TSTP Solution File: NUM701^4 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM701^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 01:15:43 EDT 2024
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 83 ( 35 unt; 19 typ; 0 def)
% Number of atoms : 296 ( 57 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 572 ( 72 ~; 60 |; 9 &; 385 @)
% ( 0 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 104 ( 75 ^ 29 !; 0 ?; 104 :)
% 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_47,type,
ordsucc: $i > $i ).
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_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_155,type,
esk1_0: $i ).
thf(decl_156,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_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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_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_lessis,axiom,
( lessis
= ( ^ [X1: $i,X230: $i] : ( l_or @ ( iii @ X1 @ X230 ) @ ( n_is @ X1 @ X230 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_lessis) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
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_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_d_29_ii) ).
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(satz10d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X237: $i] : ( in @ X237 @ nat )
@ ^ [X238: $i] :
( ( lessis @ X1 @ X238 )
=> ( d_not @ ( d_29_ii @ X1 @ X238 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10d) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X1: $i,X229: $i] : ( l_or @ ( d_29_ii @ X1 @ X229 ) @ ( n_is @ X1 @ X229 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_moreis) ).
thf(satz26a,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X333: $i] : ( in @ X333 @ nat )
@ ^ [X334: $i] :
( ( iii @ X334 @ ( ordsucc @ X1 ) )
=> ( lessis @ X334 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz26a) ).
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/benchmark/theBenchmark.p',satz10e) ).
thf(satz25a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X325: $i] : ( in @ X325 @ nat )
@ ^ [X326: $i] :
( ( d_29_ii @ X326 @ X1 )
=> ( moreis @ X326 @ ( ordsucc @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25a) ).
thf(suc_p,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( is_of @ ( ordsucc @ X1 )
@ ^ [X166: $i] : ( in @ X166 @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM007^0.ax',suc_p) ).
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,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_20,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_21,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_23,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessis]) ).
thf(c_0_24,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_19,def_n_some]) ).
thf(c_0_25,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).
thf(c_0_26,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_22]) ).
thf(c_0_27,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_28,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_29,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_30,plain,
( lessis
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) )
=> ~ $true )
=> ( Z0 = Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]) ).
thf(c_0_31,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_27,def_n_some]) ).
thf(c_0_32,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_33,plain,
! [X485: $i] :
( ( in @ X485 @ nat )
=> ! [X484: $i] :
( ( in @ X484 @ nat )
=> ( ( ( ( l_some @ nat @ ( diffprop @ X484 @ X485 ) )
=> ~ $true )
=> ( X485 = X484 ) )
=> ( ( l_some @ nat @ ( diffprop @ X485 @ X484 ) )
=> ~ $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)],[satz10d]),c_0_30]),c_0_31]),c_0_32]),c_0_21]) ).
thf(c_0_34,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_35,plain,
! [X713: $i,X714: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ X714 @ X713 ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ X713 @ X714 ) )
| ~ $true
| ~ ( in @ X714 @ nat )
| ~ ( in @ X713 @ nat ) )
& ( ( X713 != X714 )
| ~ ( l_some @ nat @ ( diffprop @ X713 @ X714 ) )
| ~ $true
| ~ ( in @ X714 @ nat )
| ~ ( in @ X713 @ 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_33])])])])]) ).
thf(c_0_36,negated_conjecture,
~ ! [X388: $i] :
( ( in @ X388 @ nat )
=> ! [X387: $i] :
( ( in @ X387 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( ordsucc @ X388 ) @ X387 ) )
=> ( ( ( l_some @ nat @ ( diffprop @ X388 @ X387 ) )
=> ~ $true )
=> ( X387 = X388 ) ) ) ) ),
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)],[satz26a])]),c_0_30]),c_0_24]),c_0_32]) ).
thf(c_0_37,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_34,c_0_31]),c_0_25]),c_0_26]) ).
