TSTP Solution File: NUM691^4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM691^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 08:56:18 EDT 2024
% Result : Theorem 4.33s 1.20s
% Output : CNFRefutation 4.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 35
% Syntax : Number of formulae : 82 ( 36 unt; 20 typ; 0 def)
% Number of atoms : 295 ( 50 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 684 ( 70 ~; 53 |; 10 &; 502 @)
% ( 0 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 119 ( 78 ^ 41 !; 0 ?; 119 :)
% 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_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_151,type,
moreis: $i > $i > $o ).
thf(decl_155,type,
esk1_0: $i ).
thf(decl_156,type,
esk2_0: $i ).
thf(decl_157,type,
esk3_0: $i ).
thf(decl_158,type,
esk4_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_imp) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_d_29_ii) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_l_or) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_e_is) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_moreis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_n_is) ).
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.GXOf1OzKnx/E---3.1_19708.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_is_of) ).
thf(satz23,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X319: $i] : ( in @ X319 @ nat )
@ ^ [X320: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( moreis @ X1 @ X320 )
=> ( ( moreis @ X4 @ X13 )
=> ( moreis @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X320 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',satz23) ).
thf(satz22b,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X313: $i] : ( in @ X313 @ nat )
@ ^ [X314: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ nat )
@ ^ [X13: $i] :
( ( d_29_ii @ X1 @ X314 )
=> ( ( moreis @ X4 @ X13 )
=> ( d_29_ii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X314 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',satz22b) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',def_iii) ).
thf(satz19c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X271: $i] : ( in @ X271 @ nat )
@ ^ [X272: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X272 )
=> ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X272 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',satz19c) ).
thf(satz19f,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X277: $i] : ( in @ X277 @ nat )
@ ^ [X278: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ X1 @ X278 )
=> ( iii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X278 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p',satz19f) ).
thf(c_0_15,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_16,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_17,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_18,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_19,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_21,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_22,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_17,def_n_some]) ).
thf(c_0_23,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_16]),c_0_19]) ).
thf(c_0_24,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_20]) ).
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,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]) ).
thf(c_0_28,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_29,negated_conjecture,
~ ! [X391: $i] :
( ( in @ X391 @ nat )
=> ! [X390: $i] :
( ( in @ X390 @ nat )
=> ! [X389: $i] :
( ( in @ X389 @ nat )
=> ! [X388: $i] :
( ( in @ X388 @ nat )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X391 @ X390 ) )
=> ~ $true )
=> ( X391 = X390 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X389 @ X388 ) )
=> ~ $true )
=> ( X389 = X388 ) )
=> ( ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X391 @ X389 ) @ ( n_pl @ X390 @ X388 ) ) )
=> ~ $true )
=> ( ( n_pl @ X391 @ X389 )
= ( n_pl @ X390 @ X388 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz23])]),c_0_27]),c_0_28]) ).
thf(c_0_30,plain,
! [X514: $i] :
( ( in @ X514 @ nat )
=> ! [X513: $i] :
( ( in @ X513 @ nat )
=> ! [X512: $i] :
( ( in @ X512 @ nat )
=> ! [X511: $i] :
( ( in @ X511 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X514 @ X513 ) )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X512 @ X511 ) )
=> ~ $true )
=> ( X512 = X511 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X514 @ X512 ) @ ( n_pl @ X513 @ X511 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz22b]),c_0_27]),c_0_22]),c_0_28]) ).
thf(c_0_31,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( in @ esk4_0 @ nat )
& ( ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ( esk1_0 = esk2_0 ) )
& ( $true
| ( esk1_0 = esk2_0 ) )
& ( ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) )
| ( esk3_0 = esk4_0 ) )
& ( $true
| ( esk3_0 = esk4_0 ) )
& ( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk4_0 ) ) )
| ~ $true )
& ( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_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_29])])])])]) ).
