TSTP Solution File: NUM765^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM765^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 01:17:10 EDT 2024
% Result : Theorem 1.18s 0.69s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 99 ( 39 unt; 26 typ; 0 def)
% Number of atoms : 387 ( 30 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1876 ( 106 ~; 87 |; 11 &;1603 @)
% ( 0 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 8 con; 0-3 aty)
% Number of variables : 163 ( 98 ^ 65 !; 0 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_67,type,
l_or: $o > $o > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_127,type,
n_some: ( $i > $o ) > $o ).
thf(decl_147,type,
diffprop: $i > $i > $i > $o ).
thf(decl_148,type,
d_29_ii: $i > $i > $o ).
thf(decl_149,type,
iii: $i > $i > $o ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_189,type,
frac: $i ).
thf(decl_191,type,
num: $i > $i ).
thf(decl_192,type,
den: $i > $i ).
thf(decl_193,type,
n_eq: $i > $i > $o ).
thf(decl_194,type,
moref: $i > $i > $o ).
thf(decl_195,type,
lessf: $i > $i > $o ).
thf(decl_196,type,
moreq: $i > $i > $o ).
thf(decl_198,type,
n_pf: $i > $i > $i ).
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/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_imp) ).
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/benchmark/theBenchmark.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/benchmark/theBenchmark.p',def_d_29_ii) ).
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/benchmark/theBenchmark.p',def_n_eq) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
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/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(def_moreq,axiom,
( moreq
= ( ^ [X1: $i,X465: $i] : ( l_or @ ( moref @ X1 @ X465 ) @ ( n_eq @ X1 @ X465 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_moreq) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(satz66,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X566: $i] : ( in @ X566 @ frac )
@ ^ [X567: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moreq @ X1 @ X567 )
=> ( ( moreq @ X4 @ X13 )
=> ( moreq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X567 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz66) ).
thf(satz56,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X508: $i] : ( in @ X508 @ frac )
@ ^ [X509: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( n_eq @ X1 @ X509 )
=> ( ( n_eq @ X4 @ X13 )
=> ( n_eq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X509 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).
thf(satz65a,axiom,
( 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/sandbox2/benchmark/theBenchmark.p',satz65a) ).
thf(satz65b,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X560: $i] : ( in @ X560 @ frac )
@ ^ [X561: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( moref @ X1 @ X561 )
=> ( ( moreq @ X4 @ X13 )
=> ( moref @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X561 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65b) ).
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/benchmark/theBenchmark.p',def_lessf) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_iii) ).
thf(satz62k,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X540: $i] : ( in @ X540 @ frac )
@ ^ [X541: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( n_eq @ X1 @ X541 )
=> ( ( lessf @ X4 @ X13 )
=> ( lessf @ ( n_pf @ X4 @ X1 ) @ ( n_pf @ X13 @ X541 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62k) ).
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/sandbox2/benchmark/theBenchmark.p',satz38) ).
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,
( 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_21,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_22,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_23,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_24,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,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_26,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_27,plain,
( moreq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) )
=> ~ $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_28,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_20,c_0_21]) ).
thf(c_0_29,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_22,def_n_is]) ).
thf(c_0_30,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_19]),c_0_24]) ).
thf(c_0_31,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_32,plain,
( moreq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) )
=> ~ $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_27,c_0_28]),c_0_29]),c_0_30]) ).
thf(c_0_33,negated_conjecture,
~ ! [X608: $i] :
( ( in @ X608 @ frac )
=> ! [X607: $i] :
( ( in @ X607 @ frac )
=> ! [X606: $i] :
( ( in @ X606 @ frac )
=> ! [X605: $i] :
( ( in @ X605 @ frac )
=> ( ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X608 ) @ ( den @ X607 ) ) @ ( n_ts @ ( num @ X607 ) @ ( den @ X608 ) ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X608 ) @ ( den @ X607 ) ) @ ( n_ts @ ( num @ X607 ) @ ( den @ X608 ) ) ) )
=> ( ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X606 ) @ ( den @ X605 ) ) @ ( n_ts @ ( num @ X605 ) @ ( den @ X606 ) ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X606 ) @ ( den @ X605 ) ) @ ( n_ts @ ( num @ X605 ) @ ( den @ X606 ) ) ) )
=> ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X608 @ X606 ) ) @ ( den @ ( n_pf @ X607 @ X605 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X607 @ X605 ) ) @ ( den @ ( n_pf @ X608 @ X606 ) ) ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X608 @ X606 ) ) @ ( den @ ( n_pf @ X607 @ X605 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X607 @ X605 ) ) @ ( den @ ( n_pf @ X608 @ X606 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz66])]),c_0_31]),c_0_32]) ).
