TSTP Solution File: SEU820^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 03:30:34 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 32
% Syntax : Number of formulae : 64 ( 18 unt; 22 typ; 0 def)
% Number of atoms : 431 ( 53 equ; 0 cnn)
% Maximal formula atoms : 97 ( 10 avg)
% Number of connectives : 1098 ( 106 ~; 188 |; 90 &; 619 @)
% ( 4 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 14 con; 0-2 aty)
% Number of variables : 107 ( 12 ^ 89 !; 6 ?; 107 :)
% 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,
vacuousDall: $o ).
thf(decl_27,type,
subset: $i > $i > $o ).
thf(decl_28,type,
subsetemptysetimpeq: $o ).
thf(decl_29,type,
powersetE1: $o ).
thf(decl_30,type,
transitiveset: $i > $o ).
thf(decl_31,type,
stricttotalorderedByIn: $i > $o ).
thf(decl_32,type,
wellorderedByIn: $i > $o ).
thf(decl_33,type,
ordinal: $i > $o ).
thf(decl_34,type,
epred1_0: $o ).
thf(decl_35,type,
esk1_0: $i ).
thf(decl_36,type,
esk2_0: $i ).
thf(decl_37,type,
esk3_0: $i ).
thf(decl_38,type,
esk4_1: $i > $i ).
thf(decl_39,type,
esk5_0: $i ).
thf(decl_40,type,
esk6_0: $i ).
thf(decl_41,type,
esk7_0: $i ).
thf(decl_42,type,
esk8_0: $i ).
thf(decl_43,type,
esk9_0: $i ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [X3: $i] :
( ( stricttotalorderedByIn @ X3 )
& ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X3 ) )
=> ( ( nonempty @ X5 )
=> ? [X1: $i] :
( ( in @ X1 @ X5 )
& ! [X6: $i] :
( ( in @ X6 @ X5 )
=> ( ( X1 = X6 )
| ( in @ X1 @ X6 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X1: $i] : ( X1 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(stricttotalorderedByIn,axiom,
( stricttotalorderedByIn
= ( ^ [X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( ( in @ X1 @ X5 )
& ( in @ X5 @ X6 ) )
=> ( in @ X1 @ X6 ) ) ) ) )
& ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ! [X6: $i] :
( ( in @ X6 @ X3 )
=> ( ( X5 = X6 )
| ( in @ X5 @ X6 )
| ( in @ X6 @ X5 ) ) ) )
& ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ~ ( in @ X5 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(ordinal,axiom,
( ordinal
= ( ^ [X1: $i] :
( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [X3: $i] :
! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( subset @ X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(emptysetOrdinal,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetOrdinal) ).
thf(powersetE1,axiom,
( powersetE1
<=> ! [X3: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X3: $i] :
( ( subset @ X3 @ emptyset )
=> ( X3 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X2: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(c_0_9,plain,
( wellorderedByIn
= ( ^ [Z0: $i] :
( ! [X12: $i] :
( ( in @ X12 @ Z0 )
=> ! [X13: $i] :
( ( in @ X13 @ Z0 )
=> ! [X14: $i] :
( ( in @ X14 @ Z0 )
=> ( ( ( in @ X12 @ X13 )
& ( in @ X13 @ X14 ) )
=> ( in @ X12 @ X14 ) ) ) ) )
& ! [X15: $i] :
( ( in @ X15 @ Z0 )
=> ! [X16: $i] :
( ( in @ X16 @ Z0 )
=> ( ( X15 = X16 )
| ( in @ X15 @ X16 )
| ( in @ X16 @ X15 ) ) ) )
& ! [X17: $i] :
( ( in @ X17 @ Z0 )
=> ~ ( in @ X17 @ X17 ) )
& ! [X5: $i] :
( ( in @ X5 @ ( powerset @ Z0 ) )
=> ( ( X5 != emptyset )
=> ? [X1: $i] :
( ( in @ X1 @ X5 )
& ! [X6: $i] :
( ( in @ X6 @ X5 )
=> ( ( X1 = X6 )
| ( in @ X1 @ X6 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[wellorderedByIn]) ).
