TSTP Solution File: NUM659^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM659^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 : Sat May 4 08:56:03 EDT 2024
% Result : Theorem 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 81 ( 40 unt; 21 typ; 0 def)
% Number of atoms : 333 ( 94 equ; 0 cnn)
% Maximal formula atoms : 63 ( 5 avg)
% Number of connectives : 737 ( 112 ~; 102 |; 14 &; 452 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 150 ( 106 ^ 44 !; 0 ?; 150 :)
% 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_71,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(decl_72,type,
l_some: $i > ( $i > $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_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_152,type,
lessis: $i > $i > $o ).
thf(decl_153,type,
esk1_0: $i ).
thf(decl_154,type,
esk2_0: $i ).
thf(decl_159,type,
esk7_2: $i > $i > $i ).
thf(decl_160,type,
esk8_2: $i > $i > $i ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_is_of) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_imp) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_e_is) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_l_some) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_l_or) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_iii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X307: $i] :
( ( in @ X307 @ nat )
=> ( non @ nat @ Z0 @ X307 ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_n_some) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_lessis) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',def_d_29_ii) ).
thf(satz10e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X239: $i] : ( in @ X239 @ nat )
@ ^ [X240: $i] :
( ( d_not @ ( d_29_ii @ X1 @ X240 ) )
=> ( lessis @ X1 @ X240 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',satz10e) ).
thf(satz10k,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X249: $i] : ( in @ X249 @ nat )
@ ^ [X250: $i] :
( ( d_not @ ( lessis @ X1 @ X250 ) )
=> ( d_29_ii @ X1 @ X250 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p',satz10k) ).
thf(c_0_15,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_16,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_17,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_18,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_19,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_20,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X306: $i] :
( ( in @ X306 @ Z0 )
=> ( non @ Z0 @ Z1 @ X306 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_21,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_22,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_24,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_19]) ).
thf(c_0_25,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X306: $i] :
( ( in @ X306 @ Z0 )
=> ( non @ Z0 @ Z1 @ X306 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_26,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_27,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X309: $i] :
( ( in @ X309 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X309 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_28,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_29,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X307: $i] :
( ( in @ X307 @ nat )
=> ( non @ nat @ Z0 @ X307 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_25]) ).
thf(c_0_30,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X311: $i] :
( ( in @ X311 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X311 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_31,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26,c_0_18]),c_0_22]) ).
thf(c_0_32,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X309: $i] :
( ( in @ X309 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X309 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_33,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X308: $i] :
( ( in @ X308 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X308 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_34,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X311: $i] :
( ( in @ X311 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X311 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_24]),c_0_31]),c_0_32]) ).
thf(c_0_35,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X308: $i] :
( ( in @ X308 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X308 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_28]),c_0_29]) ).
thf(c_0_36,plain,
! [X339: $i] :
( ( in @ X339 @ nat )
=> ! [X338: $i] :
( ( in @ X338 @ nat )
=> ( ( ( ! [X336: $i] :
( ( in @ X336 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X339
= ( n_pl @ X338 @ Z0 ) )
@ X336 ) )
=> ~ $true )
=> ~ $true )
=> ( ( ( ! [X337: $i] :
( ( in @ X337 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X338
= ( n_pl @ X339 @ Z0 ) )
@ X337 ) )
=> ~ $true )
=> ~ $true )
=> ( X339 = X338 ) ) ) ) ),
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)],[satz10e]),c_0_21]),c_0_34]),c_0_22]),c_0_35]) ).
thf(c_0_37,negated_conjecture,
~ ! [X315: $i] :
( ( in @ X315 @ nat )
=> ! [X314: $i] :
( ( in @ X314 @ nat )
=> ( ( ( ( ( ! [X312: $i] :
( ( in @ X312 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X314
= ( n_pl @ X315 @ Z0 ) )
@ X312 ) )
=> ~ $true )
=> ~ $true )
=> ( X315 = X314 ) )
=> ~ $true )
=> ( ! [X313: $i] :
( ( in @ X313 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X315
= ( n_pl @ X314 @ Z0 ) )
@ X313 ) )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz10k])]),c_0_21]),c_0_34]),c_0_22]),c_0_35]) ).