thf(c_0_34,plain,
! [X649: $i] :
( ( in @ X649 @ frac )
=> ! [X648: $i] :
( ( in @ X648 @ frac )
=> ! [X647: $i] :
( ( in @ X647 @ frac )
=> ! [X646: $i] :
( ( in @ X646 @ frac )
=> ( ( e_is @ nat @ ( n_ts @ ( num @ X649 ) @ ( den @ X648 ) ) @ ( n_ts @ ( num @ X648 ) @ ( den @ X649 ) ) )
=> ( ( e_is @ nat @ ( n_ts @ ( num @ X647 ) @ ( den @ X646 ) ) @ ( n_ts @ ( num @ X646 ) @ ( den @ X647 ) ) )
=> ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X649 @ X647 ) ) @ ( den @ ( n_pf @ X648 @ X646 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X648 @ X646 ) ) @ ( den @ ( n_pf @ X649 @ X647 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz56]),c_0_31]),c_0_29]) ).
thf(c_0_35,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 ) ) ) )
| ( 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 ) ) ) )
& ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
& ( $true
| ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
& ( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) ) )
| ~ $true )
& ~ ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ 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_33])])])])]) ).
thf(c_0_36,plain,
! [X634: $i] :
( ( in @ X634 @ frac )
=> ! [X633: $i] :
( ( in @ X633 @ frac )
=> ! [X632: $i] :
( ( in @ X632 @ frac )
=> ! [X631: $i] :
( ( in @ X631 @ frac )
=> ( ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X634 ) @ ( den @ X633 ) ) @ ( n_ts @ ( num @ X633 ) @ ( den @ X634 ) ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X634 ) @ ( den @ X633 ) ) @ ( n_ts @ ( num @ X633 ) @ ( den @ X634 ) ) ) )
=> ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X632 ) @ ( den @ X631 ) ) @ ( n_ts @ ( num @ X631 ) @ ( den @ X632 ) ) ) )
=> ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X634 @ X632 ) ) @ ( den @ ( n_pf @ X633 @ X631 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X633 @ X631 ) ) @ ( den @ ( n_pf @ X634 @ X632 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz65a]),c_0_31]),c_0_28]),c_0_32]) ).
thf(c_0_37,plain,
! [X638: $i] :
( ( in @ X638 @ frac )
=> ! [X637: $i] :
( ( in @ X637 @ frac )
=> ! [X636: $i] :
( ( in @ X636 @ frac )
=> ! [X635: $i] :
( ( in @ X635 @ frac )
=> ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X638 ) @ ( den @ X637 ) ) @ ( n_ts @ ( num @ X637 ) @ ( den @ X638 ) ) ) )
=> ( ( ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X636 ) @ ( den @ X635 ) ) @ ( n_ts @ ( num @ X635 ) @ ( den @ X636 ) ) ) )
=> ~ $true )
=> ( e_is @ nat @ ( n_ts @ ( num @ X636 ) @ ( den @ X635 ) ) @ ( n_ts @ ( num @ X635 ) @ ( den @ X636 ) ) ) )
=> ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X638 @ X636 ) ) @ ( den @ ( n_pf @ X637 @ X635 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X637 @ X635 ) ) @ ( den @ ( n_pf @ X638 @ X636 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz65b]),c_0_31]),c_0_28]),c_0_32]) ).