thf(c_0_10,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_11,plain,
( stricttotalorderedByIn
= ( ^ [Z0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ Z0 )
=> ! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ! [X6: $i] :
( ( in @ X6 @ Z0 )
=> ( ( ( in @ X1 @ X5 )
& ( in @ X5 @ X6 ) )
=> ( in @ X1 @ X6 ) ) ) ) )
& ! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ! [X6: $i] :
( ( in @ X6 @ Z0 )
=> ( ( X5 = X6 )
| ( in @ X5 @ X6 )
| ( in @ X6 @ X5 ) ) ) )
& ! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ~ ( in @ X5 @ X5 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[stricttotalorderedByIn]) ).
thf(c_0_12,plain,
( ordinal
= ( ^ [Z0: $i] :
( ! [X18: $i] :
( ( in @ X18 @ Z0 )
=> ( subset @ X18 @ Z0 ) )
& ! [X19: $i] :
( ( in @ X19 @ Z0 )
=> ! [X20: $i] :
( ( in @ X20 @ Z0 )
=> ! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ( ( ( in @ X19 @ X20 )
& ( in @ X20 @ X21 ) )
=> ( in @ X19 @ X21 ) ) ) ) )
& ! [X22: $i] :
( ( in @ X22 @ Z0 )
=> ! [X23: $i] :
( ( in @ X23 @ Z0 )
=> ( ( X22 = X23 )
| ( in @ X22 @ X23 )
| ( in @ X23 @ X22 ) ) ) )
& ! [X24: $i] :
( ( in @ X24 @ Z0 )
=> ~ ( in @ X24 @ X24 ) )
& ! [X25: $i] :
( ( in @ X25 @ ( powerset @ Z0 ) )
=> ( ( X25 != emptyset )
=> ? [X26: $i] :
( ( in @ X26 @ X25 )
& ! [X27: $i] :
( ( in @ X27 @ X25 )
=> ( ( X26 = X27 )
| ( in @ X26 @ X27 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ordinal]) ).
thf(c_0_13,plain,
( wellorderedByIn
= ( ^ [Z0: $i] :
( ! [X12: $i] :
( ( in @ X12 @ Z0 )
=> ! [X13: $i] :
( ( in @ X13 @ Z0 )
=> ! [X14: $i] :
( ( in @ X14 @ Z0 )
=> ( ( ( in @ X12 @ X13 )
& ( in @ X13 @ X14 ) )
=> ( in @ X12 @ X14 ) ) ) ) )
& ! [X15: $i] :
( ( in @ X15 @ Z0 )
=> ! [X16: $i] :
( ( in @ X16 @ Z0 )
=> ( ( X15 = X16 )
| ( in @ X15 @ X16 )
| ( in @ X16 @ X15 ) ) ) )
& ! [X17: $i] :
( ( in @ X17 @ Z0 )
=> ~ ( in @ X17 @ X17 ) )
& ! [X5: $i] :
( ( in @ X5 @ ( powerset @ Z0 ) )
=> ( ( X5 != emptyset )
=> ? [X1: $i] :
( ( in @ X1 @ X5 )
& ! [X6: $i] :
( ( in @ X6 @ X5 )
=> ( ( X1 = X6 )
| ( in @ X1 @ X6 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_14,plain,
( transitiveset
= ( ^ [Z0: $i] :
! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ( subset @ X5 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitiveset]) ).
