TSTP Solution File: SEU818^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU818^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 03:30:33 EDT 2024
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 31
% Syntax : Number of formulae : 48 ( 17 unt; 21 typ; 0 def)
% Number of atoms : 456 ( 54 equ; 0 cnn)
% Maximal formula atoms : 159 ( 16 avg)
% Number of connectives : 1393 ( 139 ~; 188 |; 84 &; 851 @)
% ( 4 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 147 ( 12 ^ 126 !; 9 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
nonempty: $i > $o ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI1: $o ).
thf(decl_28,type,
transitiveset: $i > $o ).
thf(decl_29,type,
stricttotalorderedByIn: $i > $o ).
thf(decl_30,type,
wellorderedByIn: $i > $o ).
thf(decl_31,type,
ordinal: $i > $o ).
thf(decl_32,type,
ordinalTransSet: $o ).
thf(decl_33,type,
epred1_1: $i > $o ).
thf(decl_34,type,
epred2_1: $i > $o ).
thf(decl_35,type,
esk1_2: $i > $i > $i ).
thf(decl_36,type,
esk2_1: $i > $i ).
thf(decl_37,type,
esk3_1: $i > $i ).
thf(decl_38,type,
esk4_1: $i > $i ).
thf(decl_39,type,
esk5_2: $i > $i > $i ).
thf(decl_40,type,
esk6_0: $i ).
thf(decl_41,type,
esk7_0: $i ).
thf(decl_47,type,
esk13_2: $i > $i > $i ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [X2: $i] :
( ( stricttotalorderedByIn @ X2 )
& ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( ( nonempty @ X4 )
=> ? [X1: $i] :
( ( in @ X1 @ X4 )
& ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( ( X1 = X5 )
| ( in @ X1 @ X5 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(stricttotalorderedByIn,axiom,
( stricttotalorderedByIn
= ( ^ [X2: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( ( in @ X1 @ X4 )
& ( in @ X4 @ X5 ) )
=> ( in @ X1 @ X5 ) ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( X4 = X5 )
| ( in @ X4 @ X5 )
| ( in @ X5 @ X4 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ~ ( in @ X4 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X1: $i] : ( X1 != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(ordinal,axiom,
( ordinal
= ( ^ [X1: $i] :
( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal) ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [X2: $i] :
! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( subset @ X4 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(ordinalTransSet,axiom,
( ordinalTransSet
<=> ! [X4: $i] :
( ( ordinal @ X4 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalTransSet) ).
thf(ordinalTransSet1,conjecture,
( subsetI1
=> ( ordinalTransSet
=> ! [X4: $i] :
( ( ordinal @ X4 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalTransSet1) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X2: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) )
=> ( subset @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(c_0_8,plain,
( wellorderedByIn
= ( ^ [Z0: $i] :
( ! [X14: $i] :
( ( in @ X14 @ Z0 )
=> ! [X15: $i] :
( ( in @ X15 @ Z0 )
=> ! [X16: $i] :
( ( in @ X16 @ Z0 )
=> ( ( ( in @ X14 @ X15 )
& ( in @ X15 @ X16 ) )
=> ( in @ X14 @ X16 ) ) ) ) )
& ! [X17: $i] :
( ( in @ X17 @ Z0 )
=> ! [X18: $i] :
( ( in @ X18 @ Z0 )
=> ( ( X17 = X18 )
| ( in @ X17 @ X18 )
| ( in @ X18 @ X17 ) ) ) )
& ! [X19: $i] :
( ( in @ X19 @ Z0 )
=> ~ ( in @ X19 @ X19 ) )
& ! [X4: $i] :
( ( in @ X4 @ ( powerset @ Z0 ) )
=> ( ( X4 != emptyset )
=> ? [X1: $i] :
( ( in @ X1 @ X4 )
& ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( ( X1 = X5 )
| ( in @ X1 @ X5 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[wellorderedByIn]) ).
