%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP021^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:05:16 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 33 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 620 ( 48 ~; 55 |; 34 &; 461 @)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 85 ( 0 ^; 85 !; 0 ?; 85 :)
% 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_2Eextreal_2Eextreal: $tType ).
thf(decl_23,type,
tyop_2Eextreal_2Eextreal: d ).
thf(decl_24,type,
tyop_2Emin_2Ebool: d ).
thf(decl_26,type,
s: d > u > du ).
thf(decl_42,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(decl_62,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal: $o > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
thf(decl_63,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(decl_64,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(decl_66,type,
mono_2Ec_2Eextreal_2Eextreal__le: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > $o ).
thf(decl_67,type,
mono_2Ec_2Eextreal_2Eextreal__max: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
thf(decl_69,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(decl_70,type,
i_mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Eextreal_2Eextreal > u ).
thf(decl_79,type,
j_mono_2Etyop_2Eextreal_2Eextreal: du > mono_2Etyop_2Eextreal_2Eextreal ).
thf(decl_87,type,
esk1_0: mono_2Etyop_2Eextreal_2Eextreal ).
thf(decl_88,type,
esk2_0: mono_2Etyop_2Eextreal_2Eextreal ).
thf(decl_89,type,
esk3_0: mono_2Etyop_2Eextreal_2Eextreal ).
thf(thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X1: d,X53: u,X54: u] :
( ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) @ ( s @ X1 @ X53 ) @ ( s @ X1 @ X54 ) ) )
= ( s @ X1 @ X53 ) )
& ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) ) @ ( s @ X1 @ X53 ) @ ( s @ X1 @ X54 ) ) )
= ( s @ X1 @ X54 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [X52: $o] :
( ( ( mono_2Ec_2Ebool_2ET
=> X52 )
<=> X52 )
& ( ( X52
=> mono_2Ec_2Ebool_2ET )
<=> mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Ebool_2EF
=> X52 )
<=> mono_2Ec_2Ebool_2ET )
& ( ( X52
=> X52 )
<=> mono_2Ec_2Ebool_2ET )
& ( ( X52
=> mono_2Ec_2Ebool_2EF )
<=> ~ X52 ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [X9: $o,X37: mono_2Etyop_2Eextreal_2Eextreal,X38: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X9 @ X37 @ X38 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X9 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X37 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X38 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal) ).
thf(thm_2Ebool_2EFALSITY,axiom,
! [X52: $o] :
( mono_2Ec_2Ebool_2EF
=> X52 ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Ebool_2EFALSITY) ).
thf(thm_2Eextreal_2Eextreal__max__def,axiom,
! [X58: mono_2Etyop_2Eextreal_2Eextreal,X59: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__max @ X58 @ X59 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Eextreal_2Eextreal__le @ X58 @ X59 ) @ X59 @ X58 ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Eextreal_2Eextreal__max__def) ).
thf(ji_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( j_mono_2Etyop_2Eextreal_2Eextreal @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X14 ) ) )
= X14 ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',ji_2Emono_2Etyop_2Eextreal_2Eextreal) ).
thf(thm_2Eextreal_2Emax__le,conjecture,
! [X68: mono_2Etyop_2Eextreal_2Eextreal,X69: mono_2Etyop_2Eextreal_2Eextreal,X70: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ X69 @ X70 ) @ X68 )
<=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X69 @ X68 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ X70 @ X68 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Eextreal_2Emax__le) ).
thf(thm_2Eextreal_2Ele__trans,axiom,
! [X58: mono_2Etyop_2Eextreal_2Eextreal,X59: mono_2Etyop_2Eextreal_2Eextreal,X60: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X58 @ X59 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ X59 @ X60 ) )
=> ( mono_2Ec_2Eextreal_2Eextreal__le @ X58 @ X60 ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Eextreal_2Ele__trans) ).
