TSTP Solution File: NUM783^4 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM783^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 01:17:14 EDT 2024
% Result : Theorem 1.80s 0.99s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 62
% Syntax : Number of formulae : 118 ( 67 unt; 36 typ; 0 def)
% Number of atoms : 697 ( 128 equ; 0 cnn)
% Maximal formula atoms : 152 ( 8 avg)
% Number of connectives : 1724 ( 273 ~; 69 |; 13 &;1045 @)
% ( 0 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 7 con; 0-3 aty)
% Number of variables : 271 ( 256 ^ 15 !; 0 ?; 271 :)
% 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_65,type,
l_ec: $o > $o > $o ).
thf(decl_66,type,
d_and: $o > $o > $o ).
thf(decl_67,type,
l_or: $o > $o > $o ).
thf(decl_72,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_73,type,
or3: $o > $o > $o > $o ).
thf(decl_74,type,
and3: $o > $o > $o > $o ).
thf(decl_75,type,
ec3: $o > $o > $o > $o ).
thf(decl_76,type,
orec3: $o > $o > $o > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_102,type,
esti: $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_142,type,
n_pl: $i > $i > $i ).
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_194,type,
moref: $i > $i > $o ).
thf(decl_195,type,
lessf: $i > $i > $o ).
thf(decl_203,type,
inf: $i > $i > $o ).
thf(decl_204,type,
rat: $i ).
thf(decl_205,type,
rt_is: $i > $i > $o ).
thf(decl_212,type,
class: $i > $i ).
thf(decl_215,type,
rt_more: $i > $i > $o ).
thf(decl_217,type,
rt_less: $i > $i > $o ).
thf(decl_219,type,
esk1_0: $i ).
thf(decl_220,type,
esk2_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X79: $o,X80: $o] : ( imp @ X79 @ ( d_not @ X80 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_l_ec) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^1.ax',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X81: $o,X82: $o] : ( d_not @ ( l_ec @ X81 @ X82 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_d_and) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^1.ax',def_d_29_ii) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^1.ax',def_iii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
thf(def_and3,axiom,
( and3
= ( ^ [X92: $o,X93: $o,X94: $o] : ( d_and @ X92 @ ( d_and @ X93 @ X94 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_and3) ).
thf(def_esti,axiom,
( esti
= ( ^ [X1: $i] : in ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_esti) ).
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/benchmark/Axioms/NUM007^1.ax',def_moref) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
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/benchmark/Axioms/NUM007^1.ax',def_lessf) ).
thf(def_or3,axiom,
( or3
= ( ^ [X89: $o,X90: $o,X91: $o] : ( l_or @ X89 @ ( l_or @ X90 @ X91 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_or3) ).
thf(def_ec3,axiom,
( ec3
= ( ^ [X95: $o,X96: $o,X97: $o] : ( and3 @ ( l_ec @ X95 @ X96 ) @ ( l_ec @ X96 @ X97 ) @ ( l_ec @ X97 @ X95 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_ec3) ).
thf(def_rt_more,axiom,
( rt_more
= ( ^ [X1: $i,X650: $i] :
( l_some @ frac
@ ^ [X4: $i] :
( l_some @ frac
@ ^ [X13: $i] : ( and3 @ ( inf @ X4 @ ( class @ X1 ) ) @ ( inf @ X13 @ ( class @ X650 ) ) @ ( moref @ X4 @ X13 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_rt_more) ).
thf(def_inf,axiom,
inf = in,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_inf) ).
thf(def_rt_less,axiom,
( rt_less
= ( ^ [X1: $i,X652: $i] :
( l_some @ frac
@ ^ [X4: $i] :
( l_some @ frac
@ ^ [X13: $i] : ( and3 @ ( inf @ X4 @ ( class @ X1 ) ) @ ( inf @ X13 @ ( class @ X652 ) ) @ ( lessf @ X4 @ X13 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_rt_less) ).