thf(c_0_38,plain,
! [X487: $i] :
( ( in @ X487 @ nat )
=> ! [X486: $i] :
( ( in @ X486 @ nat )
=> ( ( ( l_some @ nat @ ( diffprop @ X487 @ X486 ) )
=> ~ $true )
=> ( ( ( l_some @ nat @ ( diffprop @ X486 @ X487 ) )
=> ~ $true )
=> ( X487 = X486 ) ) ) ) ),
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_30]),c_0_31]),c_0_32]),c_0_21]) ).
thf(c_0_39,plain,
! [X1: $i,X4: $i] :
( ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) )
| ~ $true
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_40,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( l_some @ nat @ ( diffprop @ ( ordsucc @ esk1_0 ) @ esk2_0 ) )
& ( ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ~ $true )
& ( esk2_0 != esk1_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])])]) ).
thf(c_0_41,plain,
! [X545: $i] :
( ( in @ X545 @ nat )
=> ! [X544: $i] :
( ( in @ X544 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ X544 @ X545 ) )
=> ( ( ( l_some @ nat @ ( diffprop @ X544 @ ( ordsucc @ X545 ) ) )
=> ~ $true )
=> ( X544
= ( ordsucc @ X545 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz25a]),c_0_31]),c_0_32]),c_0_37]) ).
thf(c_0_42,plain,
! [X715: $i,X716: $i] :
( ( ( l_some @ nat @ ( diffprop @ X716 @ X715 ) )
| ( X715 = X716 )
| ( l_some @ nat @ ( diffprop @ X715 @ X716 ) )
| ~ ( in @ X716 @ nat )
| ~ ( in @ X715 @ nat ) )
& ( $true
| ( X715 = X716 )
| ( l_some @ nat @ ( diffprop @ X715 @ X716 ) )
| ~ ( in @ X716 @ nat )
| ~ ( in @ X715 @ nat ) )
& ( ( l_some @ nat @ ( diffprop @ X716 @ X715 ) )
| ( X715 = X716 )
| $true
| ~ ( in @ X716 @ nat )
| ~ ( in @ X715 @ nat ) )
& ( $true
| ( X715 = X716 )
| $true
| ~ ( in @ X716 @ nat )
| ~ ( in @ X715 @ 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_38])])])])]) ).
thf(c_0_43,plain,
! [X1: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ~ ( in @ X1 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ X4 @ X1 ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) ) ),
inference(cn,[status(thm)],[c_0_39]) ).
thf(c_0_44,negated_conjecture,
l_some @ nat @ ( diffprop @ ( ordsucc @ esk1_0 ) @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_45,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_46,plain,
! [X776: $i,X777: $i] :
( ( ( l_some @ nat @ ( diffprop @ X777 @ ( ordsucc @ X776 ) ) )
| ( X777
= ( ordsucc @ X776 ) )
| ~ ( l_some @ nat @ ( diffprop @ X777 @ X776 ) )
| ~ ( in @ X777 @ nat )
| ~ ( in @ X776 @ nat ) )
& ( $true
| ( X777
= ( ordsucc @ X776 ) )
| ~ ( l_some @ nat @ ( diffprop @ X777 @ X776 ) )
| ~ ( in @ X777 @ nat )
| ~ ( in @ X776 @ 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_41])])])])]) ).
thf(c_0_47,plain,
! [X1: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ( X4 = X1 )
| ( l_some @ nat @ ( diffprop @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_48,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_49,negated_conjecture,
( ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ ( ordsucc @ esk1_0 ) ) )
| ~ ( in @ ( ordsucc @ esk1_0 ) @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
thf(c_0_50,plain,
! [X1: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ X1 @ ( ordsucc @ X4 ) ) )
| ( X1
= ( ordsucc @ X4 ) )
| ~ ( l_some @ nat @ ( diffprop @ X1 @ X4 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_51,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ( l_some @ nat @ ( diffprop @ X1 @ esk2_0 ) )
| ( l_some @ nat @ ( diffprop @ esk2_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
thf(c_0_53,negated_conjecture,
esk2_0 != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_54,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_55,plain,
! [X605: $i] :
( ( in @ X605 @ nat )
=> ( in @ ( ordsucc @ X605 ) @ nat ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[suc_p]),c_0_32]),c_0_29]) ).