thf(c_0_38,plain,
! [X1146: $i,X1147: $i,X1148: $i,X1149: $i] :
( ~ ( in @ X1146 @ frac )
| ~ ( in @ X1147 @ frac )
| ~ ( in @ X1148 @ frac )
| ~ ( in @ X1149 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1146 ) @ ( den @ X1147 ) ) @ ( n_ts @ ( num @ X1147 ) @ ( den @ X1146 ) ) )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1148 ) @ ( den @ X1149 ) ) @ ( n_ts @ ( num @ X1149 ) @ ( den @ X1148 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X1146 @ X1148 ) ) @ ( den @ ( n_pf @ X1147 @ X1149 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1147 @ X1149 ) ) @ ( den @ ( n_pf @ X1146 @ X1148 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
thf(c_0_39,negated_conjecture,
( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_40,plain,
! [X1123: $i,X1124: $i,X1125: $i,X1126: $i] :
( ( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1123 ) @ ( den @ X1124 ) ) @ ( n_ts @ ( num @ X1124 ) @ ( den @ X1123 ) ) ) )
| ~ $true
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1125 ) @ ( den @ X1126 ) ) @ ( n_ts @ ( num @ X1126 ) @ ( den @ X1125 ) ) ) )
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1123 @ X1125 ) ) @ ( den @ ( n_pf @ X1124 @ X1126 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1124 @ X1126 ) ) @ ( den @ ( n_pf @ X1123 @ X1125 ) ) ) ) )
| ~ ( in @ X1126 @ frac )
| ~ ( in @ X1125 @ frac )
| ~ ( in @ X1124 @ frac )
| ~ ( in @ X1123 @ frac ) )
& ( ~ ( e_is @ nat @ ( n_ts @ ( num @ X1123 ) @ ( den @ X1124 ) ) @ ( n_ts @ ( num @ X1124 ) @ ( den @ X1123 ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1125 ) @ ( den @ X1126 ) ) @ ( n_ts @ ( num @ X1126 ) @ ( den @ X1125 ) ) ) )
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1123 @ X1125 ) ) @ ( den @ ( n_pf @ X1124 @ X1126 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1124 @ X1126 ) ) @ ( den @ ( n_pf @ X1123 @ X1125 ) ) ) ) )
| ~ ( in @ X1126 @ frac )
| ~ ( in @ X1125 @ frac )
| ~ ( in @ X1124 @ frac )
| ~ ( in @ X1123 @ 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_36])])])])]) ).
thf(c_0_41,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_42,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_43,plain,
! [X1127: $i,X1128: $i,X1129: $i,X1130: $i] :
( ( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1129 ) @ ( den @ X1130 ) ) @ ( n_ts @ ( num @ X1130 ) @ ( den @ X1129 ) ) ) )
| ~ $true
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1127 @ X1129 ) ) @ ( den @ ( n_pf @ X1128 @ X1130 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1128 @ X1130 ) ) @ ( den @ ( n_pf @ X1127 @ X1129 ) ) ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1127 ) @ ( den @ X1128 ) ) @ ( n_ts @ ( num @ X1128 ) @ ( den @ X1127 ) ) ) )
| ~ ( in @ X1130 @ frac )
| ~ ( in @ X1129 @ frac )
| ~ ( in @ X1128 @ frac )
| ~ ( in @ X1127 @ frac ) )
& ( ~ ( e_is @ nat @ ( n_ts @ ( num @ X1129 ) @ ( den @ X1130 ) ) @ ( n_ts @ ( num @ X1130 ) @ ( den @ X1129 ) ) )
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1127 @ X1129 ) ) @ ( den @ ( n_pf @ X1128 @ X1130 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1128 @ X1130 ) ) @ ( den @ ( n_pf @ X1127 @ X1129 ) ) ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1127 ) @ ( den @ X1128 ) ) @ ( n_ts @ ( num @ X1128 ) @ ( den @ X1127 ) ) ) )
| ~ ( in @ X1130 @ frac )
| ~ ( in @ X1129 @ frac )
| ~ ( in @ X1128 @ frac )
| ~ ( in @ X1127 @ 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_37])])])])]) ).
thf(c_0_44,negated_conjecture,
~ ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_45,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( e_is @ nat @ ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) )
| ~ ( 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 ) ) )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_46,negated_conjecture,
in @ esk4_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_47,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_48,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_49,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_50,negated_conjecture,
~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk4_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk4_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_39]) ).
thf(c_0_51,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X6 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X4 @ X6 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) ) )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) )
| ~ ( in @ X6 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_52,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_41,c_0_42]) ).
