TSTP Solution File: ITP015^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP015^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 08:06:27 EDT 2024
% Result : Theorem 0.37s 0.56s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 33
% Syntax : Number of formulae : 56 ( 18 unt; 26 typ; 0 def)
% Number of atoms : 107 ( 37 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 761 ( 30 ~; 29 |; 23 &; 670 @)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 51 ( 0 ^ 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
d: $tType ).
thf(decl_sort2,type,
u: $tType ).
thf(decl_sort3,type,
du: $tType ).
thf(decl_sort4,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(decl_sort5,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(decl_23,type,
tyop_2Efcp_2Ecart: d > d > d ).
thf(decl_24,type,
tyop_2Einteger_2Eint: d ).
thf(decl_25,type,
tyop_2Emin_2Ebool: d ).
thf(decl_27,type,
tyop_2Enum_2Enum: d ).
thf(decl_28,type,
s: d > u > du ).
thf(decl_47,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(decl_59,type,
c_2Einteger__word_2Ei2w_2E1: du > u ).
thf(decl_67,type,
c_2Ewords_2En2w_2E1: du > u ).
thf(decl_70,type,
c_2Ewords_2Eword__2comp_2E1: du > u ).
thf(decl_85,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(decl_86,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(decl_88,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(decl_90,type,
mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(decl_91,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(decl_93,type,
mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(decl_94,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(decl_95,type,
mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(decl_97,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(decl_109,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
thf(decl_110,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(decl_125,type,
esk1_0: d ).
thf(thm_2Ebool_2Ebool__case__thm,axiom,
! [X1: d] :
( ! [X82: u,X83: u] :
( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X1 @ X82 ) @ ( s @ X1 @ X83 ) ) )
= ( s @ X1 @ X82 ) )
& ! [X84: u,X85: u] :
( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X84 ) @ ( s @ X1 @ X85 ) ) )
= ( s @ X1 @ X85 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Ebool_2Ebool__case__thm) ).
thf(thm_2Einteger_2EINT__LT__CALCULATE,axiom,
! [X86: mono_2Etyop_2Enum_2Enum,X87: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ X86 @ X87 ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ X87 @ X86 ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
<=> ( ( X86 != mono_2Ec_2Enum_2E0 )
| ( X87 != mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
<=> mono_2Ec_2Ebool_2EF ) ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger_2EINT__LT__CALCULATE) ).
thf(thm_2Einteger__word_2Ei2w__def,axiom,
! [X1: d,X88: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X88 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ X88 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X88 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X88 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger__word_2Ei2w__def) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [X75: $o] :
( mono_2Ec_2Ebool_2EF
=> X75 ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Ebool_2EFALSITY) ).
thf(thm_2Einteger__word_2Ei2w__0,conjecture,
! [X1: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger__word_2Ei2w__0) ).
thf(thm_2Einteger_2ENUM__OF__INT,axiom,
! [X86: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) )
= X86 ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger_2ENUM__OF__INT) ).
thf(thm_2Einteger_2EINT__NEG__0,axiom,
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p',thm_2Einteger_2EINT__NEG__0) ).
thf(c_0_7,axiom,
! [X1: d] :
( ! [X82: u,X83: u] :
( ( ~ mono_2Ec_2Ebool_2ET
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X82 ) @ ( s @ X1 @ X83 ) ) )
= ( s @ X1 @ X82 ) ) )
& ( mono_2Ec_2Ebool_2ET
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X82 ) @ ( s @ X1 @ X83 ) ) )
= ( s @ X1 @ X82 ) ) ) )
& ! [X84: u,X85: u] :
( ( ~ mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X84 ) @ ( s @ X1 @ X85 ) ) )
= ( s @ X1 @ X85 ) ) )
& ( mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X84 ) @ ( s @ X1 @ X85 ) ) )
= ( s @ X1 @ X85 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[thm_2Ebool_2Ebool__case__thm]) ).