thf(c_0_56,negated_conjecture,
( ( ( ordsucc @ esk1_0 )
= esk2_0 )
| ~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ) )
| ~ ( in @ ( ordsucc @ esk1_0 ) @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_45])]) ).
thf(c_0_57,negated_conjecture,
l_some @ nat @ ( diffprop @ esk2_0 @ esk1_0 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_53]),c_0_54]) ).
thf(c_0_58,plain,
! [X867: $i] :
( ~ ( in @ X867 @ nat )
| ( in @ ( ordsucc @ X867 ) @ nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
thf(c_0_59,negated_conjecture,
( ( ( ordsucc @ esk1_0 )
= esk2_0 )
| ~ ( in @ ( ordsucc @ esk1_0 ) @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
thf(c_0_60,plain,
! [X1: $i] :
( ( in @ ( ordsucc @ X1 ) @ nat )
| ~ ( in @ X1 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
thf(c_0_61,negated_conjecture,
( ( ordsucc @ esk1_0 )
= esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_51])]) ).
thf(c_0_62,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk2_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_61]),c_0_61]),c_0_45])]) ).
thf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_61]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : NUM701^4 : TPTP v8.2.0. Released v7.1.0.
% 0.00/0.08 % Command : run_E %s %d THM
% 0.08/0.27 % Computer : n013.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon May 20 04:07:37 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 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
% 0.12/0.43 # Version: 3.1.0-ho
% 0.12/0.43 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.12/0.43 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 # Starting lpo1_fix with 900s (3) cores
% 0.12/0.43 # Starting full_lambda_9 with 300s (1) cores
% 0.12/0.43 # Starting almost_fo_4 with 300s (1) cores
% 0.12/0.43 # Starting new_ho_9 with 300s (1) cores
% 0.12/0.43 # Starting pre_casc_4 with 300s (1) cores
% 0.12/0.43 # Starting ho_unfolding_6 with 300s (1) cores
% 0.12/0.43 # full_lambda_9 with pid 30554 completed with status 0
% 0.12/0.43 # Result found by full_lambda_9
% 0.12/0.43 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.12/0.43 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 # Starting lpo1_fix with 900s (3) cores
% 0.12/0.43 # Starting full_lambda_9 with 300s (1) cores
% 0.12/0.43 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.12/0.43 # Search class: HGHSM-FSLM31-DHSMMSBN
% 0.12/0.43 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.12/0.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.12/0.43 # new_ho_10_cnf2 with pid 30559 completed with status 0
% 0.12/0.43 # Result found by new_ho_10_cnf2
% 0.12/0.43 # Preprocessing class: HSLMSMSSLLLCHSA.
% 0.12/0.43 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 # Starting lpo1_fix with 900s (3) cores
% 0.12/0.43 # Starting full_lambda_9 with 300s (1) cores
% 0.12/0.43 # SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.12/0.43 # Search class: HGHSM-FSLM31-DHSMMSBN
% 0.12/0.43 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.12/0.43 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.43 # Starting new_ho_10_cnf2 with 157s (1) cores
% 0.12/0.43 # Preprocessing time : 0.004 s
% 0.12/0.43 # Presaturation interreduction done
% 0.12/0.43
% 0.12/0.43 # Proof found!
