%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM739^4 : 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 : n007.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 08:16:58 AM UTC 2026
% Result : Theorem 2.03s 0.67s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 61 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 264 ( 78 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 919 ( 50 ~; 38 |; 9 &; 773 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 126 ( 94 ^; 32 !; 0 ?; 126 :)
% 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_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_128,type,
n_some: ( $i > $o ) > $o ).
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,
esk1_0: $i ).
thf(decl_200,type,
esk2_0: $i ).
thf(decl_201,type,
esk3_0: $i ).
thf(decl_202,type,
esk4_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_imp) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_e_is) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_moref) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_d_29_ii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.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/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_n_is) ).
thf(def_moreq,axiom,
( moreq
= ( ^ [X1: $i,X465: $i] : ( l_or @ ( moref @ X1 @ X465 ) @ ( n_eq @ X1 @ X465 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.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/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.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/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_lessf) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',def_iii) ).
thf(satz46,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X483: $i] : ( in @ X483 @ frac )
@ ^ [X484: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moreq @ X1 @ X484 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X484 @ X13 )
=> ( moreq @ X4 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',satz46) ).
thf(satz45,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X463: $i] : ( in @ X463 @ frac )
@ ^ [X464: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( lessf @ X1 @ X464 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X464 @ X13 )
=> ( lessf @ X4 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',satz45) ).
thf(satz39,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X439: $i] : ( in @ X439 @ frac )
@ ^ [X440: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( n_eq @ X1 @ X440 )
=> ( ( n_eq @ X440 @ X4 )
=> ( n_eq @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3KkPhSKkb8/E---3.1_3309860.p',satz39) ).
thf(c_0_16,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_17,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_18,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_19,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_20,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_21,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_22,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_24,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_18]) ).
thf(c_0_25,plain,
( moreq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreq]) ).
thf(c_0_26,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_27,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_17]),c_0_22]) ).
thf(c_0_28,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,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_30,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_31,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_32,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_33,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X483: $i] : ( in @ X483 @ frac )
@ ^ [X484: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moreq @ X1 @ X484 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X484 @ X13 )
=> ( moreq @ X4 @ X13 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz46]) ).
thf(c_0_34,plain,
( moreq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) )
=> ~ $true )
=> ( ( 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_25,c_0_26]),c_0_27]),c_0_28]) ).
thf(c_0_35,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_36,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_37,negated_conjecture,
~ ! [X528: $i] :
( ( in @ X528 @ frac )
=> ! [X527: $i] :
( ( in @ X527 @ frac )
=> ! [X526: $i] :
( ( in @ X526 @ frac )
=> ! [X525: $i] :
( ( in @ X525 @ frac )
=> ( ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X528 ) @ ( den @ X527 ) ) @ ( n_ts @ ( num @ X527 ) @ ( den @ X528 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ X528 ) @ ( den @ X527 ) )
= ( n_ts @ ( num @ X527 ) @ ( den @ X528 ) ) ) )
=> ( ( ( n_ts @ ( num @ X528 ) @ ( den @ X526 ) )
= ( n_ts @ ( num @ X526 ) @ ( den @ X528 ) ) )
=> ( ( ( n_ts @ ( num @ X527 ) @ ( den @ X525 ) )
= ( n_ts @ ( num @ X525 ) @ ( den @ X527 ) ) )
=> ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X526 ) @ ( den @ X525 ) ) @ ( n_ts @ ( num @ X525 ) @ ( den @ X526 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ X526 ) @ ( den @ X525 ) )
= ( n_ts @ ( num @ X525 ) @ ( den @ X526 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_33]),c_0_28]),c_0_34]),c_0_35]) ).
thf(c_0_38,plain,
! [X563: $i] :
( ( in @ X563 @ frac )
=> ! [X562: $i] :
( ( in @ X562 @ frac )
=> ! [X561: $i] :
( ( in @ X561 @ frac )
=> ! [X560: $i] :
( ( in @ X560 @ frac )
=> ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X562 ) @ ( den @ X563 ) ) @ ( n_ts @ ( num @ X563 ) @ ( den @ X562 ) ) ) )
=> ( ( ( n_ts @ ( num @ X563 ) @ ( den @ X561 ) )
= ( n_ts @ ( num @ X561 ) @ ( den @ X563 ) ) )
=> ( ( ( n_ts @ ( num @ X562 ) @ ( den @ X560 ) )
= ( n_ts @ ( num @ X560 ) @ ( den @ X562 ) ) )
=> ( n_some @ ( diffprop @ ( n_ts @ ( num @ X560 ) @ ( den @ X561 ) ) @ ( n_ts @ ( num @ X561 ) @ ( den @ X560 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz45]),c_0_36]),c_0_28]),c_0_35]) ).