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/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/sandbox/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(def_orec3,axiom,
( orec3
= ( ^ [X98: $o,X99: $o,X100: $o] : ( d_and @ ( or3 @ X98 @ X99 @ X100 ) @ ( ec3 @ X98 @ X99 @ X100 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_orec3) ).
thf(def_rt_is,axiom,
( rt_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_rt_is) ).
thf(satz81a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X656: $i] : ( in @ X656 @ rat )
@ ^ [X657: $i] : ( or3 @ ( rt_is @ X1 @ X657 ) @ ( rt_more @ X1 @ X657 ) @ ( rt_less @ X1 @ X657 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81a) ).
thf(satz81,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ rat )
@ ^ [X1: $i] :
( all_of
@ ^ [X654: $i] : ( in @ X654 @ rat )
@ ^ [X655: $i] : ( orec3 @ ( rt_is @ X1 @ X655 ) @ ( rt_more @ X1 @ X655 ) @ ( rt_less @ X1 @ X655 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81) ).
thf(c_0_26,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_27,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_28,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_29,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_ec]) ).
thf(c_0_30,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_32,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_28]) ).
thf(c_0_33,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_and]) ).
thf(c_0_34,plain,
( l_ec
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> ( Z1
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
thf(c_0_35,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_36,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_37,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_38,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_39,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_and3]) ).
thf(c_0_40,plain,
( d_and
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ( Z1
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_30]),c_0_34]) ).
thf(c_0_41,plain,
( esti
= ( ^ [Z0: $i] : in ) ),
inference(fof_simplification,[status(thm)],[def_esti]) ).
thf(c_0_42,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( 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_43,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35,c_0_36]),def_n_some]) ).
thf(c_0_44,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( 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_45,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_37,c_0_36]),def_n_some]) ).
thf(c_0_46,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_or3]) ).
thf(c_0_47,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_38,c_0_30]),c_0_27]) ).
thf(c_0_48,plain,
( ec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_ec3]) ).
thf(c_0_49,plain,
( and3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_50,plain,
( rt_more
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ frac
@ ^ [Z2: $i] :
( l_some @ frac
@ ^ [Z3: $i] :
( ( ( in @ Z2 @ ( class @ Z0 ) )
=> ( ( ( ( in @ Z3 @ ( class @ Z1 ) )
=> ( ( l_some @ nat
@ ^ [Z4: $i] :
( ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) )
= ( n_pl @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) @ Z4 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_more]) ).
thf(c_0_51,axiom,
inf = in,
inference(apply_def,[status(thm)],[def_inf,c_0_41]) ).
thf(c_0_52,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_53,plain,
( rt_less
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ frac
@ ^ [Z2: $i] :
( l_some @ frac
@ ^ [Z3: $i] :
( ( ( in @ Z2 @ ( class @ Z0 ) )
=> ( ( ( ( in @ Z3 @ ( class @ Z1 ) )
=> ( ( l_some @ nat
@ ^ [Z4: $i] :
( ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) )
= ( n_pl @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ Z4 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_rt_less]) ).
thf(c_0_54,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_55,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_56,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_57,plain,
( orec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) )
=> ( ( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_orec3]) ).
thf(c_0_58,plain,
( or3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_59,plain,
( ec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_48,c_0_49]),c_0_34]) ).
thf(c_0_60,axiom,
( rt_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_rt_is,c_0_28]) ).
thf(c_0_61,plain,
( rt_more
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ frac
@ ^ [Z2: $i] :
( l_some @ frac
@ ^ [Z3: $i] :
( ( ( in @ Z2 @ ( class @ Z0 ) )
=> ( ( ( ( in @ Z3 @ ( class @ Z1 ) )
=> ( ( l_some @ nat
@ ^ [Z4: $i] :
( ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) )
= ( n_pl @ ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) ) @ Z4 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_49]) ).