thf(c_0_9,plain,
( stricttotalorderedByIn
= ( ^ [Z0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ Z0 )
=> ! [X4: $i] :
( ( in @ X4 @ Z0 )
=> ! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ( ( ( in @ X1 @ X4 )
& ( in @ X4 @ X5 ) )
=> ( in @ X1 @ X5 ) ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ Z0 )
=> ! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ( ( X4 = X5 )
| ( in @ X4 @ X5 )
| ( in @ X5 @ X4 ) ) ) )
& ! [X4: $i] :
( ( in @ X4 @ Z0 )
=> ~ ( in @ X4 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[stricttotalorderedByIn]) ).
thf(c_0_10,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_11,plain,
( ordinal
= ( ^ [Z0: $i] :
( ! [X20: $i] :
( ( in @ X20 @ Z0 )
=> ( subset @ X20 @ Z0 ) )
& ! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ! [X22: $i] :
( ( in @ X22 @ Z0 )
=> ! [X23: $i] :
( ( in @ X23 @ Z0 )
=> ( ( ( in @ X21 @ X22 )
& ( in @ X22 @ X23 ) )
=> ( in @ X21 @ X23 ) ) ) ) )
& ! [X24: $i] :
( ( in @ X24 @ Z0 )
=> ! [X25: $i] :
( ( in @ X25 @ Z0 )
=> ( ( X24 = X25 )
| ( in @ X24 @ X25 )
| ( in @ X25 @ X24 ) ) ) )
& ! [X26: $i] :
( ( in @ X26 @ Z0 )
=> ~ ( in @ X26 @ X26 ) )
& ! [X27: $i] :
( ( in @ X27 @ ( powerset @ Z0 ) )
=> ( ( X27 != emptyset )
=> ? [X28: $i] :
( ( in @ X28 @ X27 )
& ! [X29: $i] :
( ( in @ X29 @ X27 )
=> ( ( X28 = X29 )
| ( in @ X28 @ X29 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ordinal]) ).
thf(c_0_12,plain,
( transitiveset
= ( ^ [Z0: $i] :
! [X4: $i] :
( ( in @ X4 @ Z0 )
=> ( subset @ X4 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitiveset]) ).
thf(c_0_13,plain,
( wellorderedByIn
= ( ^ [Z0: $i] :
( ! [X14: $i] :
( ( in @ X14 @ Z0 )
=> ! [X15: $i] :
( ( in @ X15 @ Z0 )
=> ! [X16: $i] :
( ( in @ X16 @ Z0 )
=> ( ( ( in @ X14 @ X15 )
& ( in @ X15 @ X16 ) )
=> ( in @ X14 @ X16 ) ) ) ) )
& ! [X17: $i] :
( ( in @ X17 @ Z0 )
=> ! [X18: $i] :
( ( in @ X18 @ Z0 )
=> ( ( X17 = X18 )
| ( in @ X17 @ X18 )
| ( in @ X18 @ X17 ) ) ) )
& ! [X19: $i] :
( ( in @ X19 @ Z0 )
=> ~ ( in @ X19 @ X19 ) )
& ! [X4: $i] :
( ( in @ X4 @ ( powerset @ Z0 ) )
=> ( ( X4 != emptyset )
=> ? [X1: $i] :
( ( in @ X1 @ X4 )
& ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( ( X1 = X5 )
| ( in @ X1 @ X5 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_14,plain,
( ordinal
= ( ^ [Z0: $i] :
( ! [X20: $i] :
( ( in @ X20 @ Z0 )
=> ( subset @ X20 @ Z0 ) )
& ! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ! [X22: $i] :
( ( in @ X22 @ Z0 )
=> ! [X23: $i] :
( ( in @ X23 @ Z0 )
=> ( ( ( in @ X21 @ X22 )
& ( in @ X22 @ X23 ) )
=> ( in @ X21 @ X23 ) ) ) ) )
& ! [X24: $i] :
( ( in @ X24 @ Z0 )
=> ! [X25: $i] :
( ( in @ X25 @ Z0 )
=> ( ( X24 = X25 )
| ( in @ X24 @ X25 )
| ( in @ X25 @ X24 ) ) ) )
& ! [X26: $i] :
( ( in @ X26 @ Z0 )
=> ~ ( in @ X26 @ X26 ) )
& ! [X27: $i] :
( ( in @ X27 @ ( powerset @ Z0 ) )
=> ( ( X27 != emptyset )
=> ? [X28: $i] :
( ( in @ X28 @ X27 )
& ! [X29: $i] :
( ( in @ X29 @ X27 )
=> ( ( X28 = X29 )