thf(c_0_39,plain,
! [X542: $i] :
( ( in @ X542 @ frac )
=> ! [X541: $i] :
( ( in @ X541 @ frac )
=> ! [X540: $i] :
( ( in @ X540 @ frac )
=> ( ( ( n_ts @ ( num @ X542 ) @ ( den @ X541 ) )
= ( n_ts @ ( num @ X541 ) @ ( den @ X542 ) ) )
=> ( ( ( n_ts @ ( num @ X541 ) @ ( den @ X540 ) )
= ( n_ts @ ( num @ X540 ) @ ( den @ X541 ) ) )
=> ( ( n_ts @ ( num @ X542 ) @ ( den @ X540 ) )
= ( n_ts @ ( num @ X540 ) @ ( den @ X542 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz39]),c_0_28]),c_0_35]) ).
thf(c_0_40,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( in @ esk4_0 @ frac )
& ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
| ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
& ( $true
| ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
& ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) )
= ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) )
& ( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk4_0 ) )
= ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk2_0 ) ) )
& ( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
| ~ $true )
& ( ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) )
!= ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) ),
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_37])])])])]) ).
thf(c_0_41,plain,
! [X908: $i,X909: $i,X910: $i,X911: $i] :
( ~ ( in @ X908 @ frac )
| ~ ( in @ X909 @ frac )
| ~ ( in @ X910 @ frac )
| ~ ( in @ X911 @ frac )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X909 ) @ ( den @ X908 ) ) @ ( n_ts @ ( num @ X908 ) @ ( den @ X909 ) ) ) )
| ( ( n_ts @ ( num @ X908 ) @ ( den @ X910 ) )
!= ( n_ts @ ( num @ X910 ) @ ( den @ X908 ) ) )
| ( ( n_ts @ ( num @ X909 ) @ ( den @ X911 ) )
!= ( n_ts @ ( num @ X911 ) @ ( den @ X909 ) ) )
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ X911 ) @ ( den @ X910 ) ) @ ( n_ts @ ( num @ X910 ) @ ( den @ X911 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
thf(c_0_42,plain,
! [X886: $i,X887: $i,X888: $i] :
( ~ ( in @ X886 @ frac )
| ~ ( in @ X887 @ frac )
| ~ ( in @ X888 @ frac )
| ( ( n_ts @ ( num @ X886 ) @ ( den @ X887 ) )
!= ( n_ts @ ( num @ X887 ) @ ( den @ X886 ) ) )
| ( ( n_ts @ ( num @ X887 ) @ ( den @ X888 ) )
!= ( n_ts @ ( num @ X888 ) @ ( den @ X887 ) ) )
| ( ( n_ts @ ( num @ X886 ) @ ( den @ X888 ) )
= ( n_ts @ ( num @ X888 ) @ ( den @ X886 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
thf(c_0_43,negated_conjecture,
( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_44,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X6 @ frac )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) ) )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ X5 ) )
!= ( n_ts @ ( num @ X5 ) @ ( den @ X1 ) ) )
| ( ( n_ts @ ( num @ X4 ) @ ( den @ X6 ) )
!= ( n_ts @ ( num @ X6 ) @ ( den @ X4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_45,negated_conjecture,
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
| ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_46,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_47,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_48,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( ( n_ts @ ( num @ X1 ) @ ( den @ X5 ) )
= ( n_ts @ ( num @ X5 ) @ ( den @ X1 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) )
!= ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ( ( n_ts @ ( num @ X4 ) @ ( den @ X5 ) )
!= ( n_ts @ ( num @ X5 ) @ ( den @ X4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_49,negated_conjecture,
( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk3_0 ) )
= ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_50,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_51,negated_conjecture,
~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) ),
inference(cn,[status(thm)],[c_0_43]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i,X4: $i] :
( ( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) )
= ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) )
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) )
| ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ X1 ) )
!= ( n_ts @ ( num @ X1 ) @ ( den @ esk1_0 ) ) )
| ( ( n_ts @ ( num @ esk2_0 ) @ ( den @ X4 ) )
!= ( n_ts @ ( num @ X4 ) @ ( den @ esk2_0 ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]) ).