thf(thm_2Eextreal_2Ele__total,axiom,
! [X58: mono_2Etyop_2Eextreal_2Eextreal,X59: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X58 @ X59 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X59 @ X58 ) ),
file('/export/starexec/sandbox/tmp/tmp.BTOjKbCMeK/E---3.1_1484110.p',thm_2Eextreal_2Ele__total) ).
thf(c_0_9,axiom,
! [X1: d,X53: u,X54: u] :
( ( ~ mono_2Ec_2Ebool_2ET
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X53 ) @ ( s @ X1 @ X54 ) ) )
= ( s @ X1 @ X53 ) ) )
& ( mono_2Ec_2Ebool_2ET
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X53 ) @ ( s @ X1 @ X54 ) ) )
= ( s @ X1 @ X53 ) ) )
& ( ~ mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X1 @ X53 ) @ ( s @ X1 @ X54 ) ) )
= ( s @ X1 @ X54 ) ) )
& ( mono_2Ec_2Ebool_2EF
| ( ( s @ X1 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X1 @ X53 ) @ ( s @ X1 @ X54 ) ) )
= ( s @ X1 @ X54 ) ) ) ),
inference(fool_unroll,[status(thm)],[thm_2Ebool_2ECOND__CLAUSES]) ).
thf(c_0_10,plain,
! [X52: $o] :
( ( ( mono_2Ec_2Ebool_2ET
=> X52 )
<=> X52 )
& ( ( X52
=> mono_2Ec_2Ebool_2ET )
<=> mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Ebool_2EF
=> X52 )
<=> mono_2Ec_2Ebool_2ET )
& mono_2Ec_2Ebool_2ET
& ( ( X52
=> mono_2Ec_2Ebool_2EF )
<=> ~ X52 ) ),
inference(fof_simplification,[status(thm)],[thm_2Ebool_2EIMP__CLAUSES]) ).
thf(c_0_11,plain,
! [X184: d,X185: u,X186: u] :
( ( ~ mono_2Ec_2Ebool_2ET
| ( ( s @ X184 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X184 @ X185 ) @ ( s @ X184 @ X186 ) ) )
= ( s @ X184 @ X185 ) ) )
& ( mono_2Ec_2Ebool_2ET
| ( ( s @ X184 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X184 @ X185 ) @ ( s @ X184 @ X186 ) ) )
= ( s @ X184 @ X185 ) ) )
& ( ~ mono_2Ec_2Ebool_2EF
| ( ( s @ X184 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) @ ( s @ X184 @ X185 ) @ ( s @ X184 @ X186 ) ) )
= ( s @ X184 @ X186 ) ) )
& ( mono_2Ec_2Ebool_2EF
| ( ( s @ X184 @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) @ ( s @ X184 @ X185 ) @ ( s @ X184 @ X186 ) ) )
= ( s @ X184 @ X186 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])]) ).
thf(c_0_12,plain,
! [X218: $o] :
( ( mono_2Ec_2Ebool_2ET
| X218 )
& ( ~ X218
| X218 )
& ( ~ X218
| ~ mono_2Ec_2Ebool_2ET
| X218 )
& ( X218
| mono_2Ec_2Ebool_2ET )
& ( ~ mono_2Ec_2Ebool_2ET
| mono_2Ec_2Ebool_2ET )
& ( ~ mono_2Ec_2Ebool_2ET
| ~ X218
| mono_2Ec_2Ebool_2ET )
& ( mono_2Ec_2Ebool_2EF
| mono_2Ec_2Ebool_2ET )
& ( ~ X218
| mono_2Ec_2Ebool_2ET )
& ( ~ mono_2Ec_2Ebool_2ET
| ~ mono_2Ec_2Ebool_2EF
| X218 )
& mono_2Ec_2Ebool_2ET
& ( X218
| ~ X218 )
& ( ~ mono_2Ec_2Ebool_2EF
| ~ X218 )
& ( X218
| ~ X218
| mono_2Ec_2Ebool_2EF ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
thf(c_0_13,plain,
! [X1: d,X4: u,X3: 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 @ X3 ) )
| ~ mono_2Ec_2Ebool_2ET ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
mono_2Ec_2Ebool_2ET,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
! [X163: $o,X164: mono_2Etyop_2Eextreal_2Eextreal,X165: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X163 @ X164 @ X165 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X163 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X164 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X165 ) ) ) ) ),
inference(variable_rename,[status(thm)],[monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eextreal_2Eextreal]) ).