thf(c_0_32,plain,
! [X710: $i,X711: $i,X712: $i,X713: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X712 @ X713 ) )
| ~ $true
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X710 @ X712 ) @ ( n_pl @ X711 @ X713 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X710 @ X711 ) )
| ~ ( in @ X713 @ nat )
| ~ ( in @ X712 @ nat )
| ~ ( in @ X711 @ nat )
| ~ ( in @ X710 @ nat ) )
& ( ( X712 != X713 )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X710 @ X712 ) @ ( n_pl @ X711 @ X713 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X710 @ X711 ) )
| ~ ( in @ X713 @ nat )
| ~ ( in @ X712 @ nat )
| ~ ( in @ X711 @ nat )
| ~ ( in @ X710 @ nat ) ) ),
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_30])])])])]) ).
thf(c_0_33,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk4_0 ) ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_34,plain,
! [X1: $i,X4: $i,X6: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_35,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_36,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk4_0 ) ) ),
inference(cn,[status(thm)],[c_0_33]) ).
thf(c_0_37,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X1 ) @ ( n_pl @ X6 @ X4 ) ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X5 @ X6 ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_34]) ).
thf(c_0_38,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_39,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,negated_conjecture,
in @ esk4_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_41,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_42,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_35,def_n_some]) ).
thf(c_0_43,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ~ ( l_some @ nat @ ( diffprop @ esk3_0 @ 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_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]) ).
thf(c_0_44,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) )
| ( esk3_0 = esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_45,plain,
! [X431: $i] :
( ( in @ X431 @ nat )
=> ! [X430: $i] :
( ( in @ X430 @ nat )
=> ! [X429: $i] :
( ( in @ X429 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X430 @ X431 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X430 @ X429 ) @ ( n_pl @ X431 @ X429 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19c]),c_0_42]),c_0_28]) ).
thf(c_0_46,negated_conjecture,
( ( esk4_0 = esk3_0 )
| ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_47,plain,
! [X628: $i,X629: $i,X630: $i] :
( ~ ( in @ X628 @ nat )
| ~ ( in @ X629 @ nat )
| ~ ( in @ X630 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X629 @ X628 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X629 @ X630 ) @ ( n_pl @ X628 @ X630 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])]) ).
thf(c_0_48,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk2_0 @ esk3_0 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_46]) ).
thf(c_0_49,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X4 @ X5 ) @ ( n_pl @ X1 @ X5 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_50,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ( esk1_0 = esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_51,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_41]),c_0_39]),c_0_38])]) ).
thf(c_0_52,plain,
! [X440: $i] :
( ( in @ X440 @ nat )
=> ! [X439: $i] :
( ( in @ X439 @ nat )
=> ! [X438: $i] :
( ( in @ X438 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X439 @ X440 ) )
=> ( l_some @ nat @ ( diffprop @ ( n_pl @ X438 @ X439 ) @ ( n_pl @ X438 @ X440 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz19f]),c_0_42]),c_0_28]) ).
thf(c_0_53,negated_conjecture,
esk2_0 = esk1_0,
inference(sr,[status(thm)],[c_0_50,c_0_51]) ).
thf(c_0_54,plain,
! [X637: $i,X638: $i,X639: $i] :
( ~ ( in @ X637 @ nat )
| ~ ( in @ X638 @ nat )
| ~ ( in @ X639 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X638 @ X637 ) )
| ( l_some @ nat @ ( diffprop @ ( n_pl @ X639 @ X638 ) @ ( n_pl @ X639 @ X637 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
thf(c_0_55,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_0 ) @ ( n_pl @ esk1_0 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_53]) ).
thf(c_0_56,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_pl @ X5 @ X4 ) @ ( n_pl @ X5 @ X1 ) ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
thf(c_0_57,negated_conjecture,
( ( n_pl @ esk1_0 @ esk3_0 )
!= ( n_pl @ esk2_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_58,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk3_0 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_39]),c_0_41]),c_0_40])]) ).
thf(c_0_59,negated_conjecture,
( ( n_pl @ esk1_0 @ esk4_0 )
!= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_57,c_0_53]) ).
thf(c_0_60,negated_conjecture,
esk4_0 = esk3_0,
inference(sr,[status(thm)],[c_0_44,c_0_58]) ).
thf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : NUM691^4 : TPTP v8.1.2. Released v7.1.0.