thf(c_0_15,plain,
( ordinal
= ( ^ [Z0: $i] :
( ! [X18: $i] :
( ( in @ X18 @ Z0 )
=> ( subset @ X18 @ Z0 ) )
& ! [X19: $i] :
( ( in @ X19 @ Z0 )
=> ! [X20: $i] :
( ( in @ X20 @ Z0 )
=> ! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ( ( ( in @ X19 @ X20 )
& ( in @ X20 @ X21 ) )
=> ( in @ X19 @ X21 ) ) ) ) )
& ! [X22: $i] :
( ( in @ X22 @ Z0 )
=> ! [X23: $i] :
( ( in @ X23 @ Z0 )
=> ( ( X22 = X23 )
| ( in @ X22 @ X23 )
| ( in @ X23 @ X22 ) ) ) )
& ! [X24: $i] :
( ( in @ X24 @ Z0 )
=> ~ ( in @ X24 @ X24 ) )
& ! [X25: $i] :
( ( in @ X25 @ ( powerset @ Z0 ) )
=> ( ( X25 != emptyset )
=> ? [X26: $i] :
( ( in @ X26 @ X25 )
& ! [X27: $i] :
( ( in @ X27 @ X25 )
=> ( ( X26 = X27 )
| ( in @ X26 @ X27 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_16,plain,
( epred1_0
<=> ( ! [X34: $i] :
( ( in @ X34 @ emptyset )
=> ! [X35: $i] :
( ( in @ X35 @ emptyset )
=> ! [X36: $i] :
( ( in @ X36 @ emptyset )
=> ( ( ( in @ X34 @ X35 )
& ( in @ X35 @ X36 ) )
=> ( in @ X34 @ X36 ) ) ) ) )
& ! [X37: $i] :
( ( in @ X37 @ emptyset )
=> ! [X38: $i] :
( ( in @ X38 @ emptyset )
=> ( ( X37 = X38 )
| ( in @ X37 @ X38 )
| ( in @ X38 @ X37 ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_17,negated_conjecture,
~ ( ! [X28: $i > $o,X29: $i] :
( ( in @ X29 @ emptyset )
=> ( X28 @ X29 ) )
=> ( ! [X30: $i] :
( ( subset @ X30 @ emptyset )
=> ( X30 = emptyset ) )
=> ( ! [X31: $i,X32: $i] :
( ( in @ X32 @ ( powerset @ X31 ) )
=> ( subset @ X32 @ X31 ) )
=> ( ! [X33: $i] :
( ( in @ X33 @ emptyset )
=> ( subset @ X33 @ emptyset ) )
& epred1_0
& ! [X39: $i] :
( ( in @ X39 @ emptyset )
=> ~ ( in @ X39 @ X39 ) )
& ! [X40: $i] :
( ( in @ X40 @ ( powerset @ emptyset ) )
=> ( ( X40 != emptyset )
=> ? [X41: $i] :
( ( in @ X41 @ X40 )
& ! [X42: $i] :
( ( in @ X42 @ X40 )
=> ( ( X41 = X42 )
| ( in @ X41 @ X42 ) ) ) ) ) ) ) ) ) ),
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(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[emptysetOrdinal]),c_0_15]),powersetE1]),subsetemptysetimpeq]),vacuousDall])]),c_0_16]) ).
thf(c_0_18,plain,
( ( ! [X34: $i] :
( ( in @ X34 @ emptyset )
=> ! [X35: $i] :
( ( in @ X35 @ emptyset )
=> ! [X36: $i] :
( ( in @ X36 @ emptyset )
=> ( ( ( in @ X34 @ X35 )
& ( in @ X35 @ X36 ) )
=> ( in @ X34 @ X36 ) ) ) ) )
& ! [X37: $i] :
( ( in @ X37 @ emptyset )
=> ! [X38: $i] :
( ( in @ X38 @ emptyset )
=> ( ( X37 = X38 )
| ( in @ X37 @ X38 )
| ( in @ X38 @ X37 ) ) ) ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X43: $i > $o,X44: $i,X45: $i,X46: $i,X47: $i,X51: $i] :
( ( ~ ( in @ X44 @ emptyset )
| ( X43 @ X44 ) )
& ( ~ ( subset @ X45 @ emptyset )
| ( X45 = emptyset ) )
& ( ~ ( in @ X47 @ ( powerset @ X46 ) )
| ( subset @ X47 @ X46 ) )
& ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( esk3_0 != emptyset )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( X51
!= ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( esk3_0 != emptyset )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( X51
!= ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ( in @ esk1_0 @ emptyset ) )
& ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( esk3_0 != emptyset )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( X51
!= ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ emptyset )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( esk3_0 != emptyset )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ( X51
!= ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) )
& ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
| ~ ( in @ X51 @ esk3_0 )
| ( in @ esk2_0 @ esk2_0 )
| ~ epred1_0
| ~ ( subset @ esk1_0 @ emptyset ) ) ),
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_17])])])])])]) ).
