TSTP Solution File: NUM702^4 by E---3.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : NUM702^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n001.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 : Mon Jun 24 12:36:51 EDT 2024
% Result : Theorem 0.35s 0.82s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 302 ( 91 equ; 0 cnn)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 622 ( 81 ~; 63 |; 11 &; 404 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 153 ( 112 ^ 41 !; 0 ?; 153 :)
% 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_130,type,
n_1: $i ).
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_152,type,
lessis: $i > $i > $o ).
thf(decl_153,type,
esk1_0: $i ).
thf(decl_154,type,
esk2_0: $i ).
thf(decl_155,type,
esk3_0: $i ).
thf(decl_197,type,
esk45_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.y7hZbN7fMJ/E---3.1_31986.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_is_of) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_imp) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.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.y7hZbN7fMJ/E---3.1_31986.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.y7hZbN7fMJ/E---3.1_31986.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_n_is) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_d_29_ii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X423: $i] :
( ( in @ X423 @ nat )
=> ( non @ nat @ Z0 @ X423 ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_n_some) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_l_or) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_iii) ).
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.y7hZbN7fMJ/E---3.1_31986.p',def_moreis) ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',def_lessis) ).
thf(satz26b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X335: $i] : ( in @ X335 @ nat )
@ ^ [X336: $i] :
( ( d_29_ii @ ( n_pl @ X336 @ n_1 ) @ X1 )
=> ( moreis @ X336 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',satz26b) ).
thf(satz26,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X331: $i] : ( in @ X331 @ nat )
@ ^ [X332: $i] :
( ( iii @ X332 @ ( n_pl @ X1 @ n_1 ) )
=> ( lessis @ X332 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p',satz26) ).
thf(c_0_16,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_17,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
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,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_21,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X422: $i] :
( ( in @ X422 @ Z0 )
=> ( non @ Z0 @ Z1 @ X422 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_22,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_25,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_20]) ).
thf(c_0_26,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X422: $i] :
( ( in @ X422 @ Z0 )
=> ( non @ Z0 @ Z1 @ X422 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_27,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X424: $i] :
( ( in @ X424 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X424 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_28,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_29,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X423: $i] :
( ( in @ X423 @ nat )
=> ( non @ nat @ Z0 @ X423 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_26]) ).
thf(c_0_30,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_31,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X425: $i] :
( ( in @ X425 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X425 ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_32,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X426: $i] :
( ( in @ X426 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X426 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moreis]) ).
thf(c_0_33,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X424: $i] :
( ( in @ X424 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X424 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_34,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_19]),c_0_23]) ).
thf(c_0_35,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X427: $i] :
( ( in @ X427 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X427 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_36,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X425: $i] :
( ( in @ X425 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X425 ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_31,c_0_28]),c_0_29]) ).
thf(c_0_37,plain,
( moreis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X426: $i] :
( ( in @ X426 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) )
@ X426 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32,c_0_33]),c_0_25]),c_0_34]) ).
thf(c_0_38,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( ! [X427: $i] :
( ( in @ X427 @ nat )
=> ( non @ nat
@ ^ [Z2: $i] :
( Z1
= ( n_pl @ Z0 @ Z2 ) )
@ X427 ) )
=> ~ $true )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35,c_0_36]),c_0_25]),c_0_34]) ).
thf(c_0_39,negated_conjecture,
~ ! [X431: $i] :
( ( in @ X431 @ nat )
=> ! [X430: $i] :
( ( in @ X430 @ nat )
=> ( ( ! [X428: $i] :
( ( in @ X428 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X430 @ n_1 )
= ( n_pl @ X431 @ Z0 ) )
@ X428 ) )
=> ~ $true )
=> ( ( ( ! [X429: $i] :
( ( in @ X429 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X430
= ( n_pl @ X431 @ Z0 ) )
@ X429 ) )
=> ~ $true )
=> ~ $true )
=> ( X430 = X431 ) ) ) ) ),
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)],[satz26b])]),c_0_22]),c_0_33]),c_0_37]) ).