% 0.17/0.18 % Command : run_E %s %d THM
% 0.17/0.39 % Computer : n007.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.39 % CPULimit : 300
% 0.24/0.39 % WCLimit : 300
% 0.24/0.39 % DateTime : Fri May 3 09:04:20 EDT 2024
% 0.24/0.39 % CPUTime :
% 0.35/0.56 Running higher-order theorem proving
% 0.35/0.56 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.GXOf1OzKnx/E---3.1_19708.p
% 0.39/0.72 # Type mismatch in argument #1 of indeq @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ (d_11_i @ ($not @ db(4)) @ ($db_lam @ db(0) @ ($db_lam @ db(0) @ ($@_var @ db(6) @ db(1) @ db(0)))) @ db(3) @ db(2) @ db(1)) @ db(0): expected $i but got $o
% 0.39/0.72 eprover: Type error
% 4.33/1.20 # Version: 3.1.0-ho
% 4.33/1.20 # Preprocessing class: HSLMSMSSLLLCHSA.
% 4.33/1.20 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 4.33/1.20 # Starting lpo1_fix with 900s (3) cores
% 4.33/1.20 # Starting full_lambda_9 with 300s (1) cores
% 4.33/1.20 # Starting almost_fo_4 with 300s (1) cores
% 4.33/1.20 # Starting new_ho_9 with 300s (1) cores
% 4.33/1.20 # Starting pre_casc_4 with 300s (1) cores
% 4.33/1.20 # Starting ho_unfolding_6 with 300s (1) cores
% 4.33/1.20 # full_lambda_9 with pid 19796 completed with status 0
% 4.33/1.20 # Result found by full_lambda_9
% 4.33/1.20 # Preprocessing class: HSLMSMSSLLLCHSA.
% 4.33/1.20 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 4.33/1.20 # Starting lpo1_fix with 900s (3) cores
% 4.33/1.20 # Starting full_lambda_9 with 300s (1) cores
% 4.33/1.20 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 4.33/1.20 # Search class: HGHSM-FSLM32-DHSMMSBN
% 4.33/1.20 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 4.33/1.20 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 4.33/1.20 # Starting full_lambda_5 with 25s (1) cores
% 4.33/1.20 # full_lambda_5 with pid 19817 completed with status 0
% 4.33/1.20 # Result found by full_lambda_5
% 4.33/1.20 # Preprocessing class: HSLMSMSSLLLCHSA.
% 4.33/1.20 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 4.33/1.20 # Starting lpo1_fix with 900s (3) cores
% 4.33/1.20 # Starting full_lambda_9 with 300s (1) cores
% 4.33/1.20 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 4.33/1.20 # Search class: HGHSM-FSLM32-DHSMMSBN
% 4.33/1.20 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 4.33/1.20 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 4.33/1.20 # Starting full_lambda_5 with 25s (1) cores
% 4.33/1.20 # Preprocessing time : 0.007 s
% 4.33/1.20 # Presaturation interreduction done
% 4.33/1.20
% 4.33/1.20 # Proof found!