thf(c_0_20,plain,
( ( ( in @ esk8_0 @ emptyset )
| ( in @ esk5_0 @ emptyset )
| epred1_0 )
& ( ( in @ esk9_0 @ emptyset )
| ( in @ esk5_0 @ emptyset )
| epred1_0 )
& ( ( esk8_0 != esk9_0 )
| ( in @ esk5_0 @ emptyset )
| epred1_0 )
& ( ~ ( in @ esk8_0 @ esk9_0 )
| ( in @ esk5_0 @ emptyset )
| epred1_0 )
& ( ~ ( in @ esk9_0 @ esk8_0 )
| ( in @ esk5_0 @ emptyset )
| epred1_0 )
& ( ( in @ esk8_0 @ emptyset )
| ( in @ esk6_0 @ emptyset )
| epred1_0 )
& ( ( in @ esk9_0 @ emptyset )
| ( in @ esk6_0 @ emptyset )
| epred1_0 )
& ( ( esk8_0 != esk9_0 )
| ( in @ esk6_0 @ emptyset )
| epred1_0 )
& ( ~ ( in @ esk8_0 @ esk9_0 )
| ( in @ esk6_0 @ emptyset )
| epred1_0 )
& ( ~ ( in @ esk9_0 @ esk8_0 )
| ( in @ esk6_0 @ emptyset )
| epred1_0 )
& ( ( in @ esk8_0 @ emptyset )
| ( in @ esk7_0 @ emptyset )
| epred1_0 )
& ( ( in @ esk9_0 @ emptyset )
| ( in @ esk7_0 @ emptyset )
| epred1_0 )
& ( ( esk8_0 != esk9_0 )
| ( in @ esk7_0 @ emptyset )
| epred1_0 )
& ( ~ ( in @ esk8_0 @ esk9_0 )
| ( in @ esk7_0 @ emptyset )
| epred1_0 )
& ( ~ ( in @ esk9_0 @ esk8_0 )
| ( in @ esk7_0 @ emptyset )
| epred1_0 )
& ( ( in @ esk8_0 @ emptyset )
| ( in @ esk5_0 @ esk6_0 )
| epred1_0 )
& ( ( in @ esk9_0 @ emptyset )
| ( in @ esk5_0 @ esk6_0 )
| epred1_0 )
& ( ( esk8_0 != esk9_0 )
| ( in @ esk5_0 @ esk6_0 )
| epred1_0 )
& ( ~ ( in @ esk8_0 @ esk9_0 )
| ( in @ esk5_0 @ esk6_0 )
| epred1_0 )
& ( ~ ( in @ esk9_0 @ esk8_0 )
| ( in @ esk5_0 @ esk6_0 )
| epred1_0 )
& ( ( in @ esk8_0 @ emptyset )
| ( in @ esk6_0 @ esk7_0 )
| epred1_0 )
& ( ( in @ esk9_0 @ emptyset )
| ( in @ esk6_0 @ esk7_0 )
| epred1_0 )
& ( ( esk8_0 != esk9_0 )
| ( in @ esk6_0 @ esk7_0 )
| epred1_0 )
& ( ~ ( in @ esk8_0 @ esk9_0 )
| ( in @ esk6_0 @ esk7_0 )
| epred1_0 )
& ( ~ ( in @ esk9_0 @ esk8_0 )
| ( in @ esk6_0 @ esk7_0 )
| epred1_0 )
& ( ( in @ esk8_0 @ emptyset )
| ~ ( in @ esk5_0 @ esk7_0 )
| epred1_0 )
& ( ( in @ esk9_0 @ emptyset )
| ~ ( in @ esk5_0 @ esk7_0 )
| epred1_0 )
& ( ( esk8_0 != esk9_0 )
| ~ ( in @ esk5_0 @ esk7_0 )
| epred1_0 )
& ( ~ ( in @ esk8_0 @ esk9_0 )
| ~ ( in @ esk5_0 @ esk7_0 )
| epred1_0 )
& ( ~ ( in @ esk9_0 @ esk8_0 )
| ~ ( in @ esk5_0 @ esk7_0 )
| epred1_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_18])])])])]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i > $o,X1: $i] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,plain,
( ( in @ esk8_0 @ emptyset )
| ( in @ esk7_0 @ emptyset )
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
( ( in @ esk8_0 @ emptyset )
| epred1_0
| ~ ( in @ esk5_0 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i > $o] :
( ( in @ esk8_0 @ emptyset )
| ( X2 @ esk7_0 )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,plain,
( ( in @ esk8_0 @ emptyset )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_26,plain,
( ( in @ esk7_0 @ emptyset )
| epred1_0
| ~ ( in @ esk9_0 @ esk8_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,negated_conjecture,
! [X2: $i > $o] :
( ( X2 @ esk8_0 )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
thf(c_0_28,plain,
( ( in @ esk7_0 @ emptyset )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_29,plain,
( epred1_0
| ~ ( in @ esk9_0 @ esk8_0 )
| ~ ( in @ esk5_0 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_30,negated_conjecture,
! [X2: $i > $o] :
( ( X2 @ esk7_0 )
| epred1_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