thf(c_0_62,plain,
( rt_less
= ( ^ [Z0: $i,Z1: $i] :
( l_some @ frac
@ ^ [Z2: $i] :
( l_some @ frac
@ ^ [Z3: $i] :
( ( ( in @ Z2 @ ( class @ Z0 ) )
=> ( ( ( ( in @ Z3 @ ( class @ Z1 ) )
=> ( ( l_some @ nat
@ ^ [Z4: $i] :
( ( n_ts @ ( num @ Z3 ) @ ( den @ Z2 ) )
= ( n_pl @ ( n_ts @ ( num @ Z2 ) @ ( den @ Z3 ) ) @ Z4 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_53,c_0_51]),c_0_54]),c_0_49]) ).
thf(c_0_63,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_64,plain,
( orec3
= ( ^ [Z0: $o,Z1: $o,Z2: $o] :
( ( ( ( Z0
=> ~ $true )
=> ( ( Z1
=> ~ $true )
=> Z2 ) )
=> ( ( ( ( Z0
=> ( Z1
=> ~ $true ) )
=> ( ( ( ( Z1
=> ( Z2
=> ~ $true ) )
=> ( ( Z2
=> ( Z0
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_40]) ).
thf(c_0_65,negated_conjecture,
~ ! [X779: $i] :
( ( in @ X779 @ rat )
=> ! [X778: $i] :
( ( in @ X778 @ rat )
=> ( ( ( X779 = X778 )
=> ~ $true )
=> ( ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X779 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X778 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
=> ~ $true )
=> ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X779 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X778 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz81a])]),c_0_58]),c_0_60]),c_0_61]),c_0_62]),c_0_63]) ).
thf(c_0_66,plain,
! [X787: $i] :
( ( in @ X787 @ rat )
=> ! [X786: $i] :
( ( in @ X786 @ rat )
=> ( ( ( ( ( X787 = X786 )
=> ~ $true )
=> ( ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X787 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X786 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
=> ~ $true )
=> ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X787 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X786 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ) )
=> ( ( ( ( ( X787 = X786 )
=> ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X787 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X786 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
=> ~ $true ) )
=> ( ( ( ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X787 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X786 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
=> ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X787 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X786 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
=> ~ $true ) )
=> ( ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X787 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X786 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
=> ( ( X787 = X786 )
=> ~ $true ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz81]),c_0_60]),c_0_61]),c_0_62]),c_0_64]),c_0_63]) ).
thf(c_0_67,negated_conjecture,
( ( in @ esk1_0 @ rat )
& ( in @ esk2_0 @ rat )
& ( ( esk1_0 != esk2_0 )
| ~ $true )
& ( ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ~ $true )
& ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
thf(c_0_68,plain,
! [X1459: $i,X1460: $i] :
( ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( X1459 = X1460 )
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( $true
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( X1459 = X1460 )
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( $true
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( ( X1459 != X1460 )
| ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1459 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X1460 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( X1459 != X1460 )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( $true
| ~ $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) )
& ( $true
| ~ $true
| ~ ( in @ X1460 @ rat )
| ~ ( in @ X1459 @ rat ) ) ),
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_66])])])])]) ).
thf(c_0_69,negated_conjecture,
( ~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_70,plain,
! [X4: $i,X1: $i] :
( ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X4 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X4 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( X1 = X4 )
| ~ $true
| ~ ( in @ X4 @ rat )
| ~ ( in @ X1 @ rat ) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_71,negated_conjecture,
~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(cn,[status(thm)],[c_0_69]) ).
thf(c_0_72,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X4 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ X1 ) )
=> ( ( ( ( in @ Z1 @ ( class @ X4 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) )
| ~ ( in @ X4 @ rat )
| ~ ( in @ X1 @ rat ) ),
inference(cn,[status(thm)],[c_0_70]) ).
thf(c_0_73,negated_conjecture,
( ( esk1_0 != esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_74,negated_conjecture,
~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
( ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ( ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) )
=> ~ $true ) )
=> ~ $true )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_75,negated_conjecture,
~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
~ ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ~ ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_71]) ).