% 0.12/0.43 # SZS status Theorem
% 0.12/0.43 # SZS output start CNFRefutation
% See solution above
% 0.12/0.43 # Parsed axioms : 406
% 0.12/0.43 # Removed by relevancy pruning/SinE : 269
% 0.12/0.43 # Initial clauses : 384
% 0.12/0.43 # Removed in clause preprocessing : 190
% 0.12/0.43 # Initial clauses in saturation : 194
% 0.12/0.43 # Processed clauses : 482
% 0.12/0.43 # ...of these trivial : 12
% 0.12/0.43 # ...subsumed : 121
% 0.12/0.43 # ...remaining for further processing : 348
% 0.12/0.43 # Other redundant clauses eliminated : 26
% 0.12/0.43 # Clauses deleted for lack of memory : 0
% 0.12/0.43 # Backward-subsumed : 3
% 0.12/0.43 # Backward-rewritten : 11
% 0.12/0.43 # Generated clauses : 827
% 0.12/0.43 # ...of the previous two non-redundant : 799
% 0.12/0.43 # ...aggressively subsumed : 0
% 0.12/0.43 # Contextual simplify-reflections : 2
% 0.12/0.43 # Paramodulations : 783
% 0.12/0.43 # Factorizations : 2
% 0.12/0.43 # NegExts : 0
% 0.12/0.43 # Equation resolutions : 30
% 0.12/0.43 # Disequality decompositions : 0
% 0.12/0.43 # Total rewrite steps : 226
% 0.12/0.43 # ...of those cached : 203
% 0.12/0.43 # Propositional unsat checks : 0
% 0.12/0.43 # Propositional check models : 0
% 0.12/0.43 # Propositional check unsatisfiable : 0
% 0.12/0.43 # Propositional clauses : 0
% 0.12/0.43 # Propositional clauses after purity: 0
% 0.12/0.43 # Propositional unsat core size : 0
% 0.12/0.43 # Propositional preprocessing time : 0.000
% 0.12/0.43 # Propositional encoding time : 0.000
% 0.12/0.43 # Propositional solver time : 0.000
% 0.12/0.43 # Success case prop preproc time : 0.000
% 0.12/0.43 # Success case prop encoding time : 0.000
% 0.12/0.43 # Success case prop solver time : 0.000
% 0.12/0.43 # Current number of processed clauses : 192
% 0.12/0.43 # Positive orientable unit clauses : 34
% 0.12/0.43 # Positive unorientable unit clauses: 0
% 0.12/0.43 # Negative unit clauses : 23
% 0.12/0.43 # Non-unit-clauses : 135
% 0.12/0.43 # Current number of unprocessed clauses: 628
% 0.12/0.43 # ...number of literals in the above : 2849
% 0.12/0.43 # Current number of archived formulas : 0
% 0.12/0.43 # Current number of archived clauses : 136
% 0.12/0.43 # Clause-clause subsumption calls (NU) : 6847
% 0.12/0.43 # Rec. Clause-clause subsumption calls : 1538
% 0.12/0.43 # Non-unit clause-clause subsumptions : 95
% 0.12/0.43 # Unit Clause-clause subsumption calls : 208
% 0.12/0.43 # Rewrite failures with RHS unbound : 0
% 0.12/0.43 # BW rewrite match attempts : 12
% 0.12/0.43 # BW rewrite match successes : 3
% 0.12/0.43 # Condensation attempts : 482
% 0.12/0.43 # Condensation successes : 7
% 0.12/0.43 # Termbank termtop insertions : 78694
% 0.12/0.43 # Search garbage collected termcells : 20070
% 0.12/0.43
% 0.12/0.43 # -------------------------------------------------
% 0.12/0.43 # User time : 0.055 s
% 0.12/0.43 # System time : 0.009 s
% 0.12/0.43 # Total time : 0.064 s
% 0.12/0.43 # Maximum resident set size: 5400 pages
% 0.12/0.43
% 0.12/0.43 # -------------------------------------------------
% 0.12/0.43 # User time : 0.061 s
% 0.12/0.43 # System time : 0.011 s
% 0.12/0.43 # Total time : 0.072 s
% 0.12/0.43 # Maximum resident set size: 2408 pages
% 0.12/0.43 % E---3.1 exiting
% 0.12/0.43 % E exiting
%------------------------------------------------------------------------------