thf(c_0_8,plain,
! [X86: mono_2Etyop_2Enum_2Enum,X87: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ X86 @ X87 ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ X87 @ X86 ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) )
<=> ( ( X86 != mono_2Ec_2Enum_2E0 )
| ( X87 != mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X86 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X87 ) ) )
<=> mono_2Ec_2Ebool_2EF ) ),
inference(fof_simplification,[status(thm)],[thm_2Einteger_2EINT__LT__CALCULATE]) ).
thf(c_0_9,axiom,
! [X1: d,X88: mono_2Etyop_2Einteger_2Eint] :
( ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ X88 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X88 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X88 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X88 ) ) ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ X88 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X88 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X88 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X88 ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[thm_2Einteger__word_2Ei2w__def]) ).
thf(c_0_10,plain,
! [X195: d,X196: u,X197: u,X198: u,X199: u] :
( ( ~ mono_2Ec_2Ebool_2ET
| ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X195 @ X196 ) @ ( s @ X195 @ X197 ) ) )
= ( s @ X195 @ X196 ) ) )
& ( mono_2Ec_2Ebool_2ET
| ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X195 @ X196 ) @ ( s @ X195 @ X197 ) ) )
= ( s @ X195 @ X196 ) ) )
& ( ~ mono_2Ec_2Ebool_2EF
| ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X195 @ X198 ) @ ( s @ X195 @ X199 ) ) )
= ( s @ X195 @ X199 ) ) )
& ( mono_2Ec_2Ebool_2EF
| ( ( s @ X195 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X195 @ X198 ) @ ( s @ X195 @ X199 ) ) )
= ( s @ X195 @ X199 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).
thf(c_0_11,plain,
! [X208: $o] :
( ~ mono_2Ec_2Ebool_2EF
| X208 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).
thf(c_0_12,plain,
! [X172: mono_2Etyop_2Enum_2Enum,X173: mono_2Etyop_2Enum_2Enum] :
( ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) )
| ( mono_2Ec_2Eprim__rec_2E_3C @ X172 @ X173 ) )
& ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X172 @ X173 )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
& ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
| ( mono_2Ec_2Eprim__rec_2E_3C @ X173 @ X172 ) )
& ( ~ ( mono_2Ec_2Eprim__rec_2E_3C @ X173 @ X172 )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) ) )
& ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) )
| ( X172 != mono_2Ec_2Enum_2E0 )
| ( X173 != mono_2Ec_2Enum_2E0 ) )
& ( ( X172 = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
& ( ( X173 = mono_2Ec_2Enum_2E0 )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
& ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) )
| mono_2Ec_2Ebool_2EF )
& ( ~ mono_2Ec_2Ebool_2EF
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X172 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X173 ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
thf(c_0_13,plain,
! [X169: d,X170: mono_2Etyop_2Einteger_2Eint] :
( ( ~ ( mono_2Ec_2Einteger_2Eint__lt @ X170 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X170 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X170 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X170 ) ) ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ X170 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X170 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X170 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X169 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X170 ) ) ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
thf(c_0_14,plain,
! [X1: d,X3: u,X4: u] :
( mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
= ( s @ X1 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
~ mono_2Ec_2Ebool_2EF,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11])])]) ).
thf(c_0_16,plain,
! [X26: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
( mono_2Ec_2Ebool_2EF
| ~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X32 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,negated_conjecture,
~ ! [X1: d] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm_2Einteger__word_2Ei2w__0]) ).
thf(c_0_18,plain,
! [X1: d,X25: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ X25 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X25 ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2Eword__2comp_2E1 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ X25 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X25 ) ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
! [X1: d,X3: u,X4: u] :
( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ~ $true ) ) @ ( s @ X1 @ X3 ) @ ( s @ X1 @ X4 ) ) )
= ( s @ X1 @ X4 ) ),
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,plain,
! [X179: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X179 ) )
= X179 ),
inference(variable_rename,[status(thm)],[thm_2Einteger_2ENUM__OF__INT]) ).