thf(c_0_53,negated_conjecture,
( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk4_0 ) )
= ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_54,negated_conjecture,
in @ esk4_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( ( n_ts @ ( num @ X1 ) @ ( den @ esk3_0 ) )
= ( n_ts @ ( num @ esk3_0 ) @ ( den @ X1 ) ) )
| ( ( 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_48,c_0_49]),c_0_50]),c_0_46])]) ).
thf(c_0_56,negated_conjecture,
( ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) )
= ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_49]),c_0_53]),c_0_50]),c_0_54])]) ).
thf(c_0_57,negated_conjecture,
! [X1: $i] :
( ( ( n_ts @ ( num @ X1 ) @ ( den @ esk4_0 ) )
= ( n_ts @ ( num @ esk4_0 ) @ ( den @ X1 ) ) )
| ( ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) )
!= ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) )
| ~ ( in @ X1 @ frac ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_53]),c_0_54]),c_0_47])]) ).
thf(c_0_58,negated_conjecture,
( ( 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(spm,[status(thm)],[c_0_55,c_0_56]),c_0_47])]) ).
thf(c_0_59,negated_conjecture,
( ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) )
!= ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_50])]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM739^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:44:55 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.20/0.30 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.3KkPhSKkb8/E---3.1_3309860.p
% 2.03/0.67 % Version: 3.5.1-ho
% 2.03/0.67 % Preprocessing class: HSLMSMSMLLLCHSA.
% 2.03/0.67 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.67 % Starting pre_casc_4 with 1200s (4) cores
% 2.03/0.67 % Starting full_lambda_6 with 300s (1) cores
% 2.03/0.67 % Starting sh10 with 300s (1) cores
% 2.03/0.67 % Starting post_as_ho9 with 300s (1) cores
% 2.03/0.67 % Starting post_as_ho8 with 300s (1) cores
% 2.03/0.67 % pre_casc_4 with pid 3309873 completed with status 0
% 2.03/0.67 % Result found by pre_casc_4
% 2.03/0.67 % Preprocessing class: HSLMSMSMLLLCHSA.
% 2.03/0.67 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.67 % Starting pre_casc_4 with 1200s (4) cores
% 2.03/0.67 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 2.03/0.67 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 2.03/0.67 % Search class: HGHSM-FSLM31-DHSMMFBN
% 2.03/0.67 % partial match(2): HGHSM-FSLM31-DHSFFFBN
% 2.03/0.67 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 2.03/0.67 % Starting SubtermCWHack with 109s (1) cores
% 2.03/0.67 % Starting pre_casc_4 with 121s (1) cores
% 2.03/0.67 % Starting full_lambda_10 with 211s (1) cores
% 2.03/0.67 % Starting new_bool_8 with 210s (1) cores
% 2.03/0.67 % full_lambda_10 with pid 3309881 completed with status 0
% 2.03/0.67 % Result found by full_lambda_10
% 2.03/0.67 % Preprocessing class: HSLMSMSMLLLCHSA.
% 2.03/0.67 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.67 % Starting pre_casc_4 with 1200s (4) cores
% 2.03/0.67 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 2.03/0.67 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 2.03/0.67 % Search class: HGHSM-FSLM31-DHSMMFBN
% 2.03/0.67 % partial match(2): HGHSM-FSLM31-DHSFFFBN
% 2.03/0.67 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 2.03/0.67 % Starting SubtermCWHack with 109s (1) cores
% 2.03/0.67 % Starting pre_casc_4 with 121s (1) cores
% 2.03/0.67 % Starting full_lambda_10 with 211s (1) cores
% 2.03/0.67 % Preprocessing time : 0.008 s
% 2.03/0.67 % Presaturation interreduction done
% 2.03/0.67
% 2.03/0.67 % Proof found!