thf(c_0_40,plain,
! [X652: $i] :
( ( in @ X652 @ nat )
=> ! [X651: $i] :
( ( in @ X651 @ nat )
=> ( ( ! [X649: $i] :
( ( in @ X649 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X652 @ n_1 )
= ( n_pl @ X651 @ Z0 ) )
@ X649 ) )
=> ~ $true )
=> ( ( ( ! [X650: $i] :
( ( in @ X650 @ nat )
=> ( non @ nat
@ ^ [Z0: $i] :
( X652
= ( n_pl @ X651 @ Z0 ) )
@ X650 ) )
=> ~ $true )
=> ~ $true )
=> ( X651 = X652 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz26]),c_0_22]),c_0_36]),c_0_38]) ).
thf(c_0_41,negated_conjecture,
! [X803: $i] :
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ( in @ esk3_0 @ nat )
| ~ $true )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ esk2_0 @ n_1 )
= ( n_pl @ esk1_0 @ Z0 ) )
@ esk3_0 )
| ~ $true )
& ( ~ ( in @ X803 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X803 )
| ~ $true )
& ( $true
| ~ $true )
& ( esk2_0 != esk1_0 ) ),
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_39])])])])])]) ).
thf(c_0_42,plain,
! [X1028: $i,X1029: $i,X1030: $i] :
( ( ( in @ ( esk45_2 @ X1028 @ X1029 ) @ nat )
| ~ $true
| ( X1029 = X1028 )
| ~ ( in @ X1030 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1028 @ n_1 )
= ( n_pl @ X1029 @ Z0 ) )
@ X1030 )
| ~ ( in @ X1029 @ nat )
| ~ ( in @ X1028 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X1028
= ( n_pl @ X1029 @ Z0 ) )
@ ( esk45_2 @ X1028 @ X1029 ) )
| ~ $true
| ( X1029 = X1028 )
| ~ ( in @ X1030 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1028 @ n_1 )
= ( n_pl @ X1029 @ Z0 ) )
@ X1030 )
| ~ ( in @ X1029 @ nat )
| ~ ( in @ X1028 @ nat ) )
& ( $true
| ( X1029 = X1028 )
| ~ ( in @ X1030 @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1028 @ n_1 )
= ( n_pl @ X1029 @ Z0 ) )
@ X1030 )
| ~ ( in @ X1029 @ nat )
| ~ ( in @ X1028 @ nat ) )
& ( ( in @ ( esk45_2 @ X1028 @ X1029 ) @ nat )
| ~ $true
| ( X1029 = X1028 )
| $true
| ~ ( in @ X1029 @ nat )
| ~ ( in @ X1028 @ nat ) )
& ( ~ ( non @ nat
@ ^ [Z0: $i] :
( X1028
= ( n_pl @ X1029 @ Z0 ) )
@ ( esk45_2 @ X1028 @ X1029 ) )
| ~ $true
| ( X1029 = X1028 )
| $true
| ~ ( in @ X1029 @ nat )
| ~ ( in @ X1028 @ nat ) )
& ( $true
| ( X1029 = X1028 )
| $true
| ~ ( in @ X1029 @ nat )
| ~ ( in @ X1028 @ 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_40])])])])])]) ).
thf(c_0_43,negated_conjecture,
( ~ ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ esk2_0 @ n_1 )
= ( n_pl @ esk1_0 @ Z0 ) )
@ esk3_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_44,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X4 = X1 )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1 @ n_1 )
= ( n_pl @ X4 @ Z0 ) )
@ X5 )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk45_2 @ X1 @ X4 ) )
| ~ $true
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_45,negated_conjecture,
( ( in @ esk3_0 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_46,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk45_2 @ X1 @ X4 ) @ nat )
| ( X4 = X1 )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1 @ n_1 )
= ( n_pl @ X4 @ Z0 ) )
@ X5 )
| ~ $true
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_47,negated_conjecture,
~ ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ esk2_0 @ n_1 )
= ( n_pl @ esk1_0 @ Z0 ) )
@ esk3_0 ),
inference(cn,[status(thm)],[c_0_43]) ).
thf(c_0_48,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( X1 = X4 )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1 @ n_1 )
= ( n_pl @ X4 @ Z0 ) )
@ X5 )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( non @ nat
@ ^ [Z0: $i] :
( X1
= ( n_pl @ X4 @ Z0 ) )
@ ( esk45_2 @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_44]) ).
thf(c_0_49,negated_conjecture,
in @ esk3_0 @ nat,
inference(cn,[status(thm)],[c_0_45]) ).