thf(c_0_53,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X5 @ X1 ) ) @ ( den @ ( n_pf @ X6 @ X4 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X6 @ X4 ) ) @ ( den @ ( n_pf @ X5 @ X1 ) ) ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) )
| ~ $true
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X6 @ frac )
| ~ ( in @ X5 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_54,negated_conjecture,
( ~ ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) )
| ~ ( 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(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_49])]) ).
thf(c_0_55,negated_conjecture,
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_56,negated_conjecture,
( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) ) )
| ~ ( 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(spm,[status(thm)],[c_0_50,c_0_51]),c_0_46]),c_0_47]),c_0_48]),c_0_49])]) ).
thf(c_0_57,plain,
! [X731: $i] :
( ( in @ X731 @ frac )
=> ! [X730: $i] :
( ( in @ X730 @ frac )
=> ! [X729: $i] :
( ( in @ X729 @ frac )
=> ! [X728: $i] :
( ( in @ X728 @ frac )
=> ( ( e_is @ nat @ ( n_ts @ ( num @ X731 ) @ ( den @ X730 ) ) @ ( n_ts @ ( num @ X730 ) @ ( den @ X731 ) ) )
=> ( ( n_some @ ( diffprop @ ( n_ts @ ( num @ X728 ) @ ( den @ X729 ) ) @ ( n_ts @ ( num @ X729 ) @ ( den @ X728 ) ) ) )
=> ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X728 @ X730 ) ) @ ( den @ ( n_pf @ X729 @ X731 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X729 @ X731 ) ) @ ( den @ ( n_pf @ X728 @ X730 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz62k]),c_0_31]),c_0_52]),c_0_29]) ).
thf(c_0_58,plain,
! [X6: $i,X5: $i,X4: $i,X1: $i] :
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X5 @ X1 ) ) @ ( den @ ( n_pf @ X6 @ X4 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X6 @ X4 ) ) @ ( den @ ( n_pf @ X5 @ X1 ) ) ) ) )
| ~ ( in @ X6 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_59,negated_conjecture,
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
| ( 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_35]) ).
thf(c_0_60,negated_conjecture,
~ ( e_is @ nat @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
thf(c_0_61,plain,
! [X1224: $i,X1225: $i,X1226: $i,X1227: $i] :
( ~ ( in @ X1224 @ frac )
| ~ ( in @ X1225 @ frac )
| ~ ( in @ X1226 @ frac )
| ~ ( in @ X1227 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1224 ) @ ( den @ X1225 ) ) @ ( n_ts @ ( num @ X1225 ) @ ( den @ X1224 ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X1227 ) @ ( den @ X1226 ) ) @ ( n_ts @ ( num @ X1226 ) @ ( den @ X1227 ) ) ) )
| ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1227 @ X1225 ) ) @ ( den @ ( n_pf @ X1226 @ X1224 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1226 @ X1224 ) ) @ ( den @ ( n_pf @ X1227 @ X1225 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
thf(c_0_62,plain,
! [X642: $i] :
( ( in @ X642 @ frac )
=> ! [X641: $i] :
( ( in @ X641 @ frac )
=> ( ( e_is @ nat @ ( n_ts @ ( num @ X642 ) @ ( den @ X641 ) ) @ ( n_ts @ ( num @ X641 ) @ ( den @ X642 ) ) )
=> ( e_is @ nat @ ( n_ts @ ( num @ X641 ) @ ( den @ X642 ) ) @ ( n_ts @ ( num @ X642 ) @ ( den @ X641 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz38]),c_0_31]),c_0_29]) ).
thf(c_0_63,negated_conjecture,
( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_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_50,c_0_58]),c_0_48]),c_0_49]),c_0_46]),c_0_47])]) ).
