TSTP Solution File: SEU823^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU823^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 03:30:35 EDT 2024
% Result : Theorem 4.44s 1.03s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 35
% Syntax : Number of formulae : 163 ( 23 unt; 26 typ; 0 def)
% Number of atoms : 991 ( 67 equ; 0 cnn)
% Maximal formula atoms : 145 ( 7 avg)
% Number of connectives : 3351 ( 359 ~; 556 |; 125 &;2158 @)
% ( 5 <=>; 148 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 5 con; 0-2 aty)
% Number of variables : 301 ( 8 ^ 282 !; 11 ?; 301 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
powerset: $i > $i ).
thf(decl_24,type,
nonempty: $i > $o ).
thf(decl_25,type,
transitiveset: $i > $o ).
thf(decl_26,type,
stricttotalorderedByIn: $i > $o ).
thf(decl_27,type,
wellorderedByIn: $i > $o ).
thf(decl_28,type,
ordinal: $i > $o ).
thf(decl_29,type,
ordinalTransSet: $o ).
thf(decl_30,type,
ordinalIrrefl: $o ).
thf(decl_31,type,
epred1_1: $i > $o ).
thf(decl_32,type,
epred2_1: $i > $o ).
thf(decl_33,type,
epred3_1: $i > $o ).
thf(decl_34,type,
esk1_1: $i > $i ).
thf(decl_35,type,
esk2_1: $i > $i ).
thf(decl_36,type,
esk3_2: $i > $i > $i ).
thf(decl_37,type,
esk4_1: $i > $i ).
thf(decl_38,type,
esk5_1: $i > $i ).
thf(decl_39,type,
esk6_2: $i > $i > $i ).
thf(decl_40,type,
esk7_0: $i ).
thf(decl_41,type,
esk8_0: $i ).
thf(decl_42,type,
esk9_1: $i > $i ).
thf(decl_43,type,
esk10_1: $i > $i ).
thf(decl_44,type,
esk11_1: $i > $i ).
thf(decl_45,type,
esk12_1: $i > $i ).
thf(decl_46,type,
esk13_1: $i > $i ).
thf(decl_52,type,
esk19_2: $i > $i > $i ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [X1: $i] :
( ( stricttotalorderedByIn @ X1 )
& ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( nonempty @ X3 )
=> ? [X2: $i] :
( ( in @ X2 @ X3 )
& ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X2 = X4 )
| ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).
thf(stricttotalorderedByIn,axiom,
( stricttotalorderedByIn
= ( ^ [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X3 = X4 )
| ( in @ X3 @ X4 )
| ( in @ X4 @ X3 ) ) ) )
& ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X3 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).
thf(ordinal,axiom,
( ordinal
= ( ^ [X2: $i] :
( ( transitiveset @ X2 )
& ( wellorderedByIn @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).
thf(ordinalTransSet,axiom,
( ordinalTransSet
<=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet) ).
thf(ordinalIrrefl,axiom,
( ordinalIrrefl
<=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ~ ( in @ X1 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalIrrefl) ).
thf(ordinalNoCycle,conjecture,
( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X1: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalNoCycle) ).