thf(c_0_50,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_51,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_52,negated_conjecture,
esk2_0 != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ X1 )
| ~ ( in @ X1 @ nat )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_54,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( X1 = X4 )
| ( in @ ( esk45_2 @ X1 @ X4 ) @ nat )
| ( non @ nat
@ ^ [Z0: $i] :
( ( n_pl @ X1 @ n_1 )
= ( n_pl @ X4 @ Z0 ) )
@ X5 )
| ~ ( in @ X5 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_46]) ).
thf(c_0_55,negated_conjecture,
~ ( non @ nat
@ ^ [Z0: $i] :
( esk2_0
= ( n_pl @ esk1_0 @ Z0 ) )
@ ( esk45_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_47,c_0_48]),c_0_49]),c_0_50]),c_0_51])]),c_0_52]) ).
thf(c_0_56,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_53]) ).
thf(c_0_57,negated_conjecture,
in @ ( esk45_2 @ esk2_0 @ esk1_0 ) @ nat,
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_47,c_0_54]),c_0_49]),c_0_50]),c_0_51])]),c_0_52]) ).
thf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM702^4 : TPTP v8.2.0. Released v7.1.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 03:54:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.51 Running higher-order theorem proving
% 0.19/0.51 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.y7hZbN7fMJ/E---3.1_31986.p
% 0.35/0.67 # Type mismatch in argument #1 of indeq @ ($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 $o
% 0.35/0.67 eprover: Type error
% 0.35/0.69 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.35/0.69 eprover: Type error
% 0.35/0.71 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.35/0.71 eprover: Type error
% 0.35/0.73 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.35/0.73 eprover: Type error
% 0.35/0.76 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.35/0.76 eprover: Type error
% 0.35/0.77 # Type mismatch in argument #1 of prop2 @ ($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 $o
% 0.35/0.78 eprover: Type error
% 0.35/0.80 # Type mismatch in argument #1 of prop2 @ ($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
% 0.35/0.80 eprover: Type error
% 0.35/0.82 # Version: 3.2.0-ho
% 0.35/0.82 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.35/0.82 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.82 # Starting lpo1_fix with 900s (3) cores
% 0.35/0.82 # Starting full_lambda_9 with 300s (1) cores
% 0.35/0.82 # Starting almost_fo_4 with 300s (1) cores
% 0.35/0.82 # Starting new_ho_9 with 300s (1) cores
% 0.35/0.82 # Starting pre_casc_4 with 300s (1) cores
% 0.35/0.82 # Starting ho_unfolding_6 with 300s (1) cores
% 0.35/0.82 # pre_casc_4 with pid 32134 completed with status 0
% 0.35/0.82 # Result found by pre_casc_4
% 0.35/0.82 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.35/0.82 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.82 # Starting lpo1_fix with 900s (3) cores
% 0.35/0.82 # Starting full_lambda_9 with 300s (1) cores
% 0.35/0.82 # Starting almost_fo_4 with 300s (1) cores
% 0.35/0.82 # Starting new_ho_9 with 300s (1) cores
% 0.35/0.82 # Starting pre_casc_4 with 300s (1) cores
% 0.35/0.82 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.35/0.82 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.35/0.82 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.35/0.82 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.82 # Starting full_lambda_5 with 28s (1) cores
% 0.35/0.82 # full_lambda_5 with pid 32149 completed with status 0
% 0.35/0.82 # Result found by full_lambda_5
% 0.35/0.82 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.35/0.82 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.82 # Starting lpo1_fix with 900s (3) cores
% 0.35/0.82 # Starting full_lambda_9 with 300s (1) cores
% 0.35/0.82 # Starting almost_fo_4 with 300s (1) cores
% 0.35/0.82 # Starting new_ho_9 with 300s (1) cores
% 0.35/0.82 # Starting pre_casc_4 with 300s (1) cores
% 0.35/0.82 # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.35/0.82 # Search class: HGHSM-FSLM32-DHSMMSBN
% 0.35/0.82 # partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.35/0.82 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.82 # Starting full_lambda_5 with 28s (1) cores
% 0.35/0.82 # Preprocessing time : 0.011 s
% 0.35/0.82 # Presaturation interreduction done
% 0.35/0.82
% 0.35/0.82 # Proof found!
