%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP015^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:05:13 AM UTC 2026
% Result : Theorem 0.25s 0.29s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 18 unt; 0 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 : 0 ( 0 >; 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_24,type,
tyop_2Efcp_2Ecart: d > d > d ).
thf(decl_25,type,
tyop_2Einteger_2Eint: d ).
thf(decl_26,type,
tyop_2Emin_2Ebool: d ).
thf(decl_28,type,
tyop_2Enum_2Enum: d ).
thf(decl_29,type,
s: d > u > du ).
thf(decl_48,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(decl_60,type,
c_2Einteger__word_2Ei2w_2E1: du > u ).
thf(decl_68,type,
c_2Ewords_2En2w_2E1: du > u ).
thf(decl_71,type,
c_2Ewords_2Eword__2comp_2E1: du > u ).
thf(decl_86,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(decl_87,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(decl_89,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(decl_91,type,
mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(decl_92,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(decl_94,type,
mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(decl_95,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(decl_96,type,
mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(decl_98,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(decl_110,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
thf(decl_111,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(decl_126,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.6FXz5XpVL9/E---3.1_1240195.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.6FXz5XpVL9/E---3.1_1240195.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.6FXz5XpVL9/E---3.1_1240195.p',thm_2Einteger__word_2Ei2w__def) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [X75: $o] :
( mono_2Ec_2Ebool_2EF
=> X75 ),
file('/export/starexec/sandbox2/tmp/tmp.6FXz5XpVL9/E---3.1_1240195.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.6FXz5XpVL9/E---3.1_1240195.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.6FXz5XpVL9/E---3.1_1240195.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.6FXz5XpVL9/E---3.1_1240195.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
% 0.00/0.03 % Problem : ITP015^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:29:23 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.6FXz5XpVL9/E---3.1_1240195.p
% 0.25/0.29 % Version: 3.5.1-ho
% 0.25/0.29 % partial match(1): HSLSSLSMSSSNSFA
% 0.25/0.29 % Preprocessing class: HSLMSLSMSSSNSFA.
% 0.25/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.29 % Starting additional_ho_4 with 1500s (5) cores
% 0.25/0.29 % Starting pre_casc_8 with 300s (1) cores
% 0.25/0.29 % Starting pre_casc_5 with 300s (1) cores
% 0.25/0.29 % Starting pre_casc_6 with 300s (1) cores
% 0.25/0.29 % pre_casc_5 with pid 1240226 completed with status 0
% 0.25/0.29 % Result found by pre_casc_5
% 0.25/0.29 % partial match(1): HSLSSLSMSSSNSFA
% 0.25/0.29 % Preprocessing class: HSLMSLSMSSSNSFA.
% 0.25/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.29 % Starting additional_ho_4 with 1500s (5) cores
% 0.25/0.29 % Starting pre_casc_8 with 300s (1) cores
% 0.25/0.29 % Starting pre_casc_5 with 300s (1) cores
% 0.25/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.25/0.29 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.25/0.29 % Search class: HGHSM-FFMS31-DSFFFSBN
% 0.25/0.29 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.25/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.29 % SubtermCWHack with pid 1240228 completed with status 0
% 0.25/0.29 % Result found by SubtermCWHack
% 0.25/0.29 % partial match(1): HSLSSLSMSSSNSFA
% 0.25/0.29 % Preprocessing class: HSLMSLSMSSSNSFA.
% 0.25/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.29 % Starting additional_ho_4 with 1500s (5) cores
% 0.25/0.29 % Starting pre_casc_8 with 300s (1) cores
% 0.25/0.29 % Starting pre_casc_5 with 300s (1) cores
% 0.25/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.25/0.29 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.25/0.29 % Search class: HGHSM-FFMS31-DSFFFSBN
% 0.25/0.29 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.25/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.29 % Preprocessing time : 0.001 s
% 0.25/0.29
% 0.25/0.29 % Proof found!