thf(c_0_16,plain,
! [X215: $o] :
( ~ mono_2Ec_2Ebool_2EF
| X215 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Ebool_2EFALSITY])])]) ).
thf(c_0_17,axiom,
! [X58: mono_2Etyop_2Eextreal_2Eextreal,X59: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X58 @ X59 )
| ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X58 @ X59 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X59 @ X58 ) ) )
& ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X58 @ X59 )
| ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X58 @ X59 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $false @ X59 @ X58 ) ) ) ),
inference(fool_unroll,[status(thm)],[thm_2Eextreal_2Eextreal__max__def]) ).
thf(c_0_18,plain,
! [X188: mono_2Etyop_2Eextreal_2Eextreal] :
( ( j_mono_2Etyop_2Eextreal_2Eextreal @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X188 ) ) )
= X188 ),
inference(variable_rename,[status(thm)],[ji_2Emono_2Etyop_2Eextreal_2Eextreal]) ).
thf(c_0_19,plain,
! [X1: d,X4: u,X3: 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 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_20,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X9: $o,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ X9 @ X14 @ X30 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X9 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X14 ) ) @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X30 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,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_11]) ).
thf(c_0_22,plain,
~ mono_2Ec_2Ebool_2EF,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16])])]) ).
thf(c_0_23,negated_conjecture,
~ ! [X68: mono_2Etyop_2Eextreal_2Eextreal,X69: mono_2Etyop_2Eextreal_2Eextreal,X70: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ X69 @ X70 ) @ X68 )
<=> ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X69 @ X68 )
& ( mono_2Ec_2Eextreal_2Eextreal__le @ X70 @ X68 ) ) ),
inference(assume_negation,[status(cth)],[thm_2Eextreal_2Emax__le]) ).
thf(c_0_24,plain,
! [X161: mono_2Etyop_2Eextreal_2Eextreal,X162: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X161 @ X162 )
| ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X161 @ X162 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X162 @ X161 ) ) )
& ( ( mono_2Ec_2Eextreal_2Eextreal__le @ X161 @ X162 )
| ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X161 @ X162 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $false @ X162 @ X161 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
thf(c_0_25,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( j_mono_2Etyop_2Eextreal_2Eextreal @ ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X14 ) ) )
= X14 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,plain,
! [X30: mono_2Etyop_2Eextreal_2Eextreal,X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X14 @ X30 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X14 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_27,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_21,c_0_22]) ).
thf(c_0_28,negated_conjecture,
( ( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk1_0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 ) )
& ( ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk1_0 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 ) )
& ( ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])]) ).
thf(c_0_29,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X14 @ X30 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X30 @ X14 ) )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,plain,
! [X30: mono_2Etyop_2Eextreal_2Eextreal,X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ $true @ X14 @ X30 )
= X14 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
thf(c_0_31,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ~ $true @ X14 @ X30 ) ) )
= ( s @ tyop_2Eextreal_2Eextreal @ ( i_mono_2Etyop_2Eextreal_2Eextreal @ X30 ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
thf(c_0_32,plain,
! [X156: mono_2Etyop_2Eextreal_2Eextreal,X157: mono_2Etyop_2Eextreal_2Eextreal,X158: mono_2Etyop_2Eextreal_2Eextreal] :
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X156 @ X157 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X157 @ X158 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X156 @ X158 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thm_2Eextreal_2Ele__trans])])]) ).