% 0.35/0.82 # SZS status Theorem
% 0.35/0.82 # SZS output start CNFRefutation
% See solution above
% 0.35/0.82 # Parsed axioms : 407
% 0.35/0.82 # Removed by relevancy pruning/SinE : 255
% 0.35/0.82 # Initial clauses : 576
% 0.35/0.82 # Removed in clause preprocessing : 301
% 0.35/0.82 # Initial clauses in saturation : 275
% 0.35/0.82 # Processed clauses : 618
% 0.35/0.82 # ...of these trivial : 6
% 0.35/0.82 # ...subsumed : 52
% 0.35/0.82 # ...remaining for further processing : 560
% 0.35/0.82 # Other redundant clauses eliminated : 939
% 0.35/0.82 # Clauses deleted for lack of memory : 0
% 0.35/0.82 # Backward-subsumed : 0
% 0.35/0.82 # Backward-rewritten : 7
% 0.35/0.82 # Generated clauses : 4254
% 0.35/0.82 # ...of the previous two non-redundant : 3300
% 0.35/0.82 # ...aggressively subsumed : 0
% 0.35/0.82 # Contextual simplify-reflections : 0
% 0.35/0.82 # Paramodulations : 2405
% 0.35/0.82 # Factorizations : 2
% 0.35/0.82 # NegExts : 1
% 0.35/0.82 # Equation resolutions : 944
% 0.35/0.82 # Disequality decompositions : 0
% 0.35/0.82 # Total rewrite steps : 905
% 0.35/0.82 # ...of those cached : 864
% 0.35/0.82 # Propositional unsat checks : 0
% 0.35/0.82 # Propositional check models : 0
% 0.35/0.82 # Propositional check unsatisfiable : 0
% 0.35/0.82 # Propositional clauses : 0
% 0.35/0.82 # Propositional clauses after purity: 0
% 0.35/0.82 # Propositional unsat core size : 0
% 0.35/0.82 # Propositional preprocessing time : 0.000
% 0.35/0.82 # Propositional encoding time : 0.000
% 0.35/0.82 # Propositional solver time : 0.000
% 0.35/0.82 # Success case prop preproc time : 0.000
% 0.35/0.82 # Success case prop encoding time : 0.000
% 0.35/0.82 # Success case prop solver time : 0.000
% 0.35/0.82 # Current number of processed clauses : 257
% 0.35/0.82 # Positive orientable unit clauses : 57
% 0.35/0.82 # Positive unorientable unit clauses: 2
% 0.35/0.82 # Negative unit clauses : 9
% 0.35/0.82 # Non-unit-clauses : 189
% 0.35/0.82 # Current number of unprocessed clauses: 3194
% 0.35/0.82 # ...number of literals in the above : 21523
% 0.35/0.82 # Current number of archived formulas : 0
% 0.35/0.82 # Current number of archived clauses : 262
% 0.35/0.82 # Clause-clause subsumption calls (NU) : 60259
% 0.35/0.82 # Rec. Clause-clause subsumption calls : 2178
% 0.35/0.82 # Non-unit clause-clause subsumptions : 45
% 0.35/0.82 # Unit Clause-clause subsumption calls : 160
% 0.35/0.82 # Rewrite failures with RHS unbound : 0
% 0.35/0.82 # BW rewrite match attempts : 43
% 0.35/0.82 # BW rewrite match successes : 11
% 0.35/0.82 # Condensation attempts : 0
% 0.35/0.82 # Condensation successes : 0
% 0.35/0.82 # Termbank termtop insertions : 211730
% 0.35/0.82 # Search garbage collected termcells : 32506
% 0.35/0.82
% 0.35/0.82 # -------------------------------------------------
% 0.35/0.82 # User time : 0.266 s
% 0.35/0.82 # System time : 0.013 s
% 0.35/0.82 # Total time : 0.279 s
% 0.35/0.82 # Maximum resident set size: 6440 pages
% 0.35/0.82
% 0.35/0.82 # -------------------------------------------------
% 0.35/0.82 # User time : 0.279 s
% 0.35/0.82 # System time : 0.015 s
% 0.35/0.82 # Total time : 0.294 s
% 0.35/0.82 # Maximum resident set size: 2408 pages
% 0.35/0.82 % E---3.1 exiting
% 0.35/0.82 % E exiting
%------------------------------------------------------------------------------