| ( in @ X28 @ X29 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_15,axiom,
( ordinalTransSet
= ( ! [X4: $i] :
( ( ! [X30: $i] :
( ( in @ X30 @ X4 )
=> ( subset @ X30 @ X4 ) )
& ! [X31: $i] :
( ( in @ X31 @ X4 )
=> ! [X32: $i] :
( ( in @ X32 @ X4 )
=> ! [X33: $i] :
( ( in @ X33 @ X4 )
=> ( ( ( in @ X31 @ X32 )
& ( in @ X32 @ X33 ) )
=> ( in @ X31 @ X33 ) ) ) ) )
& ! [X34: $i] :
( ( in @ X34 @ X4 )
=> ! [X35: $i] :
( ( in @ X35 @ X4 )
=> ( ( X34 = X35 )
| ( in @ X34 @ X35 )
| ( in @ X35 @ X34 ) ) ) )
& ! [X36: $i] :
( ( in @ X36 @ X4 )
=> ~ ( in @ X36 @ X36 ) )
& ! [X37: $i] :
( ( in @ X37 @ ( powerset @ X4 ) )
=> ( ( X37 != emptyset )
=> ? [X38: $i] :
( ( in @ X38 @ X37 )
& ! [X39: $i] :
( ( in @ X39 @ X37 )
=> ( ( X38 = X39 )
| ( in @ X38 @ X39 ) ) ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X4 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[ordinalTransSet,c_0_14]) ).
thf(c_0_16,plain,
! [X43: $i] :
( ( epred1_1 @ X43 )
<=> ( ! [X45: $i] :
( ( in @ X45 @ X43 )
=> ! [X46: $i] :
( ( in @ X46 @ X43 )
=> ! [X47: $i] :
( ( in @ X47 @ X43 )
=> ( ( ( in @ X45 @ X46 )
& ( in @ X46 @ X47 ) )
=> ( in @ X45 @ X47 ) ) ) ) )
& ! [X48: $i] :
( ( in @ X48 @ X43 )
=> ! [X49: $i] :
( ( in @ X49 @ X43 )
=> ( ( X48 = X49 )
| ( in @ X48 @ X49 )
| ( in @ X49 @ X48 ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_17,plain,
! [X4: $i] :
( ( epred2_1 @ X4 )
<=> ( ! [X56: $i] :
( ( in @ X56 @ X4 )
=> ( subset @ X56 @ X4 ) )
& ! [X57: $i] :
( ( in @ X57 @ X4 )
=> ! [X58: $i] :
( ( in @ X58 @ X4 )
=> ! [X59: $i] :
( ( in @ X59 @ X4 )
=> ( ( ( in @ X57 @ X58 )
& ( in @ X58 @ X59 ) )
=> ( in @ X57 @ X59 ) ) ) ) )
& ! [X60: $i] :
( ( in @ X60 @ X4 )
=> ! [X61: $i] :
( ( in @ X61 @ X4 )
=> ( ( X60 = X61 )
| ( in @ X60 @ X61 )
| ( in @ X61 @ X60 ) ) ) )
& ! [X62: $i] :
( ( in @ X62 @ X4 )
=> ~ ( in @ X62 @ X62 ) )
& ! [X63: $i] :
( ( in @ X63 @ ( powerset @ X4 ) )
=> ( ( X63 != emptyset )
=> ? [X64: $i] :
( ( in @ X64 @ X63 )
& ! [X65: $i] :
( ( in @ X65 @ X63 )
=> ( ( X64 = X65 )
| ( in @ X64 @ X65 ) ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_18,negated_conjecture,
~ ( ! [X40: $i,X41: $i] :
( ! [X42: $i] :
( ( in @ X42 @ X40 )
=> ( in @ X42 @ X41 ) )
=> ( subset @ X40 @ X41 ) )
=> ( ! [X43: $i] :
( ( ! [X44: $i] :
( ( in @ X44 @ X43 )
=> ( subset @ X44 @ X43 ) )
& ( epred1_1 @ X43 )
& ! [X50: $i] :
( ( in @ X50 @ X43 )
=> ~ ( in @ X50 @ X50 ) )
& ! [X51: $i] :
( ( in @ X51 @ ( powerset @ X43 ) )
=> ( ( X51 != emptyset )
=> ? [X52: $i] :
( ( in @ X52 @ X51 )
& ! [X53: $i] :
( ( in @ X53 @ X51 )
=> ( ( X52 = X53 )
| ( in @ X52 @ X53 ) ) ) ) ) ) )
=> ! [X54: $i,X55: $i] :
( ( in @ X55 @ X43 )
=> ( ( in @ X54 @ X55 )
=> ( in @ X54 @ X43 ) ) ) )
=> ! [X4: $i] :
( ( epred2_1 @ X4 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( subset @ X2 @ X4 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ordinalTransSet1]),subsetI1]),c_0_14]),c_0_15])]),c_0_16]),c_0_17]) ).
thf(c_0_19,plain,