thf(c_0_64,negated_conjecture,
n_some @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
inference(sr,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_65,plain,
! [X1: $i,X4: $i,X5: $i,X6: $i] :
( ( n_some @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X6 @ X4 ) ) @ ( den @ ( n_pf @ X5 @ X1 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X5 @ X1 ) ) @ ( den @ ( n_pf @ X6 @ X4 ) ) ) ) )
| ~ ( 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 ) ) )
| ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ X6 ) @ ( den @ X5 ) ) @ ( n_ts @ ( num @ X5 ) @ ( den @ X6 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_66,plain,
! [X1141: $i,X1142: $i] :
( ~ ( in @ X1141 @ frac )
| ~ ( in @ X1142 @ frac )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ X1141 ) @ ( den @ X1142 ) ) @ ( n_ts @ ( num @ X1142 ) @ ( den @ X1141 ) ) )
| ( e_is @ nat @ ( n_ts @ ( num @ X1142 ) @ ( den @ X1141 ) ) @ ( n_ts @ ( num @ X1141 ) @ ( den @ X1142 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
thf(c_0_67,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)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
thf(c_0_68,negated_conjecture,
( ~ ( n_some @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
| ~ ( e_is @ nat @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_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_50,c_0_65]),c_0_49]),c_0_48]),c_0_47]),c_0_46])]) ).
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_66]) ).
thf(c_0_70,negated_conjecture,
e_is @ nat @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ),
inference(sr,[status(thm)],[c_0_55,c_0_67]) ).
thf(c_0_71,negated_conjecture,
~ ( e_is @ nat @ ( n_ts @ ( num @ esk4_0 ) @ ( den @ esk3_0 ) ) @ ( n_ts @ ( num @ esk3_0 ) @ ( den @ esk4_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_64])]) ).
thf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_46]),c_0_47])]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM765^4 : TPTP v8.2.0. Released v7.1.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 04:11:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 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/benchmark/theBenchmark.p
% 1.18/0.69 # Version: 3.1.0-ho
% 1.18/0.69 # Preprocessing class: HSLMSMSMLLLCHSA.
% 1.18/0.69 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.69 # Starting pre_casc_4 with 1200s (4) cores
% 1.18/0.69 # Starting full_lambda_6 with 300s (1) cores
% 1.18/0.69 # Starting sh10 with 300s (1) cores
% 1.18/0.69 # Starting post_as_ho9 with 300s (1) cores
% 1.18/0.69 # Starting post_as_ho8 with 300s (1) cores
% 1.18/0.69 # post_as_ho8 with pid 2943 completed with status 0
% 1.18/0.69 # Result found by post_as_ho8
% 1.18/0.69 # Preprocessing class: HSLMSMSMLLLCHSA.
% 1.18/0.69 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.69 # Starting pre_casc_4 with 1200s (4) cores
% 1.18/0.69 # Starting full_lambda_6 with 300s (1) cores
% 1.18/0.69 # Starting sh10 with 300s (1) cores
% 1.18/0.69 # Starting post_as_ho9 with 300s (1) cores
% 1.18/0.69 # Starting post_as_ho8 with 300s (1) cores
% 1.18/0.69 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 1.18/0.69 # Search class: HGHSM-FSLM31-MHSMMFBN
% 1.18/0.69 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 1.18/0.69 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.18/0.69 # Starting new_ho_10_cnf2 with 157s (1) cores
% 1.18/0.69 # new_ho_10_cnf2 with pid 2947 completed with status 0
% 1.18/0.69 # Result found by new_ho_10_cnf2
% 1.18/0.69 # Preprocessing class: HSLMSMSMLLLCHSA.
% 1.18/0.69 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.18/0.69 # Starting pre_casc_4 with 1200s (4) cores
% 1.18/0.69 # Starting full_lambda_6 with 300s (1) cores
% 1.18/0.69 # Starting sh10 with 300s (1) cores
% 1.18/0.69 # Starting post_as_ho9 with 300s (1) cores
% 1.18/0.69 # Starting post_as_ho8 with 300s (1) cores
% 1.18/0.69 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 1.18/0.69 # Search class: HGHSM-FSLM31-MHSMMFBN
% 1.18/0.69 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 1.18/0.69 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.18/0.69 # Starting new_ho_10_cnf2 with 157s (1) cores
% 1.18/0.69 # Preprocessing time : 0.010 s
% 1.18/0.69 # Presaturation interreduction done
% 1.18/0.69
% 1.18/0.69 # Proof found!