thf(c_0_6,plain,
! [X3: $i] :
( ( epred3_1 @ X3 )
<=> ( ( transitiveset @ X3 )
& ! [X68: $i] :
( ( in @ X68 @ X3 )
=> ! [X69: $i] :
( ( in @ X69 @ X3 )
=> ! [X70: $i] :
( ( in @ X70 @ X3 )
=> ( ( ( in @ X68 @ X69 )
& ( in @ X69 @ X70 ) )
=> ( in @ X68 @ X70 ) ) ) ) )
& ! [X71: $i] :
( ( in @ X71 @ X3 )
=> ! [X72: $i] :
( ( in @ X72 @ X3 )
=> ( ( X71 = X72 )
| ( in @ X71 @ X72 )
| ( in @ X72 @ X71 ) ) ) )
& ! [X73: $i] :
( ( in @ X73 @ X3 )
=> ~ ( in @ X73 @ X73 ) )
& ! [X74: $i] :
( ( in @ X74 @ ( powerset @ X3 ) )
=> ( ( nonempty @ X74 )
=> ? [X75: $i] :
( ( in @ X75 @ X74 )
& ! [X76: $i] :
( ( in @ X76 @ X74 )
=> ( ( X75 = X76 )
| ( in @ X75 @ X76 ) ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_7,plain,
! [X45: $i] :
( ( epred1_1 @ X45 )
<=> ( ! [X46: $i] :
( ( in @ X46 @ X45 )
=> ! [X47: $i] :
( ( in @ X47 @ X45 )
=> ! [X48: $i] :
( ( in @ X48 @ X45 )
=> ( ( ( in @ X46 @ X47 )
& ( in @ X47 @ X48 ) )
=> ( in @ X46 @ X48 ) ) ) ) )
& ! [X49: $i] :
( ( in @ X49 @ X45 )
=> ! [X50: $i] :
( ( in @ X50 @ X45 )
=> ( ( X49 = X50 )
| ( in @ X49 @ X50 )
| ( in @ X50 @ X49 ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_8,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 ) )
& ! [X3: $i] :
( ( in @ X3 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X3 )
=> ? [X2: $i] :
( ( in @ X2 @ X3 )
& ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X2 = X4 )
| ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[wellorderedByIn]) ).
thf(c_0_9,plain,
( stricttotalorderedByIn
= ( ^ [Z0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ! [X4: $i] :
( ( in @ X4 @ Z0 )
=> ( ( ( in @ X2 @ X3 )
& ( in @ X3 @ X4 ) )
=> ( in @ X2 @ X4 ) ) ) ) )
& ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ! [X4: $i] :
( ( in @ X4 @ Z0 )
=> ( ( X3 = X4 )
| ( in @ X3 @ X4 )
| ( in @ X4 @ X3 ) ) ) )
& ! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ~ ( in @ X3 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[stricttotalorderedByIn]) ).
thf(c_0_10,plain,
! [X3: $i] :
( ( epred3_1 @ X3 )
=> ( ( transitiveset @ X3 )
& ! [X68: $i] :
( ( in @ X68 @ X3 )
=> ! [X69: $i] :
( ( in @ X69 @ X3 )
=> ! [X70: $i] :
( ( in @ X70 @ X3 )
=> ( ( ( in @ X68 @ X69 )
& ( in @ X69 @ X70 ) )
=> ( in @ X68 @ X70 ) ) ) ) )
& ! [X71: $i] :
( ( in @ X71 @ X3 )
=> ! [X72: $i] :
( ( in @ X72 @ X3 )
=> ( ( X71 = X72 )
| ( in @ X71 @ X72 )
| ( in @ X72 @ X71 ) ) ) )
& ! [X73: $i] :
( ( in @ X73 @ X3 )
=> ~ ( in @ X73 @ X73 ) )
& ! [X74: $i] :
( ( in @ X74 @ ( powerset @ X3 ) )
=> ( ( nonempty @ X74 )
=> ? [X75: $i] :