thf(c_0_38,plain,
! [X458: $i,X459: $i] :
( ( ( in @ ( esk8_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ( X458 = X459 )
| ( in @ ( esk7_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X459
= ( n_pl @ X458 @ Z0 ) )
@ ( esk8_2 @ X458 @ X459 ) )
| ~ $true
| ( X458 = X459 )
| ( in @ ( esk7_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( $true
| ( X458 = X459 )
| ( in @ ( esk7_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ( in @ ( esk8_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ( X458 = X459 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X458
= ( n_pl @ X459 @ Z0 ) )
@ ( esk7_2 @ X458 @ X459 ) )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X459
= ( n_pl @ X458 @ Z0 ) )
@ ( esk8_2 @ X458 @ X459 ) )
| ~ $true
| ( X458 = X459 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X458
= ( n_pl @ X459 @ Z0 ) )
@ ( esk7_2 @ X458 @ X459 ) )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( $true
| ( X458 = X459 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X458
= ( n_pl @ X459 @ Z0 ) )
@ ( esk7_2 @ X458 @ X459 ) )
| ~ $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ( in @ ( esk8_2 @ X458 @ X459 ) @ nat )
| ~ $true
| ( X458 = X459 )
| $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X459
= ( n_pl @ X458 @ Z0 ) )
@ ( esk8_2 @ X458 @ X459 ) )
| ~ $true
| ( X458 = X459 )
| $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) )
& ( $true
| ( X458 = X459 )
| $true
| ~ ( in @ X459 @ nat )
| ~ ( in @ X458 @ nat ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])])])]) ).
thf(c_0_39,negated_conjecture,
! [X436: $i,X437: $i] :
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ~ ( in @ X436 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X436 )
| ~ $true
| ~ $true )
& ( $true
| ~ $true
| ~ $true )
& ( ( esk1_0 != esk2_0 )
| ~ $true )
& ( ~ ( in @ X437 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X437 ) )
& $true ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])])]) ).
thf(c_0_40,plain,
! [X1: $i,X4: $i] :
( ( X4 = X1 )
| ( in @ ( esk7_2 @ X4 @ X1 ) @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) )
| ~ $true
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_41,negated_conjecture,
( ( esk1_0 != esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_42,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( in @ ( esk7_2 @ X4 @ X1 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_40]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_44,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_45,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_46,negated_conjecture,
esk2_0 != esk1_0,
inference(cn,[status(thm)],[c_0_41]) ).
thf(c_0_47,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ( in @ ( esk7_2 @ X1 @ X4 ) @ nat )
| ~ $true
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_48,plain,
! [X1: $i,X4: $i] :
( ( X4 = X1 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X4
= ( n_pl @ X1 @ Z0 ) )
@ ( esk7_2 @ X4 @ X1 ) )
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_50,negated_conjecture,
( ( in @ ( esk7_2 @ esk2_0 @ esk1_0 ) @ nat )
| ~ ( in @ ( esk8_2 @ esk2_0 @ esk1_0 ) @ nat ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).
thf(c_0_51,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ( in @ ( esk7_2 @ X1 @ X4 ) @ nat )
| ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_47]) ).
thf(c_0_52,plain,
! [X4: $i,X1: $i] :
( ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ( X1 = X4 )
| ~ $true
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk7_2 @ X1 @ X4 ) )
| ~ $true
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_53,plain,
! [X4: $i,X1: $i] :
( ( X1 = X4 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X4
= ( n_pl @ X1 @ Z0 ) )
@ ( esk7_2 @ X4 @ X1 ) )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk8_2 @ X4 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_49]) ).