thf(c_0_33,negated_conjecture,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_34,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X14 @ X30 )
= X30 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_35,plain,
! [X30: mono_2Etyop_2Eextreal_2Eextreal,X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 )
| ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X14 @ X30 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ~ $true @ X30 @ X14 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_36,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eextreal_2Eextreal @ ~ $true @ X14 @ X30 )
= X30 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_31]),c_0_25]) ).
thf(c_0_37,negated_conjecture,
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk1_0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_38,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal,X32: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X32 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X30 @ X32 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,negated_conjecture,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_40,negated_conjecture,
( ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk1_0 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_41,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( ( mono_2Ec_2Eextreal_2Eextreal__max @ X14 @ X30 )
= X14 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_42,negated_conjecture,
~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk3_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_38]),c_0_39]) ).
thf(c_0_43,plain,
! [X159: mono_2Etyop_2Eextreal_2Eextreal,X160: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X159 @ X160 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X160 @ X159 ) ),
inference(variable_rename,[status(thm)],[thm_2Eextreal_2Ele__total]) ).
thf(c_0_44,negated_conjecture,
mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ esk1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
thf(c_0_45,plain,
! [X30: mono_2Etyop_2Eextreal_2Eextreal,X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X30 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_46,negated_conjecture,
( ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ ( mono_2Ec_2Eextreal_2Eextreal__max @ esk2_0 @ esk3_0 ) @ esk1_0 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_44])]) ).
thf(c_0_47,plain,
! [X14: mono_2Etyop_2Eextreal_2Eextreal,X32: mono_2Etyop_2Eextreal_2Eextreal,X30: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ X30 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X32 @ X14 )
| ~ ( mono_2Ec_2Eextreal_2Eextreal__le @ X32 @ X30 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
thf(c_0_48,negated_conjecture,
~ ( mono_2Ec_2Eextreal_2Eextreal__le @ esk3_0 @ esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_41]),c_0_44])]),c_0_42]) ).
thf(c_0_49,negated_conjecture,
! [X14: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le @ esk2_0 @ X14 )
| ( mono_2Ec_2Eextreal_2Eextreal__le @ X14 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_44]) ).
thf(c_0_50,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP021^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:35:04 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.24 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.BTOjKbCMeK/E---3.1_1484110.p
% 0.20/0.28 % Version: 3.5.1-ho
% 0.20/0.28 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting additional_ho_4 with 1500s (5) cores
% 0.20/0.28 % Starting pre_casc_8 with 300s (1) cores
% 0.20/0.28 % Starting pre_casc_5 with 300s (1) cores
% 0.20/0.28 % Starting pre_casc_6 with 300s (1) cores
% 0.20/0.28 % additional_ho_4 with pid 1484146 completed with status 0
% 0.20/0.28 % Result found by additional_ho_4
% 0.20/0.28 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting additional_ho_4 with 1500s (5) cores
% 0.20/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMM31-DSFFFFBN
% 0.20/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.28 % Starting additional_ho_4 with 151s (1) cores
% 0.20/0.28 % Starting pre_casc_8 with 136s (1) cores
% 0.20/0.28 % Starting new_ho_5 with 136s (1) cores
% 0.20/0.28 % Starting ehoh_best8_lambda with 136s (1) cores
% 0.20/0.28 % SubtermCWHack with pid 1484153 completed with status 0
% 0.20/0.28 % Result found by SubtermCWHack
% 0.20/0.28 % Preprocessing class: HSLSSLSMSSSNSFA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting additional_ho_4 with 1500s (5) cores
% 0.20/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMM31-DSFFFFBN
% 0.20/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.28 % Preprocessing time : 0.001 s
% 0.20/0.28
% 0.20/0.28 % Proof found!