( ( in @ X75 @ X74 )
& ! [X76: $i] :
( ( in @ X76 @ X74 )
=> ( ( X75 = X76 )
| ( in @ X75 @ X76 ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
! [X45: $i] :
( ( ! [X46: $i] :
( ( in @ X46 @ X45 )
=> ! [X47: $i] :
( ( in @ X47 @ X45 )
=> ! [X48: $i] :
( ( in @ X48 @ X45 )
=> ( ( ( in @ X46 @ X47 )
& ( in @ X47 @ X48 ) )
=> ( in @ X46 @ X48 ) ) ) ) )
& ! [X49: $i] :
( ( in @ X49 @ X45 )
=> ! [X50: $i] :
( ( in @ X50 @ X45 )
=> ( ( X49 = X50 )
| ( in @ X49 @ X50 )
| ( in @ X50 @ X49 ) ) ) ) )
=> ( epred1_1 @ X45 ) ),
inference(split_equiv,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
( ordinal
= ( ^ [Z0: $i] :
( ( transitiveset @ Z0 )
& ! [X18: $i] :
( ( in @ X18 @ Z0 )
=> ! [X19: $i] :
( ( in @ X19 @ Z0 )
=> ! [X20: $i] :
( ( in @ X20 @ Z0 )
=> ( ( ( in @ X18 @ X19 )
& ( in @ X19 @ X20 ) )
=> ( in @ X18 @ X20 ) ) ) ) )
& ! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ! [X22: $i] :
( ( in @ X22 @ Z0 )
=> ( ( X21 = X22 )
| ( in @ X21 @ X22 )
| ( in @ X22 @ X21 ) ) ) )
& ! [X23: $i] :
( ( in @ X23 @ Z0 )
=> ~ ( in @ X23 @ X23 ) )
& ! [X24: $i] :
( ( in @ X24 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X24 )
=> ? [X25: $i] :
( ( in @ X25 @ X24 )
& ! [X26: $i] :
( ( in @ X26 @ X24 )
=> ( ( X25 = X26 )
| ( in @ X25 @ X26 ) ) ) ) ) ) ) ) ),
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 ) )
& ! [X3: $i] :
( ( in @ X3 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X3 )
=> ? [X2: $i] :
( ( in @ X2 @ X3 )
& ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( ( X2 = X4 )
| ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,plain,
! [X104: $i,X105: $i,X106: $i,X107: $i,X108: $i,X109: $i,X110: $i,X111: $i,X113: $i] :
( ( ( transitiveset @ X104 )
| ~ ( epred3_1 @ X104 ) )
& ( ~ ( in @ X105 @ X104 )
| ~ ( in @ X106 @ X104 )
| ~ ( in @ X107 @ X104 )
| ~ ( in @ X105 @ X106 )
| ~ ( in @ X106 @ X107 )
| ( in @ X105 @ X107 )
| ~ ( epred3_1 @ X104 ) )
& ( ~ ( in @ X108 @ X104 )
| ~ ( in @ X109 @ X104 )
| ( X108 = X109 )
| ( in @ X108 @ X109 )
| ( in @ X109 @ X108 )
| ~ ( epred3_1 @ X104 ) )
& ( ~ ( in @ X110 @ X104 )
| ~ ( in @ X110 @ X110 )
| ~ ( epred3_1 @ X104 ) )
& ( ( in @ ( esk19_2 @ X104 @ X111 ) @ X111 )
| ~ ( nonempty @ X111 )
| ~ ( in @ X111 @ ( powerset @ X104 ) )
| ~ ( epred3_1 @ X104 ) )
& ( ~ ( in @ X113 @ X111 )
| ( ( esk19_2 @ X104 @ X111 )
= X113 )
| ( in @ ( esk19_2 @ X104 @ X111 ) @ X113 )
| ~ ( nonempty @ X111 )
| ~ ( in @ X111 @ ( powerset @ X104 ) )
| ~ ( epred3_1 @ X104 ) ) ),
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_10])])])])])]) ).