thf(c_0_76,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
~ ( ( in @ Z0 @ ( class @ X1 ) )
=> ( ( in @ Z1 @ ( class @ X4 ) )
=> ~ ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_pl @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ Z2 ) ) ) ) ) ) )
| ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
~ ( ( in @ Z0 @ ( class @ X1 ) )
=> ( ( in @ Z1 @ ( class @ X4 ) )
=> ~ ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ) ) )
| ~ ( in @ X4 @ rat )
| ~ ( in @ X1 @ rat ) ),
inference(cn,[status(thm)],[c_0_72]) ).
thf(c_0_77,negated_conjecture,
in @ esk2_0 @ rat,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_78,negated_conjecture,
in @ esk1_0 @ rat,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_79,negated_conjecture,
esk2_0 != esk1_0,
inference(cn,[status(thm)],[c_0_73]) ).
thf(c_0_80,negated_conjecture,
~ ( l_some @ frac
@ ^ [Z0: $i] :
( l_some @ frac
@ ^ [Z1: $i] :
~ ( ( in @ Z0 @ ( class @ esk1_0 ) )
=> ( ( in @ Z1 @ ( class @ esk2_0 ) )
=> ~ ( l_some @ nat
@ ^ [Z2: $i] :
( ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) )
= ( n_pl @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ Z2 ) ) ) ) ) ) ),
inference(cn,[status(thm)],[c_0_74]) ).
thf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]),c_0_79]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM783^4 : TPTP v8.2.0. Released v7.1.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 06:23:37 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running higher-order theorem proving
% 0.19/0.46 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/benchmark/theBenchmark.p
% 1.80/0.99 # Version: 3.1.0-ho
% 1.80/0.99 # Preprocessing class: HSLMSMSMLLLCHSA.
% 1.80/0.99 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.80/0.99 # Starting pre_casc_4 with 1200s (4) cores
% 1.80/0.99 # Starting full_lambda_6 with 300s (1) cores
% 1.80/0.99 # Starting sh10 with 300s (1) cores
% 1.80/0.99 # Starting post_as_ho9 with 300s (1) cores
% 1.80/0.99 # Starting post_as_ho8 with 300s (1) cores
% 1.80/0.99 # full_lambda_6 with pid 7481 completed with status 0
% 1.80/0.99 # Result found by full_lambda_6
% 1.80/0.99 # Preprocessing class: HSLMSMSMLLLCHSA.
% 1.80/0.99 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.80/0.99 # Starting pre_casc_4 with 1200s (4) cores
% 1.80/0.99 # Starting full_lambda_6 with 300s (1) cores
% 1.80/0.99 # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 1.80/0.99 # Search class: HGHSS-FSLM32-DHSMMSBN
% 1.80/0.99 # partial match(2): HGHSM-FSLM32-MHSMMSBN
% 1.80/0.99 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 1.80/0.99 # Starting full_lambda_5 with 25s (1) cores
% 1.80/0.99 # full_lambda_5 with pid 7485 completed with status 0
% 1.80/0.99 # Result found by full_lambda_5
% 1.80/0.99 # Preprocessing class: HSLMSMSMLLLCHSA.
% 1.80/0.99 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.80/0.99 # Starting pre_casc_4 with 1200s (4) cores
% 1.80/0.99 # Starting full_lambda_6 with 300s (1) cores
% 1.80/0.99 # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 1.80/0.99 # Search class: HGHSS-FSLM32-DHSMMSBN
% 1.80/0.99 # partial match(2): HGHSM-FSLM32-MHSMMSBN
% 1.80/0.99 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 1.80/0.99 # Starting full_lambda_5 with 25s (1) cores
% 1.80/0.99 # Preprocessing time : 0.019 s
% 1.80/0.99 # Presaturation interreduction done
% 1.80/0.99
% 1.80/0.99 # Proof found!