% 1.18/0.69 # SZS status Theorem
% 1.18/0.69 # SZS output start CNFRefutation
% See solution above
% 1.18/0.69 # Parsed axioms : 604
% 1.18/0.69 # Removed by relevancy pruning/SinE : 380
% 1.18/0.69 # Initial clauses : 386
% 1.18/0.69 # Removed in clause preprocessing : 93
% 1.18/0.69 # Initial clauses in saturation : 293
% 1.18/0.69 # Processed clauses : 629
% 1.18/0.69 # ...of these trivial : 5
% 1.18/0.69 # ...subsumed : 155
% 1.18/0.69 # ...remaining for further processing : 469
% 1.18/0.69 # Other redundant clauses eliminated : 2
% 1.18/0.69 # Clauses deleted for lack of memory : 0
% 1.18/0.69 # Backward-subsumed : 9
% 1.18/0.69 # Backward-rewritten : 11
% 1.18/0.69 # Generated clauses : 1617
% 1.18/0.69 # ...of the previous two non-redundant : 1483
% 1.18/0.69 # ...aggressively subsumed : 0
% 1.18/0.69 # Contextual simplify-reflections : 11
% 1.18/0.69 # Paramodulations : 1592
% 1.18/0.69 # Factorizations : 0
% 1.18/0.69 # NegExts : 0
% 1.18/0.69 # Equation resolutions : 4
% 1.18/0.69 # Disequality decompositions : 0
% 1.18/0.69 # Total rewrite steps : 691
% 1.18/0.69 # ...of those cached : 605
% 1.18/0.69 # Propositional unsat checks : 0
% 1.18/0.69 # Propositional check models : 0
% 1.18/0.69 # Propositional check unsatisfiable : 0
% 1.18/0.69 # Propositional clauses : 0
% 1.18/0.69 # Propositional clauses after purity: 0
% 1.18/0.69 # Propositional unsat core size : 0
% 1.18/0.69 # Propositional preprocessing time : 0.000
% 1.18/0.69 # Propositional encoding time : 0.000
% 1.18/0.69 # Propositional solver time : 0.000
% 1.18/0.69 # Success case prop preproc time : 0.000
% 1.18/0.69 # Success case prop encoding time : 0.000
% 1.18/0.69 # Success case prop solver time : 0.000
% 1.18/0.69 # Current number of processed clauses : 259
% 1.18/0.69 # Positive orientable unit clauses : 71
% 1.18/0.69 # Positive unorientable unit clauses: 0
% 1.18/0.69 # Negative unit clauses : 10
% 1.18/0.69 # Non-unit-clauses : 178
% 1.18/0.69 # Current number of unprocessed clauses: 1324
% 1.18/0.69 # ...number of literals in the above : 8132
% 1.18/0.69 # Current number of archived formulas : 0
% 1.18/0.69 # Current number of archived clauses : 208
% 1.18/0.69 # Clause-clause subsumption calls (NU) : 36355
% 1.18/0.69 # Rec. Clause-clause subsumption calls : 5820
% 1.18/0.69 # Non-unit clause-clause subsumptions : 161
% 1.18/0.69 # Unit Clause-clause subsumption calls : 389
% 1.18/0.69 # Rewrite failures with RHS unbound : 0
% 1.18/0.69 # BW rewrite match attempts : 77
% 1.18/0.69 # BW rewrite match successes : 7
% 1.18/0.69 # Condensation attempts : 629
% 1.18/0.69 # Condensation successes : 0
% 1.18/0.69 # Termbank termtop insertions : 186877
% 1.18/0.69 # Search garbage collected termcells : 36104
% 1.18/0.69
% 1.18/0.69 # -------------------------------------------------
% 1.18/0.69 # User time : 0.169 s
% 1.18/0.69 # System time : 0.012 s
% 1.18/0.69 # Total time : 0.181 s
% 1.18/0.69 # Maximum resident set size: 7976 pages
% 1.18/0.69
% 1.18/0.69 # -------------------------------------------------
% 1.18/0.69 # User time : 0.187 s
% 1.18/0.69 # System time : 0.015 s
% 1.18/0.69 # Total time : 0.203 s
% 1.18/0.69 # Maximum resident set size: 2860 pages
% 1.18/0.69 % E---3.1 exiting
% 1.18/0.69 % E exiting
%------------------------------------------------------------------------------