thf(c_0_15,plain,
! [X92: $i] :
( ( ( in @ ( esk12_1 @ X92 ) @ X92 )
| ( in @ ( esk9_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk13_1 @ X92 ) @ X92 )
| ( in @ ( esk9_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( ( esk12_1 @ X92 )
!= ( esk13_1 @ X92 ) )
| ( in @ ( esk9_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk12_1 @ X92 ) @ ( esk13_1 @ X92 ) )
| ( in @ ( esk9_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk13_1 @ X92 ) @ ( esk12_1 @ X92 ) )
| ( in @ ( esk9_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk12_1 @ X92 ) @ X92 )
| ( in @ ( esk10_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk13_1 @ X92 ) @ X92 )
| ( in @ ( esk10_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( ( esk12_1 @ X92 )
!= ( esk13_1 @ X92 ) )
| ( in @ ( esk10_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk12_1 @ X92 ) @ ( esk13_1 @ X92 ) )
| ( in @ ( esk10_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk13_1 @ X92 ) @ ( esk12_1 @ X92 ) )
| ( in @ ( esk10_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk12_1 @ X92 ) @ X92 )
| ( in @ ( esk11_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk13_1 @ X92 ) @ X92 )
| ( in @ ( esk11_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( ( esk12_1 @ X92 )
!= ( esk13_1 @ X92 ) )
| ( in @ ( esk11_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk12_1 @ X92 ) @ ( esk13_1 @ X92 ) )
| ( in @ ( esk11_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk13_1 @ X92 ) @ ( esk12_1 @ X92 ) )
| ( in @ ( esk11_1 @ X92 ) @ X92 )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk12_1 @ X92 ) @ X92 )
| ( in @ ( esk9_1 @ X92 ) @ ( esk10_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk13_1 @ X92 ) @ X92 )
| ( in @ ( esk9_1 @ X92 ) @ ( esk10_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( ( esk12_1 @ X92 )
!= ( esk13_1 @ X92 ) )
| ( in @ ( esk9_1 @ X92 ) @ ( esk10_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk12_1 @ X92 ) @ ( esk13_1 @ X92 ) )
| ( in @ ( esk9_1 @ X92 ) @ ( esk10_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk13_1 @ X92 ) @ ( esk12_1 @ X92 ) )
| ( in @ ( esk9_1 @ X92 ) @ ( esk10_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk12_1 @ X92 ) @ X92 )
| ( in @ ( esk10_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk13_1 @ X92 ) @ X92 )
| ( in @ ( esk10_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( ( esk12_1 @ X92 )
!= ( esk13_1 @ X92 ) )
| ( in @ ( esk10_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk12_1 @ X92 ) @ ( esk13_1 @ X92 ) )
| ( in @ ( esk10_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk13_1 @ X92 ) @ ( esk12_1 @ X92 ) )
| ( in @ ( esk10_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk12_1 @ X92 ) @ X92 )
| ~ ( in @ ( esk9_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( in @ ( esk13_1 @ X92 ) @ X92 )
| ~ ( in @ ( esk9_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ( ( esk12_1 @ X92 )
!= ( esk13_1 @ X92 ) )
| ~ ( in @ ( esk9_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk12_1 @ X92 ) @ ( esk13_1 @ X92 ) )
| ~ ( in @ ( esk9_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) )
& ( ~ ( in @ ( esk13_1 @ X92 ) @ ( esk12_1 @ X92 ) )
| ~ ( in @ ( esk9_1 @ X92 ) @ ( esk11_1 @ X92 ) )
| ( epred1_1 @ X92 ) ) ),
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_11])])])])]) ).