thf(c_0_31,negated_conjecture,
( ( in @ esk3_0 @ ( powerset @ emptyset ) )
| ( in @ esk2_0 @ emptyset )
| ( in @ esk1_0 @ emptyset )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_32,plain,
epred1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X3: $i] :
( ( subset @ X1 @ X3 )
| ~ ( in @ X1 @ ( powerset @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_34,negated_conjecture,
( ( in @ esk3_0 @ ( powerset @ emptyset ) )
| ( in @ esk2_0 @ emptyset )
| ( in @ esk1_0 @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
thf(c_0_35,negated_conjecture,
( ( in @ esk2_0 @ emptyset )
| ( in @ esk1_0 @ emptyset )
| ( esk3_0 != emptyset )
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
( ( X1 = emptyset )
| ~ ( subset @ X1 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_37,negated_conjecture,
( ( in @ esk1_0 @ emptyset )
| ( in @ esk2_0 @ emptyset )
| ( subset @ esk3_0 @ emptyset ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,negated_conjecture,
( ( in @ esk2_0 @ emptyset )
| ( in @ esk1_0 @ emptyset )
| ( esk3_0 != emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_32])]) ).
thf(c_0_39,negated_conjecture,
( ( in @ esk2_0 @ emptyset )
| ( in @ esk1_0 @ emptyset ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
thf(c_0_40,negated_conjecture,
! [X2: $i > $o] :
( ( in @ esk2_0 @ emptyset )
| ( X2 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
thf(c_0_41,negated_conjecture,
$false,
inference(flex_resolve,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:12:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 # Version: 3.1.0-ho
% 0.21/0.51 # partial match(1): HSSSSLSSSLSNSFA
% 0.21/0.51 # Preprocessing class: HSSSSLSSMLSNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.51 # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.51 # Starting post_as_ho4 with 300s (1) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # post_as_ho5 with pid 21841 completed with status 8
% 0.21/0.51 # sh5l with pid 21844 completed with status 0
% 0.21/0.51 # Result found by sh5l
% 0.21/0.51 # partial match(1): HSSSSLSSSLSNSFA
% 0.21/0.51 # Preprocessing class: HSSSSLSSMLSNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.51 # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.51 # Starting post_as_ho4 with 300s (1) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.51 # Search class: HGUSF-FFMM11-SSFSMFBN
% 0.21/0.51 # partial match(4): HGHSF-FFMM11-SSSFFFBN
% 0.21/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 181s (1) cores
% 0.21/0.51 # ho_unfolding_3 with pid 21850 completed with status 0
% 0.21/0.51 # Result found by ho_unfolding_3
% 0.21/0.51 # partial match(1): HSSSSLSSSLSNSFA
% 0.21/0.51 # Preprocessing class: HSSSSLSSMLSNSFA.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.51 # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.51 # Starting post_as_ho4 with 300s (1) cores
% 0.21/0.51 # Starting sh5l with 300s (1) cores
% 0.21/0.51 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.51 # Search class: HGUSF-FFMM11-SSFSMFBN
% 0.21/0.51 # partial match(4): HGHSF-FFMM11-SSSFFFBN
% 0.21/0.51 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 181s (1) cores
% 0.21/0.51 # Preprocessing time : 0.002 s
% 0.21/0.51 # Presaturation interreduction done
% 0.21/0.51
% 0.21/0.51 # Proof found!