% 1.80/0.99 # SZS status Theorem
% 1.80/0.99 # SZS output start CNFRefutation
% See solution above
% 1.80/0.99 # Parsed axioms : 685
% 1.80/0.99 # Removed by relevancy pruning/SinE : 342
% 1.80/0.99 # Initial clauses : 622
% 1.80/0.99 # Removed in clause preprocessing : 210
% 1.80/0.99 # Initial clauses in saturation : 412
% 1.80/0.99 # Processed clauses : 833
% 1.80/0.99 # ...of these trivial : 0
% 1.80/0.99 # ...subsumed : 290
% 1.80/0.99 # ...remaining for further processing : 543
% 1.80/0.99 # Other redundant clauses eliminated : 52
% 1.80/0.99 # Clauses deleted for lack of memory : 0
% 1.80/0.99 # Backward-subsumed : 0
% 1.80/0.99 # Backward-rewritten : 1
% 1.80/0.99 # Generated clauses : 5140
% 1.80/0.99 # ...of the previous two non-redundant : 5080
% 1.80/0.99 # ...aggressively subsumed : 0
% 1.80/0.99 # Contextual simplify-reflections : 0
% 1.80/0.99 # Paramodulations : 1965
% 1.80/0.99 # Factorizations : 0
% 1.80/0.99 # NegExts : 0
% 1.80/0.99 # Equation resolutions : 72
% 1.80/0.99 # Disequality decompositions : 0
% 1.80/0.99 # Total rewrite steps : 313
% 1.80/0.99 # ...of those cached : 301
% 1.80/0.99 # Propositional unsat checks : 0
% 1.80/0.99 # Propositional check models : 0
% 1.80/0.99 # Propositional check unsatisfiable : 0
% 1.80/0.99 # Propositional clauses : 0
% 1.80/0.99 # Propositional clauses after purity: 0
% 1.80/0.99 # Propositional unsat core size : 0
% 1.80/0.99 # Propositional preprocessing time : 0.000
% 1.80/0.99 # Propositional encoding time : 0.000
% 1.80/0.99 # Propositional solver time : 0.000
% 1.80/0.99 # Success case prop preproc time : 0.000
% 1.80/0.99 # Success case prop encoding time : 0.000
% 1.80/0.99 # Success case prop solver time : 0.000
% 1.80/0.99 # Current number of processed clauses : 280
% 1.80/0.99 # Positive orientable unit clauses : 25
% 1.80/0.99 # Positive unorientable unit clauses: 5
% 1.80/0.99 # Negative unit clauses : 45
% 1.80/0.99 # Non-unit-clauses : 205
% 1.80/0.99 # Current number of unprocessed clauses: 4756
% 1.80/0.99 # ...number of literals in the above : 38325
% 1.80/0.99 # Current number of archived formulas : 0
% 1.80/0.99 # Current number of archived clauses : 219
% 1.80/0.99 # Clause-clause subsumption calls (NU) : 52657
% 1.80/0.99 # Rec. Clause-clause subsumption calls : 4592
% 1.80/0.99 # Non-unit clause-clause subsumptions : 230
% 1.80/0.99 # Unit Clause-clause subsumption calls : 1009
% 1.80/0.99 # Rewrite failures with RHS unbound : 56
% 1.80/0.99 # BW rewrite match attempts : 28
% 1.80/0.99 # BW rewrite match successes : 5
% 1.80/0.99 # Condensation attempts : 0
% 1.80/0.99 # Condensation successes : 0
% 1.80/0.99 # Termbank termtop insertions : 385778
% 1.80/0.99 # Search garbage collected termcells : 57755
% 1.80/0.99
% 1.80/0.99 # -------------------------------------------------
% 1.80/0.99 # User time : 0.440 s
% 1.80/0.99 # System time : 0.028 s
% 1.80/0.99 # Total time : 0.467 s
% 1.80/0.99 # Maximum resident set size: 11272 pages
% 1.80/0.99
% 1.80/0.99 # -------------------------------------------------
% 1.80/0.99 # User time : 0.460 s
% 1.80/0.99 # System time : 0.033 s
% 1.80/0.99 # Total time : 0.493 s
% 1.80/0.99 # Maximum resident set size: 3052 pages
% 1.80/0.99 % E---3.1 exiting
% 1.80/0.99 % E exiting
%------------------------------------------------------------------------------