! [X4: $i] :
( ( epred2_1 @ X4 )
=> ( ! [X56: $i] :
( ( in @ X56 @ X4 )
=> ( subset @ X56 @ X4 ) )
& ! [X57: $i] :
( ( in @ X57 @ X4 )
=> ! [X58: $i] :
( ( in @ X58 @ X4 )
=> ! [X59: $i] :
( ( in @ X59 @ X4 )
=> ( ( ( in @ X57 @ X58 )
& ( in @ X58 @ X59 ) )
=> ( in @ X57 @ X59 ) ) ) ) )
& ! [X60: $i] :
( ( in @ X60 @ X4 )
=> ! [X61: $i] :
( ( in @ X61 @ X4 )
=> ( ( X60 = X61 )
| ( in @ X60 @ X61 )
| ( in @ X61 @ X60 ) ) ) )
& ! [X62: $i] :
( ( in @ X62 @ X4 )
=> ~ ( in @ X62 @ X62 ) )
& ! [X63: $i] :
( ( in @ X63 @ ( powerset @ X4 ) )
=> ( ( X63 != emptyset )
=> ? [X64: $i] :
( ( in @ X64 @ X63 )
& ! [X65: $i] :
( ( in @ X65 @ X63 )
=> ( ( X64 = X65 )
| ( in @ X64 @ X65 ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X66: $i,X67: $i,X69: $i,X73: $i,X75: $i,X76: $i] :
( ( ( in @ ( esk1_2 @ X66 @ X67 ) @ X66 )
| ( subset @ X66 @ X67 ) )
& ( ~ ( in @ ( esk1_2 @ X66 @ X67 ) @ X67 )
| ( subset @ X66 @ X67 ) )
& ( ( in @ ( esk4_1 @ X69 ) @ ( powerset @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( ( esk4_1 @ X69 )
!= emptyset )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk5_2 @ X69 @ X73 ) @ ( esk4_1 @ X69 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( X73
!= ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ~ ( in @ X73 @ ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk4_1 @ X69 ) @ ( powerset @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( ( esk4_1 @ X69 )
!= emptyset )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk5_2 @ X69 @ X73 ) @ ( esk4_1 @ X69 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( X73
!= ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ~ ( in @ X73 @ ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ( in @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk4_1 @ X69 ) @ ( powerset @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( ( esk4_1 @ X69 )
!= emptyset )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk5_2 @ X69 @ X73 ) @ ( esk4_1 @ X69 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( X73
!= ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ~ ( in @ X73 @ ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ X69 )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk4_1 @ X69 ) @ ( powerset @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( ( esk4_1 @ X69 )
!= emptyset )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( in @ ( esk5_2 @ X69 @ X73 ) @ ( esk4_1 @ X69 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ( X73
!= ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( ~ ( in @ X73 @ ( esk5_2 @ X69 @ X73 ) )
| ~ ( in @ X73 @ ( esk4_1 @ X69 ) )
| ( in @ ( esk3_1 @ X69 ) @ ( esk3_1 @ X69 ) )
| ~ ( epred1_1 @ X69 )
| ~ ( subset @ ( esk2_1 @ X69 ) @ X69 )
| ~ ( in @ X76 @ X69 )
| ~ ( in @ X75 @ X76 )
| ( in @ X75 @ X69 ) )
& ( epred2_1 @ esk6_0 )
& ( in @ esk7_0 @ esk6_0 )
& ~ ( subset @ esk7_0 @ esk6_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])]) ).