% 4.33/1.20 # SZS status Theorem
% 4.33/1.20 # SZS output start CNFRefutation
% See solution above
% 4.33/1.20 # Parsed axioms : 395
% 4.33/1.20 # Removed by relevancy pruning/SinE : 263
% 4.33/1.20 # Initial clauses : 350
% 4.33/1.20 # Removed in clause preprocessing : 176
% 4.33/1.20 # Initial clauses in saturation : 174
% 4.33/1.20 # Processed clauses : 388
% 4.33/1.20 # ...of these trivial : 5
% 4.33/1.20 # ...subsumed : 99
% 4.33/1.20 # ...remaining for further processing : 284
% 4.33/1.20 # Other redundant clauses eliminated : 24
% 4.33/1.20 # Clauses deleted for lack of memory : 0
% 4.33/1.20 # Backward-subsumed : 5
% 4.33/1.20 # Backward-rewritten : 9
% 4.33/1.20 # Generated clauses : 788
% 4.33/1.20 # ...of the previous two non-redundant : 758
% 4.33/1.20 # ...aggressively subsumed : 0
% 4.33/1.20 # Contextual simplify-reflections : 1
% 4.33/1.20 # Paramodulations : 592
% 4.33/1.20 # Factorizations : 2
% 4.33/1.20 # NegExts : 2
% 4.33/1.20 # Equation resolutions : 30
% 4.33/1.20 # Disequality decompositions : 0
% 4.33/1.20 # Total rewrite steps : 138
% 4.33/1.20 # ...of those cached : 121
% 4.33/1.20 # Propositional unsat checks : 0
% 4.33/1.20 # Propositional check models : 0
% 4.33/1.20 # Propositional check unsatisfiable : 0
% 4.33/1.20 # Propositional clauses : 0
% 4.33/1.20 # Propositional clauses after purity: 0
% 4.33/1.20 # Propositional unsat core size : 0
% 4.33/1.20 # Propositional preprocessing time : 0.000
% 4.33/1.20 # Propositional encoding time : 0.000
% 4.33/1.20 # Propositional solver time : 0.000
% 4.33/1.20 # Success case prop preproc time : 0.000
% 4.33/1.20 # Success case prop encoding time : 0.000
% 4.33/1.20 # Success case prop solver time : 0.000
% 4.33/1.20 # Current number of processed clauses : 139
% 4.33/1.20 # Positive orientable unit clauses : 20
% 4.33/1.20 # Positive unorientable unit clauses: 0
% 4.33/1.20 # Negative unit clauses : 16
% 4.33/1.20 # Non-unit-clauses : 103
% 4.33/1.20 # Current number of unprocessed clauses: 654
% 4.33/1.20 # ...number of literals in the above : 3312
% 4.33/1.20 # Current number of archived formulas : 0
% 4.33/1.20 # Current number of archived clauses : 129
% 4.33/1.20 # Clause-clause subsumption calls (NU) : 4784
% 4.33/1.20 # Rec. Clause-clause subsumption calls : 1213
% 4.33/1.20 # Non-unit clause-clause subsumptions : 93
% 4.33/1.20 # Unit Clause-clause subsumption calls : 127
% 4.33/1.20 # Rewrite failures with RHS unbound : 0
% 4.33/1.20 # BW rewrite match attempts : 6
% 4.33/1.20 # BW rewrite match successes : 2
% 4.33/1.20 # Condensation attempts : 0
% 4.33/1.20 # Condensation successes : 0
% 4.33/1.20 # Termbank termtop insertions : 66625
% 4.33/1.20 # Search garbage collected termcells : 17827
% 4.33/1.20
% 4.33/1.20 # -------------------------------------------------
% 4.33/1.20 # User time : 0.091 s
% 4.33/1.20 # System time : 0.009 s
% 4.33/1.20 # Total time : 0.100 s
% 4.33/1.20 # Maximum resident set size: 4992 pages
% 4.33/1.20
% 4.33/1.20 # -------------------------------------------------
% 4.33/1.20 # User time : 0.102 s
% 4.33/1.20 # System time : 0.012 s
% 4.33/1.20 # Total time : 0.114 s
% 4.33/1.20 # Maximum resident set size: 2372 pages
% 4.33/1.20 % E---3.1 exiting
% 4.33/1.20 % E exiting
%------------------------------------------------------------------------------