thf(c_0_21,plain,
! [X26: mono_2Etyop_2Enum_2Enum,X32: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ X32 ) ) ),
inference(sr,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_22,plain,
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ),
inference(split_conjunct,[status(thm)],[thm_2Einteger_2EINT__NEG__0]) ).
thf(c_0_23,negated_conjecture,
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
!= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
thf(c_0_24,plain,
! [X1: d,X25: mono_2Etyop_2Einteger_2Eint] :
( ( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2ENum @ X25 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ X25 ) ) ) ) )
| ( mono_2Ec_2Einteger_2Eint__lt @ X25 @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,plain,
! [X26: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) )
= X26 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
! [X26: mono_2Etyop_2Enum_2Enum] :
~ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_27,negated_conjecture,
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
!= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ esk1_0 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,plain,
! [X1: d,X26: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Einteger__word_2Ei2w_2E1 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__of__num @ X26 ) ) ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ X1 ) @ ( c_2Ewords_2En2w_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X26 ) ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : ITP015^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.15/0.16 % Command : run_E %s %d THM
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 3 12:45:18 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.23/0.52 Running higher-order theorem proving
% 0.23/0.52 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.yrIqfEXtiq/E---3.1_14254.p
% 0.37/0.56 # Version: 3.1.0-ho
% 0.37/0.56 # partial match(1): HSLSSLSMSSSNSFA
% 0.37/0.56 # Preprocessing class: HSLMSLSMSSSNSFA.
% 0.37/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56 # Starting additional_ho_4 with 1500s (5) cores
% 0.37/0.56 # Starting pre_casc_8 with 300s (1) cores
% 0.37/0.56 # Starting pre_casc_5 with 300s (1) cores
% 0.37/0.56 # Starting pre_casc_6 with 300s (1) cores
% 0.37/0.56 # pre_casc_5 with pid 14335 completed with status 0
% 0.37/0.56 # Result found by pre_casc_5
% 0.37/0.56 # partial match(1): HSLSSLSMSSSNSFA
% 0.37/0.56 # Preprocessing class: HSLMSLSMSSSNSFA.
% 0.37/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56 # Starting additional_ho_4 with 1500s (5) cores
% 0.37/0.56 # Starting pre_casc_8 with 300s (1) cores
% 0.37/0.56 # Starting pre_casc_5 with 300s (1) cores
% 0.37/0.56 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.37/0.56 # Search class: HGHSM-FFMS31-DSFFFSBN
% 0.37/0.56 # partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.37/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.56 # Starting sh5 with 163s (1) cores
% 0.37/0.56 # sh5 with pid 14337 completed with status 0
% 0.37/0.56 # Result found by sh5
% 0.37/0.56 # partial match(1): HSLSSLSMSSSNSFA
% 0.37/0.56 # Preprocessing class: HSLMSLSMSSSNSFA.
% 0.37/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.56 # Starting additional_ho_4 with 1500s (5) cores
% 0.37/0.56 # Starting pre_casc_8 with 300s (1) cores
% 0.37/0.56 # Starting pre_casc_5 with 300s (1) cores
% 0.37/0.56 # SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.37/0.56 # Search class: HGHSM-FFMS31-DSFFFSBN
% 0.37/0.56 # partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.37/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.56 # Starting sh5 with 163s (1) cores
% 0.37/0.56 # Preprocessing time : 0.003 s
% 0.37/0.56 # Presaturation interreduction done
% 0.37/0.56
% 0.37/0.56 # Proof found!