thf(c_0_21,plain,
! [X85: $i,X86: $i,X87: $i,X88: $i,X89: $i,X90: $i,X91: $i,X92: $i,X93: $i,X95: $i] :
( ( ~ ( in @ X86 @ X85 )
| ( subset @ X86 @ X85 )
| ~ ( epred2_1 @ X85 ) )
& ( ~ ( in @ X87 @ X85 )
| ~ ( in @ X88 @ X85 )
| ~ ( in @ X89 @ X85 )
| ~ ( in @ X87 @ X88 )
| ~ ( in @ X88 @ X89 )
| ( in @ X87 @ X89 )
| ~ ( epred2_1 @ X85 ) )
& ( ~ ( in @ X90 @ X85 )
| ~ ( in @ X91 @ X85 )
| ( X90 = X91 )
| ( in @ X90 @ X91 )
| ( in @ X91 @ X90 )
| ~ ( epred2_1 @ X85 ) )
& ( ~ ( in @ X92 @ X85 )
| ~ ( in @ X92 @ X92 )
| ~ ( epred2_1 @ X85 ) )
& ( ( in @ ( esk13_2 @ X85 @ X93 ) @ X93 )
| ( X93 = emptyset )
| ~ ( in @ X93 @ ( powerset @ X85 ) )
| ~ ( epred2_1 @ X85 ) )
& ( ~ ( in @ X95 @ X93 )
| ( ( esk13_2 @ X85 @ X93 )
= X95 )
| ( in @ ( esk13_2 @ X85 @ X93 ) @ X95 )
| ( X93 = emptyset )
| ~ ( in @ X93 @ ( powerset @ X85 ) )
| ~ ( epred2_1 @ X85 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).
thf(c_0_22,negated_conjecture,
~ ( subset @ esk7_0 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ X1 @ X2 )
| ~ ( epred2_1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
in @ esk7_0 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_25,negated_conjecture,
epred2_1 @ esk6_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU818^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 16:17:23 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.48 Running higher-order theorem proving
% 0.19/0.48 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/benchmark/theBenchmark.p
% 0.19/0.50 # Version: 3.1.0-ho
% 0.19/0.50 # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.19/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.50 # Starting lpo1_def_fix with 300s (1) cores
% 0.19/0.50 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.19/0.50 # ehoh_best_sine_rwall with pid 25699 completed with status 0
% 0.19/0.50 # Result found by ehoh_best_sine_rwall
% 0.19/0.50 # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.19/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.50 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.50 # Search class: HGHSF-FFMF21-SSFFMFNN
% 0.19/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.19/0.50 # new_ho_10 with pid 25703 completed with status 0
% 0.19/0.50 # Result found by new_ho_10
% 0.19/0.50 # Preprocessing class: HSSSSLSSSLSNSFN.
% 0.19/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.50 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.19/0.50 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.19/0.50 # Search class: HGHSF-FFMF21-SSFFMFNN
% 0.19/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.19/0.50 # Preprocessing time : 0.001 s
% 0.19/0.50 # Presaturation interreduction done
% 0.19/0.50
% 0.19/0.50 # Proof found!