thf(c_0_55,negated_conjecture,
in @ ( esk7_2 @ esk2_0 @ esk1_0 ) @ nat,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_45]),c_0_44])]),c_0_46]) ).
thf(c_0_56,plain,
! [X1: $i,X4: $i] :
( ( X1 = X4 )
| ( in @ ( esk8_2 @ X1 @ X4 ) @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk7_2 @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_52]) ).
thf(c_0_57,negated_conjecture,
~ ( non @ nat
@ ^ [Z0: $i] :
( esk1_0
= ( n_pl @ esk2_0 @ Z0 ) )
@ ( esk8_2 @ esk2_0 @ esk1_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_44]),c_0_45]),c_0_55])]),c_0_46]) ).
thf(c_0_58,negated_conjecture,
in @ ( esk8_2 @ esk2_0 @ esk1_0 ) @ nat,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_54]),c_0_45]),c_0_44])]),c_0_46]),c_0_55])]) ).
thf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUM659^4 : TPTP v8.1.2. Released v7.1.0.
% 0.02/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n017.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 : Fri May 3 08:49:51 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.46 Running higher-order theorem proving
% 0.18/0.46 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/tmp/tmp.jRMG5ZyTbM/E---3.1_16006.p
% 0.18/0.53 # Version: 3.1.0-ho
% 0.18/0.53 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.18/0.53 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting lpo1_fix with 900s (3) cores
% 0.18/0.53 # Starting full_lambda_9 with 300s (1) cores
% 0.18/0.53 # Starting almost_fo_4 with 300s (1) cores
% 0.18/0.53 # Starting new_ho_9 with 300s (1) cores
% 0.18/0.53 # Starting pre_casc_4 with 300s (1) cores
% 0.18/0.53 # Starting ho_unfolding_6 with 300s (1) cores
% 0.18/0.53 # pre_casc_4 with pid 16088 completed with status 0
% 0.18/0.53 # Result found by pre_casc_4
% 0.18/0.53 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.18/0.53 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting lpo1_fix with 900s (3) cores
% 0.18/0.53 # Starting full_lambda_9 with 300s (1) cores
% 0.18/0.53 # Starting almost_fo_4 with 300s (1) cores
% 0.18/0.53 # Starting new_ho_9 with 300s (1) cores
% 0.18/0.53 # Starting pre_casc_4 with 300s (1) cores
% 0.18/0.53 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.18/0.53 # Search class: HGHSM-FSLM31-DHSMMSBN
% 0.18/0.53 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.18/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.18/0.53 # new_ho_10_cnf2 with pid 16090 completed with status 0
% 0.18/0.53 # Result found by new_ho_10_cnf2
% 0.18/0.53 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.18/0.53 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting lpo1_fix with 900s (3) cores
% 0.18/0.53 # Starting full_lambda_9 with 300s (1) cores
% 0.18/0.53 # Starting almost_fo_4 with 300s (1) cores
% 0.18/0.53 # Starting new_ho_9 with 300s (1) cores
% 0.18/0.53 # Starting pre_casc_4 with 300s (1) cores
% 0.18/0.53 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.18/0.53 # Search class: HGHSM-FSLM31-DHSMMSBN
% 0.18/0.53 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.18/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.18/0.53 # Preprocessing time : 0.003 s
% 0.18/0.53 # Presaturation interreduction done
% 0.18/0.53
% 0.18/0.53 # Proof found!