% 0.21/0.51 # SZS status Theorem
% 0.21/0.51 # SZS output start CNFRefutation
% See solution above
% 0.21/0.51 # Parsed axioms : 21
% 0.21/0.51 # Removed by relevancy pruning/SinE : 12
% 0.21/0.51 # Initial clauses : 53
% 0.21/0.51 # Removed in clause preprocessing : 0
% 0.21/0.51 # Initial clauses in saturation : 53
% 0.21/0.51 # Processed clauses : 140
% 0.21/0.51 # ...of these trivial : 0
% 0.21/0.51 # ...subsumed : 1
% 0.21/0.51 # ...remaining for further processing : 138
% 0.21/0.51 # Other redundant clauses eliminated : 0
% 0.21/0.51 # Clauses deleted for lack of memory : 0
% 0.21/0.51 # Backward-subsumed : 33
% 0.21/0.51 # Backward-rewritten : 36
% 0.21/0.51 # Generated clauses : 113
% 0.21/0.51 # ...of the previous two non-redundant : 133
% 0.21/0.51 # ...aggressively subsumed : 0
% 0.21/0.51 # Contextual simplify-reflections : 3
% 0.21/0.51 # Paramodulations : 113
% 0.21/0.51 # Factorizations : 0
% 0.21/0.51 # NegExts : 0
% 0.21/0.51 # Equation resolutions : 0
% 0.21/0.51 # Disequality decompositions : 0
% 0.21/0.51 # Total rewrite steps : 36
% 0.21/0.51 # ...of those cached : 35
% 0.21/0.51 # Propositional unsat checks : 0
% 0.21/0.51 # Propositional check models : 0
% 0.21/0.51 # Propositional check unsatisfiable : 0
% 0.21/0.51 # Propositional clauses : 0
% 0.21/0.51 # Propositional clauses after purity: 0
% 0.21/0.51 # Propositional unsat core size : 0
% 0.21/0.51 # Propositional preprocessing time : 0.000
% 0.21/0.51 # Propositional encoding time : 0.000
% 0.21/0.51 # Propositional solver time : 0.000
% 0.21/0.51 # Success case prop preproc time : 0.000
% 0.21/0.51 # Success case prop encoding time : 0.000
% 0.21/0.51 # Success case prop solver time : 0.000
% 0.21/0.51 # Current number of processed clauses : 16
% 0.21/0.51 # Positive orientable unit clauses : 1
% 0.21/0.51 # Positive unorientable unit clauses: 0
% 0.21/0.51 # Negative unit clauses : 0
% 0.21/0.51 # Non-unit-clauses : 15
% 0.21/0.51 # Current number of unprocessed clauses: 71
% 0.21/0.51 # ...number of literals in the above : 364
% 0.21/0.51 # Current number of archived formulas : 0
% 0.21/0.51 # Current number of archived clauses : 122
% 0.21/0.51 # Clause-clause subsumption calls (NU) : 1011
% 0.21/0.51 # Rec. Clause-clause subsumption calls : 589
% 0.21/0.51 # Non-unit clause-clause subsumptions : 34
% 0.21/0.51 # Unit Clause-clause subsumption calls : 3
% 0.21/0.51 # Rewrite failures with RHS unbound : 0
% 0.21/0.51 # BW rewrite match attempts : 1
% 0.21/0.51 # BW rewrite match successes : 1
% 0.21/0.51 # Condensation attempts : 140
% 0.21/0.51 # Condensation successes : 0
% 0.21/0.51 # Termbank termtop insertions : 6183
% 0.21/0.51 # Search garbage collected termcells : 782
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.015 s
% 0.21/0.51 # System time : 0.003 s
% 0.21/0.51 # Total time : 0.018 s
% 0.21/0.51 # Maximum resident set size: 1912 pages
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.050 s
% 0.21/0.51 # System time : 0.022 s
% 0.21/0.51 # Total time : 0.072 s
% 0.21/0.51 # Maximum resident set size: 1728 pages
% 0.21/0.51 % E---3.1 exiting
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------