% 2.03/0.67 % SZS status Theorem
% 2.03/0.67 % SZS output start CNFRefutation
% See solution above
% 2.03/0.67 % Parsed axioms : 560
% 2.03/0.67 % Removed by relevancy pruning/SinE : 385
% 2.03/0.67 % Initial clauses : 283
% 2.03/0.67 % Removed in clause preprocessing : 101
% 2.03/0.67 % Initial clauses in saturation : 182
% 2.03/0.67 % Processed clauses : 817
% 2.03/0.67 % ...of these trivial : 11
% 2.03/0.67 % ...subsumed : 339
% 2.03/0.67 % ...remaining for further processing : 467
% 2.03/0.67 % Other redundant clauses eliminated : 45
% 2.03/0.67 % Clauses deleted for lack of memory : 0
% 2.03/0.67 % Backward-subsumed : 3
% 2.03/0.67 % Backward-rewritten : 16
% 2.03/0.67 % Generated clauses : 5435
% 2.03/0.67 % ...of the previous two non-redundant : 5106
% 2.03/0.67 % ...aggressively subsumed : 0
% 2.03/0.67 % Contextual simplify-reflections : 7
% 2.03/0.67 % Paramodulations : 5336
% 2.03/0.67 % Factorizations : 0
% 2.03/0.67 % NegExts : 4
% 2.03/0.67 % Equation resolutions : 59
% 2.03/0.67 % Disequality decompositions : 0
% 2.03/0.67 % Total rewrite steps : 2977
% 2.03/0.67 % ...of those cached : 2914
% 2.03/0.67 % Propositional unsat checks : 0
% 2.03/0.67 % Propositional check models : 0
% 2.03/0.67 % Propositional check unsatisfiable : 0
% 2.03/0.67 % Propositional clauses : 0
% 2.03/0.67 % Propositional clauses after purity: 0
% 2.03/0.67 % Propositional unsat core size : 0
% 2.03/0.67 % Propositional preprocessing time : 0.000
% 2.03/0.67 % Propositional encoding time : 0.000
% 2.03/0.67 % Propositional solver time : 0.000
% 2.03/0.67 % Success case prop preproc time : 0.000
% 2.03/0.67 % Success case prop encoding time : 0.000
% 2.03/0.67 % Success case prop solver time : 0.000
% 2.03/0.67 % Current number of processed clauses : 325
% 2.03/0.67 % Positive orientable unit clauses : 53
% 2.03/0.67 % Positive unorientable unit clauses: 4
% 2.03/0.67 % Negative unit clauses : 21
% 2.03/0.67 % Non-unit-clauses : 247
% 2.03/0.67 % Current number of unprocessed clauses: 4492
% 2.03/0.67 % ...number of literals in the above : 22641
% 2.03/0.67 % Current number of archived formulas : 0
% 2.03/0.67 % Current number of archived clauses : 114
% 2.03/0.67 % Clause-clause subsumption calls (NU) : 33692
% 2.03/0.67 % Rec. Clause-clause subsumption calls : 8664
% 2.03/0.67 % Non-unit clause-clause subsumptions : 214
% 2.03/0.67 % Unit Clause-clause subsumption calls : 665
% 2.03/0.67 % Rewrite failures with RHS unbound : 0
% 2.03/0.67 % BW rewrite match attempts : 45
% 2.03/0.67 % BW rewrite match successes : 25
% 2.03/0.67 % Condensation attempts : 817
% 2.03/0.67 % Condensation successes : 0
% 2.03/0.67 % Termbank termtop insertions : 392102
% 2.03/0.67 % Search garbage collected termcells : 26033
% 2.03/0.67
% 2.03/0.67 % -------------------------------------------------
% 2.03/0.67 % User time : 0.269 s
% 2.03/0.67 % System time : 0.014 s
% 2.03/0.67 % Total time : 0.283 s
% 2.03/0.67 % Maximum resident set size: 7972 pages
% 2.03/0.67
% 2.03/0.67 % -------------------------------------------------
% 2.03/0.67 % User time : 0.928 s
% 2.03/0.67 % System time : 0.050 s
% 2.03/0.67 % Total time : 0.978 s
% 2.03/0.67 % Maximum resident set size: 5888 pages
% 2.03/0.67 % E exiting
%------------------------------------------------------------------------------