% 0.18/0.53 # SZS status Theorem
% 0.18/0.53 # SZS output start CNFRefutation
% See solution above
% 0.18/0.53 # Parsed axioms : 358
% 0.18/0.53 # Removed by relevancy pruning/SinE : 273
% 0.18/0.53 # Initial clauses : 203
% 0.18/0.53 # Removed in clause preprocessing : 73
% 0.18/0.53 # Initial clauses in saturation : 130
% 0.18/0.53 # Processed clauses : 351
% 0.18/0.53 # ...of these trivial : 5
% 0.18/0.53 # ...subsumed : 36
% 0.18/0.53 # ...remaining for further processing : 310
% 0.18/0.53 # Other redundant clauses eliminated : 15
% 0.18/0.53 # Clauses deleted for lack of memory : 0
% 0.18/0.53 # Backward-subsumed : 0
% 0.18/0.53 # Backward-rewritten : 11
% 0.18/0.53 # Generated clauses : 641
% 0.18/0.53 # ...of the previous two non-redundant : 609
% 0.18/0.53 # ...aggressively subsumed : 0
% 0.18/0.53 # Contextual simplify-reflections : 0
% 0.18/0.53 # Paramodulations : 618
% 0.18/0.53 # Factorizations : 2
% 0.18/0.53 # NegExts : 0
% 0.18/0.53 # Equation resolutions : 17
% 0.18/0.53 # Disequality decompositions : 0
% 0.18/0.53 # Total rewrite steps : 182
% 0.18/0.53 # ...of those cached : 152
% 0.18/0.53 # Propositional unsat checks : 0
% 0.18/0.53 # Propositional check models : 0
% 0.18/0.53 # Propositional check unsatisfiable : 0
% 0.18/0.53 # Propositional clauses : 0
% 0.18/0.53 # Propositional clauses after purity: 0
% 0.18/0.53 # Propositional unsat core size : 0
% 0.18/0.53 # Propositional preprocessing time : 0.000
% 0.18/0.53 # Propositional encoding time : 0.000
% 0.18/0.53 # Propositional solver time : 0.000
% 0.18/0.53 # Success case prop preproc time : 0.000
% 0.18/0.53 # Success case prop encoding time : 0.000
% 0.18/0.53 # Success case prop solver time : 0.000
% 0.18/0.53 # Current number of processed clauses : 181
% 0.18/0.53 # Positive orientable unit clauses : 43
% 0.18/0.53 # Positive unorientable unit clauses: 0
% 0.18/0.53 # Negative unit clauses : 34
% 0.18/0.53 # Non-unit-clauses : 104
% 0.18/0.53 # Current number of unprocessed clauses: 496
% 0.18/0.53 # ...number of literals in the above : 2416
% 0.18/0.53 # Current number of archived formulas : 0
% 0.18/0.53 # Current number of archived clauses : 124
% 0.18/0.53 # Clause-clause subsumption calls (NU) : 8194
% 0.18/0.53 # Rec. Clause-clause subsumption calls : 1039
% 0.18/0.53 # Non-unit clause-clause subsumptions : 26
% 0.18/0.53 # Unit Clause-clause subsumption calls : 1487
% 0.18/0.53 # Rewrite failures with RHS unbound : 0
% 0.18/0.53 # BW rewrite match attempts : 16
% 0.18/0.53 # BW rewrite match successes : 10
% 0.18/0.53 # Condensation attempts : 351
% 0.18/0.53 # Condensation successes : 0
% 0.18/0.53 # Termbank termtop insertions : 52147
% 0.18/0.53 # Search garbage collected termcells : 10724
% 0.18/0.53
% 0.18/0.53 # -------------------------------------------------
% 0.18/0.53 # User time : 0.044 s
% 0.18/0.53 # System time : 0.005 s
% 0.18/0.53 # Total time : 0.050 s
% 0.18/0.53 # Maximum resident set size: 3684 pages
% 0.18/0.53
% 0.18/0.53 # -------------------------------------------------
% 0.18/0.53 # User time : 0.051 s
% 0.18/0.53 # System time : 0.009 s
% 0.18/0.53 # Total time : 0.060 s
% 0.18/0.53 # Maximum resident set size: 2252 pages
% 0.18/0.53 % E---3.1 exiting
% 0.18/0.53 % E exiting
%------------------------------------------------------------------------------