thf(c_0_16,plain,
( ordinal
= ( ^ [Z0: $i] :
( ( transitiveset @ Z0 )
& ! [X18: $i] :
( ( in @ X18 @ Z0 )
=> ! [X19: $i] :
( ( in @ X19 @ Z0 )
=> ! [X20: $i] :
( ( in @ X20 @ Z0 )
=> ( ( ( in @ X18 @ X19 )
& ( in @ X19 @ X20 ) )
=> ( in @ X18 @ X20 ) ) ) ) )
& ! [X21: $i] :
( ( in @ X21 @ Z0 )
=> ! [X22: $i] :
( ( in @ X22 @ Z0 )
=> ( ( X21 = X22 )
| ( in @ X21 @ X22 )
| ( in @ X22 @ X21 ) ) ) )
& ! [X23: $i] :
( ( in @ X23 @ Z0 )
=> ~ ( in @ X23 @ X23 ) )
& ! [X24: $i] :
( ( in @ X24 @ ( powerset @ Z0 ) )
=> ( ( nonempty @ X24 )
=> ? [X25: $i] :
( ( in @ X25 @ X24 )
& ! [X26: $i] :
( ( in @ X26 @ X24 )
=> ( ( X25 = X26 )
| ( in @ X25 @ X26 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,plain,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X4 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X4 @ X2 )
| ~ ( in @ X1 @ X3 )
| ~ ( in @ X3 @ X4 )
| ~ ( epred3_1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( in @ ( esk11_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,axiom,
( ordinalTransSet
= ( ! [X3: $i] :
( ( ( transitiveset @ X3 )
& ! [X27: $i] :
( ( in @ X27 @ X3 )
=> ! [X28: $i] :
( ( in @ X28 @ X3 )
=> ! [X29: $i] :
( ( in @ X29 @ X3 )
=> ( ( ( in @ X27 @ X28 )
& ( in @ X28 @ X29 ) )
=> ( in @ X27 @ X29 ) ) ) ) )
& ! [X30: $i] :
( ( in @ X30 @ X3 )
=> ! [X31: $i] :
( ( in @ X31 @ X3 )
=> ( ( X30 = X31 )
| ( in @ X30 @ X31 )
| ( in @ X31 @ X30 ) ) ) )
& ! [X32: $i] :
( ( in @ X32 @ X3 )
=> ~ ( in @ X32 @ X32 ) )
& ! [X33: $i] :
( ( in @ X33 @ ( powerset @ X3 ) )
=> ( ( nonempty @ X33 )
=> ? [X34: $i] :
( ( in @ X34 @ X33 )
& ! [X35: $i] :
( ( in @ X35 @ X33 )
=> ( ( X34 = X35 )
| ( in @ X34 @ X35 ) ) ) ) ) ) )
=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[ordinalTransSet,c_0_16]) ).
thf(c_0_20,axiom,
( ordinalIrrefl
= ( ! [X3: $i] :
( ( ( transitiveset @ X3 )
& ! [X36: $i] :
( ( in @ X36 @ X3 )
=> ! [X37: $i] :
( ( in @ X37 @ X3 )
=> ! [X38: $i] :
( ( in @ X38 @ X3 )
=> ( ( ( in @ X36 @ X37 )
& ( in @ X37 @ X38 ) )
=> ( in @ X36 @ X38 ) ) ) ) )
& ! [X39: $i] :
( ( in @ X39 @ X3 )
=> ! [X40: $i] :
( ( in @ X40 @ X3 )
=> ( ( X39 = X40 )
| ( in @ X39 @ X40 )
| ( in @ X40 @ X39 ) ) ) )
& ! [X41: $i] :
( ( in @ X41 @ X3 )
=> ~ ( in @ X41 @ X41 ) )
& ! [X42: $i] :
( ( in @ X42 @ ( powerset @ X3 ) )
=> ( ( nonempty @ X42 )
=> ? [X43: $i] :
( ( in @ X43 @ X42 )
& ! [X44: $i] :
( ( in @ X44 @ X42 )
=> ( ( X43 = X44 )
| ( in @ X43 @ X44 ) ) ) ) ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ~ ( in @ X1 @ X1 ) ) ) ) ),
inference(apply_def,[status(thm)],[ordinalIrrefl,c_0_16]) ).
