000
% 2.34/0.71 % Propositional solver time : 0.000
% 2.34/0.71 % Success case prop preproc time : 0.000
% 2.34/0.71 % Success case prop encoding time : 0.000
% 2.34/0.71 % Success case prop solver time : 0.000
% 2.34/0.71 % Current number of processed clauses : 264
% 2.34/0.71 % Positive orientable unit clauses : 51
% 2.34/0.71 % Positive unorientable unit clauses: 0
% 2.34/0.71 % Negative unit clauses : 12
% 2.34/0.71 % Non-unit-clauses : 201
% 2.34/0.71 % Current number of unprocessed clauses: 6253
% 2.34/0.71 % ...number of literals in the above : 59999
% 2.34/0.71 % Current number of archived formulas : 0
% 2.34/0.71 % Current number of archived clauses : 191
% 2.34/0.71 % Clause-clause subsumption calls (NU) : 43174
% 2.34/0.71 % Rec. Clause-clause subsumption calls : 6013
% 2.34/0.71 % Non-unit clause-clause subsumptions : 128
% 2.34/0.71 % Unit Clause-clause subsumption calls : 253
% 2.34/0.71 % Rewrite failures with RHS unbound : 0
% 2.34/0.71 % BW rewrite match attempts : 25
% 2.34/0.71 % BW rewrite match successes : 6
% 2.34/0.71 % Condensation attempts : 0
% 2.34/0.71 % Condensation successes : 0
% 2.34/0.71 % Termbank termtop insertions : 350760
% 2.34/0.71 % Search garbage collected termcells : 35816
% 2.34/0.71
% 2.34/0.71 % -------------------------------------------------
% 2.34/0.71 % User time : 0.311 s
% 2.34/0.71 % System time : 0.021 s
% 2.34/0.71 % Total time : 0.332 s
% 2.34/0.71 % Maximum resident set size: 9840 pages
% 2.34/0.71
% 2.34/0.71 % -------------------------------------------------
% 2.34/0.71 % User time : 0.834 s
% 2.34/0.71 % System time : 0.068 s
% 2.34/0.71 % Total time : 0.902 s
% 2.34/0.71 % Maximum resident set size: 5888 pages
% 2.34/0.71 % E exiting
%------------------------------------------------------------------------------