% 0.37/0.56 # SZS status Theorem
% 0.37/0.56 # SZS output start CNFRefutation
% See solution above
% 0.37/0.56 # Parsed axioms : 194
% 0.37/0.56 # Removed by relevancy pruning/SinE : 156
% 0.37/0.56 # Initial clauses : 64
% 0.37/0.56 # Removed in clause preprocessing : 9
% 0.37/0.56 # Initial clauses in saturation : 55
% 0.37/0.56 # Processed clauses : 112
% 0.37/0.56 # ...of these trivial : 5
% 0.37/0.56 # ...subsumed : 16
% 0.37/0.56 # ...remaining for further processing : 91
% 0.37/0.56 # Other redundant clauses eliminated : 2
% 0.37/0.56 # Clauses deleted for lack of memory : 0
% 0.37/0.56 # Backward-subsumed : 1
% 0.37/0.56 # Backward-rewritten : 1
% 0.37/0.56 # Generated clauses : 122
% 0.37/0.56 # ...of the previous two non-redundant : 43
% 0.37/0.56 # ...aggressively subsumed : 0
% 0.37/0.56 # Contextual simplify-reflections : 0
% 0.37/0.56 # Paramodulations : 95
% 0.37/0.56 # Factorizations : 2
% 0.37/0.56 # NegExts : 0
% 0.37/0.56 # Equation resolutions : 2
% 0.37/0.56 # Disequality decompositions : 0
% 0.37/0.56 # Total rewrite steps : 69
% 0.37/0.56 # ...of those cached : 21
% 0.37/0.56 # Propositional unsat checks : 0
% 0.37/0.56 # Propositional check models : 0
% 0.37/0.56 # Propositional check unsatisfiable : 0
% 0.37/0.56 # Propositional clauses : 0
% 0.37/0.56 # Propositional clauses after purity: 0
% 0.37/0.56 # Propositional unsat core size : 0
% 0.37/0.56 # Propositional preprocessing time : 0.000
% 0.37/0.56 # Propositional encoding time : 0.000
% 0.37/0.56 # Propositional solver time : 0.000
% 0.37/0.56 # Success case prop preproc time : 0.000
% 0.37/0.56 # Success case prop encoding time : 0.000
% 0.37/0.56 # Success case prop solver time : 0.000
% 0.37/0.56 # Current number of processed clauses : 39
% 0.37/0.56 # Positive orientable unit clauses : 17
% 0.37/0.56 # Positive unorientable unit clauses: 0
% 0.37/0.56 # Negative unit clauses : 5
% 0.37/0.56 # Non-unit-clauses : 17
% 0.37/0.56 # Current number of unprocessed clauses: 34
% 0.37/0.56 # ...number of literals in the above : 55
% 0.37/0.56 # Current number of archived formulas : 0
% 0.37/0.56 # Current number of archived clauses : 51
% 0.37/0.56 # Clause-clause subsumption calls (NU) : 63
% 0.37/0.56 # Rec. Clause-clause subsumption calls : 58
% 0.37/0.56 # Non-unit clause-clause subsumptions : 8
% 0.37/0.56 # Unit Clause-clause subsumption calls : 11
% 0.37/0.56 # Rewrite failures with RHS unbound : 0
% 0.37/0.56 # BW rewrite match attempts : 16
% 0.37/0.56 # BW rewrite match successes : 1
% 0.37/0.56 # Condensation attempts : 112
% 0.37/0.56 # Condensation successes : 0
% 0.37/0.56 # Termbank termtop insertions : 11053
% 0.37/0.56 # Search garbage collected termcells : 1276
% 0.37/0.56
% 0.37/0.56 # -------------------------------------------------
% 0.37/0.56 # User time : 0.015 s
% 0.37/0.56 # System time : 0.003 s
% 0.37/0.56 # Total time : 0.018 s
% 0.37/0.56 # Maximum resident set size: 2304 pages
% 0.37/0.56
% 0.37/0.56 # -------------------------------------------------
% 0.37/0.56 # User time : 0.020 s
% 0.37/0.56 # System time : 0.007 s
% 0.37/0.56 # Total time : 0.026 s
% 0.37/0.56 # Maximum resident set size: 1984 pages
% 0.37/0.56 % E---3.1 exiting
% 0.37/0.56 % E exiting
%------------------------------------------------------------------------------