% 0.19/0.50 # SZS status Theorem
% 0.19/0.50 # SZS output start CNFRefutation
% See solution above
% 0.19/0.50 # Parsed axioms : 19
% 0.19/0.50 # Removed by relevancy pruning/SinE : 11
% 0.19/0.50 # Initial clauses : 61
% 0.19/0.50 # Removed in clause preprocessing : 0
% 0.19/0.50 # Initial clauses in saturation : 61
% 0.19/0.50 # Processed clauses : 66
% 0.19/0.50 # ...of these trivial : 0
% 0.19/0.50 # ...subsumed : 0
% 0.19/0.50 # ...remaining for further processing : 66
% 0.19/0.50 # Other redundant clauses eliminated : 0
% 0.19/0.50 # Clauses deleted for lack of memory : 0
% 0.19/0.50 # Backward-subsumed : 0
% 0.19/0.50 # Backward-rewritten : 0
% 0.19/0.50 # Generated clauses : 1
% 0.19/0.50 # ...of the previous two non-redundant : 0
% 0.19/0.50 # ...aggressively subsumed : 0
% 0.19/0.50 # Contextual simplify-reflections : 0
% 0.19/0.50 # Paramodulations : 1
% 0.19/0.50 # Factorizations : 0
% 0.19/0.50 # NegExts : 0
% 0.19/0.50 # Equation resolutions : 0
% 0.19/0.50 # Disequality decompositions : 0
% 0.19/0.50 # Total rewrite steps : 2
% 0.19/0.50 # ...of those cached : 0
% 0.19/0.50 # Propositional unsat checks : 0
% 0.19/0.50 # Propositional check models : 0
% 0.19/0.50 # Propositional check unsatisfiable : 0
% 0.19/0.50 # Propositional clauses : 0
% 0.19/0.50 # Propositional clauses after purity: 0
% 0.19/0.50 # Propositional unsat core size : 0
% 0.19/0.50 # Propositional preprocessing time : 0.000
% 0.19/0.50 # Propositional encoding time : 0.000
% 0.19/0.50 # Propositional solver time : 0.000
% 0.19/0.50 # Success case prop preproc time : 0.000
% 0.19/0.50 # Success case prop encoding time : 0.000
% 0.19/0.50 # Success case prop solver time : 0.000
% 0.19/0.50 # Current number of processed clauses : 5
% 0.19/0.50 # Positive orientable unit clauses : 2
% 0.19/0.50 # Positive unorientable unit clauses: 0
% 0.19/0.50 # Negative unit clauses : 1
% 0.19/0.50 # Non-unit-clauses : 2
% 0.19/0.50 # Current number of unprocessed clauses: 56
% 0.19/0.50 # ...number of literals in the above : 270
% 0.19/0.50 # Current number of archived formulas : 0
% 0.19/0.50 # Current number of archived clauses : 61
% 0.19/0.50 # Clause-clause subsumption calls (NU) : 932
% 0.19/0.50 # Rec. Clause-clause subsumption calls : 158
% 0.19/0.50 # Non-unit clause-clause subsumptions : 0
% 0.19/0.50 # Unit Clause-clause subsumption calls : 0
% 0.19/0.50 # Rewrite failures with RHS unbound : 0
% 0.19/0.50 # BW rewrite match attempts : 0
% 0.19/0.50 # BW rewrite match successes : 0
% 0.19/0.50 # Condensation attempts : 66
% 0.19/0.50 # Condensation successes : 0
% 0.19/0.50 # Termbank termtop insertions : 6632
% 0.19/0.50 # Search garbage collected termcells : 1245
% 0.19/0.50
% 0.19/0.50 # -------------------------------------------------
% 0.19/0.50 # User time : 0.009 s
% 0.19/0.50 # System time : 0.002 s
% 0.19/0.50 # Total time : 0.012 s
% 0.19/0.50 # Maximum resident set size: 2096 pages
% 0.19/0.50
% 0.19/0.50 # -------------------------------------------------
% 0.19/0.50 # User time : 0.010 s
% 0.19/0.50 # System time : 0.004 s
% 0.19/0.50 # Total time : 0.014 s
% 0.19/0.50 # Maximum resident set size: 1716 pages
% 0.19/0.50 % E---3.1 exiting
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------