% 0.20/0.28 % SZS status Theorem
% 0.20/0.28 % SZS output start CNFRefutation
% See solution above
% 0.20/0.28 % Parsed axioms : 145
% 0.20/0.28 % Removed by relevancy pruning/SinE : 95
% 0.20/0.28 % Initial clauses : 112
% 0.20/0.28 % Removed in clause preprocessing : 38
% 0.20/0.28 % Initial clauses in saturation : 74
% 0.20/0.28 % Processed clauses : 256
% 0.20/0.28 % ...of these trivial : 16
% 0.20/0.28 % ...subsumed : 137
% 0.20/0.28 % ...remaining for further processing : 103
% 0.20/0.28 % Other redundant clauses eliminated : 0
% 0.20/0.28 % Clauses deleted for lack of memory : 0
% 0.20/0.28 % Backward-subsumed : 3
% 0.20/0.28 % Backward-rewritten : 12
% 0.20/0.28 % Generated clauses : 845
% 0.20/0.28 % ...of the previous two non-redundant : 608
% 0.20/0.28 % ...aggressively subsumed : 0
% 0.20/0.28 % Contextual simplify-reflections : 2
% 0.20/0.28 % Paramodulations : 738
% 0.20/0.28 % Factorizations : 68
% 0.20/0.28 % NegExts : 0
% 0.20/0.28 % Equation resolutions : 0
% 0.20/0.28 % Disequality decompositions : 0
% 0.20/0.28 % Total rewrite steps : 245
% 0.20/0.28 % ...of those cached : 118
% 0.20/0.28 % Propositional unsat checks : 0
% 0.20/0.28 % Propositional check models : 0
% 0.20/0.28 % Propositional check unsatisfiable : 0
% 0.20/0.28 % Propositional clauses : 0
% 0.20/0.28 % Propositional clauses after purity: 0
% 0.20/0.28 % Propositional unsat core size : 0
% 0.20/0.28 % Propositional preprocessing time : 0.000
% 0.20/0.28 % Propositional encoding time : 0.000
% 0.20/0.28 % Propositional solver time : 0.000
% 0.20/0.28 % Success case prop preproc time : 0.000
% 0.20/0.28 % Success case prop encoding time : 0.000
% 0.20/0.28 % Success case prop solver time : 0.000
% 0.20/0.28 % Current number of processed clauses : 78
% 0.20/0.28 % Positive orientable unit clauses : 40
% 0.20/0.28 % Positive unorientable unit clauses: 0
% 0.20/0.28 % Negative unit clauses : 4
% 0.20/0.28 % Non-unit-clauses : 34
% 0.20/0.28 % Current number of unprocessed clauses: 403
% 0.20/0.28 % ...number of literals in the above : 1865
% 0.20/0.28 % Current number of archived formulas : 0
% 0.20/0.28 % Current number of archived clauses : 25
% 0.20/0.28 % Clause-clause subsumption calls (NU) : 1256
% 0.20/0.28 % Rec. Clause-clause subsumption calls : 843
% 0.20/0.28 % Non-unit clause-clause subsumptions : 126
% 0.20/0.28 % Unit Clause-clause subsumption calls : 103
% 0.20/0.28 % Rewrite failures with RHS unbound : 0
% 0.20/0.28 % BW rewrite match attempts : 20
% 0.20/0.28 % BW rewrite match successes : 4
% 0.20/0.28 % Condensation attempts : 0
% 0.20/0.28 % Condensation successes : 0
% 0.20/0.28 % Termbank termtop insertions : 22131
% 0.20/0.28 % Search garbage collected termcells : 1569
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.021 s
% 0.20/0.28 % System time : 0.004 s
% 0.20/0.28 % Total time : 0.025 s
% 0.20/0.28 % Maximum resident set size: 4092 pages
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.053 s
% 0.20/0.28 % System time : 0.020 s
% 0.20/0.28 % Total time : 0.072 s
% 0.20/0.28 % Maximum resident set size: 5120 pages
% 0.20/0.28 % E exiting
%------------------------------------------------------------------------------