% 0.25/0.29 % SZS status Theorem
% 0.25/0.29 % SZS output start CNFRefutation
% See solution above
% 0.25/0.29 % Parsed axioms : 194
% 0.25/0.29 % Removed by relevancy pruning/SinE : 156
% 0.25/0.29 % Initial clauses : 64
% 0.25/0.29 % Removed in clause preprocessing : 9
% 0.25/0.29 % Initial clauses in saturation : 55
% 0.25/0.29 % Processed clauses : 188
% 0.25/0.29 % ...of these trivial : 4
% 0.25/0.29 % ...subsumed : 99
% 0.25/0.29 % ...remaining for further processing : 85
% 0.25/0.29 % Other redundant clauses eliminated : 2
% 0.25/0.29 % Clauses deleted for lack of memory : 0
% 0.25/0.29 % Backward-subsumed : 0
% 0.25/0.29 % Backward-rewritten : 1
% 0.25/0.29 % Generated clauses : 644
% 0.25/0.29 % ...of the previous two non-redundant : 345
% 0.25/0.29 % ...aggressively subsumed : 0
% 0.25/0.29 % Contextual simplify-reflections : 0
% 0.25/0.29 % Paramodulations : 579
% 0.25/0.29 % Factorizations : 32
% 0.25/0.30 % NegExts : 0
% 0.25/0.30 % Equation resolutions : 4
% 0.25/0.30 % Disequality decompositions : 0
% 0.25/0.30 % Total rewrite steps : 251
% 0.25/0.30 % ...of those cached : 156
% 0.25/0.30 % Propositional unsat checks : 0
% 0.25/0.30 % Propositional check models : 0
% 0.25/0.30 % Propositional check unsatisfiable : 0
% 0.25/0.30 % Propositional clauses : 0
% 0.25/0.30 % Propositional clauses after purity: 0
% 0.25/0.30 % Propositional unsat core size : 0
% 0.25/0.30 % Propositional preprocessing time : 0.000
% 0.25/0.30 % Propositional encoding time : 0.000
% 0.25/0.30 % Propositional solver time : 0.000
% 0.25/0.30 % Success case prop preproc time : 0.000
% 0.25/0.30 % Success case prop encoding time : 0.000
% 0.25/0.30 % Success case prop solver time : 0.000
% 0.25/0.30 % Current number of processed clauses : 74
% 0.25/0.30 % Positive orientable unit clauses : 28
% 0.25/0.30 % Positive unorientable unit clauses: 0
% 0.25/0.30 % Negative unit clauses : 5
% 0.25/0.30 % Non-unit-clauses : 41
% 0.25/0.30 % Current number of unprocessed clauses: 212
% 0.25/0.30 % ...number of literals in the above : 818
% 0.25/0.30 % Current number of archived formulas : 0
% 0.25/0.30 % Current number of archived clauses : 10
% 0.25/0.30 % Clause-clause subsumption calls (NU) : 341
% 0.25/0.30 % Rec. Clause-clause subsumption calls : 329
% 0.25/0.30 % Non-unit clause-clause subsumptions : 86
% 0.25/0.30 % Unit Clause-clause subsumption calls : 2
% 0.25/0.30 % Rewrite failures with RHS unbound : 0
% 0.25/0.30 % BW rewrite match attempts : 7
% 0.25/0.30 % BW rewrite match successes : 1
% 0.25/0.30 % Condensation attempts : 0
% 0.25/0.30 % Condensation successes : 0
% 0.25/0.30 % Termbank termtop insertions : 20999
% 0.25/0.30 % Search garbage collected termcells : 1276
% 0.25/0.30
% 0.25/0.30 % -------------------------------------------------
% 0.25/0.30 % User time : 0.013 s
% 0.25/0.30 % System time : 0.004 s
% 0.25/0.30 % Total time : 0.017 s
% 0.25/0.30 % Maximum resident set size: 4148 pages
% 0.25/0.30
% 0.25/0.30 % -------------------------------------------------
% 0.25/0.30 % User time : 0.020 s
% 0.25/0.30 % System time : 0.008 s
% 0.25/0.30 % Total time : 0.028 s
% 0.25/0.30 % Maximum resident set size: 4864 pages
% 0.25/0.30 % E exiting
%------------------------------------------------------------------------------