thf(c_0_21,plain,
! [X57: $i] :
( ( epred2_1 @ X57 )
<=> ( ! [X58: $i] :
( ( in @ X58 @ X57 )
=> ! [X59: $i] :
( ( in @ X59 @ X57 )
=> ! [X60: $i] :
( ( in @ X60 @ X57 )
=> ( ( ( in @ X58 @ X59 )
& ( in @ X59 @ X60 ) )
=> ( in @ X58 @ X60 ) ) ) ) )
& ! [X61: $i] :
( ( in @ X61 @ X57 )
=> ! [X62: $i] :
( ( in @ X62 @ X57 )
=> ( ( X61 = X62 )
| ( in @ X61 @ X62 )
| ( in @ X62 @ X61 ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_22,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( in @ X2 @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ~ ( in @ X3 @ ( esk11_1 @ X1 ) )
| ~ ( in @ X3 @ X1 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X2 @ X1 )
| ~ ( epred3_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_23,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( in @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_24,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( in @ ( esk10_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_25,negated_conjecture,
~ ( ! [X45: $i] :
( ( ( transitiveset @ X45 )
& ( epred1_1 @ X45 )
& ! [X51: $i] :
( ( in @ X51 @ X45 )
=> ~ ( in @ X51 @ X51 ) )
& ! [X52: $i] :
( ( in @ X52 @ ( powerset @ X45 ) )
=> ( ( nonempty @ X52 )
=> ? [X53: $i] :
( ( in @ X53 @ X52 )
& ! [X54: $i] :
( ( in @ X54 @ X52 )
=> ( ( X53 = X54 )
| ( in @ X53 @ X54 ) ) ) ) ) ) )
=> ! [X55: $i,X56: $i] :
( ( in @ X56 @ X45 )
=> ( ( in @ X55 @ X56 )
=> ( in @ X55 @ X45 ) ) ) )
=> ( ! [X57: $i] :
( ( ( transitiveset @ X57 )
& ( epred2_1 @ X57 )
& ! [X63: $i] :
( ( in @ X63 @ X57 )
=> ~ ( in @ X63 @ X63 ) )
& ! [X64: $i] :
( ( in @ X64 @ ( powerset @ X57 ) )
=> ( ( nonempty @ X64 )
=> ? [X65: $i] :
( ( in @ X65 @ X64 )
& ! [X66: $i] :
( ( in @ X66 @ X64 )
=> ( ( X65 = X66 )
| ( in @ X65 @ X66 ) ) ) ) ) ) )
=> ! [X67: $i] :
( ( in @ X67 @ X57 )
=> ~ ( in @ X67 @ X67 ) ) )
=> ! [X3: $i] :
( ( epred3_1 @ X3 )
=> ! [X1: $i] :
( ( in @ X3 @ X1 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ),
inference(apply_def,[status(thm)],[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)],[ordinalNoCycle]),c_0_16]),c_0_19]),c_0_20])]),c_0_7]),c_0_21]),c_0_6]) ).
thf(c_0_26,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( in @ ( esk11_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_27,plain,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( esk11_1 @ X2 ) )
| ( in @ ( esk13_1 @ X2 ) @ X2 )
| ( epred1_1 @ X2 )
| ~ ( in @ X1 @ ( esk10_1 @ X2 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( epred3_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
thf(c_0_28,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( in @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_29,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( in @ ( esk9_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_30,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_31,negated_conjecture,
! [X77: $i,X80: $i,X82: $i,X83: $i,X84: $i,X87: $i,X89: $i] :
( ( ( in @ ( esk2_1 @ X77 ) @ ( powerset @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ X77 )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( nonempty @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ X77 )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( in @ ( esk3_2 @ X77 @ X80 ) @ ( esk2_1 @ X77 ) )
| ~ ( in @ X80 @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ X77 )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( X80
!= ( esk3_2 @ X77 @ X80 ) )
| ~ ( in @ X80 @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ X77 )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ~ ( in @ X80 @ ( esk3_2 @ X77 @ X80 ) )
| ~ ( in @ X80 @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ X77 )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( in @ ( esk2_1 @ X77 ) @ ( powerset @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ ( esk1_1 @ X77 ) )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( nonempty @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ ( esk1_1 @ X77 ) )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( in @ ( esk3_2 @ X77 @ X80 ) @ ( esk2_1 @ X77 ) )
| ~ ( in @ X80 @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ ( esk1_1 @ X77 ) )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( X80
!= ( esk3_2 @ X77 @ X80 ) )
| ~ ( in @ X80 @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ ( esk1_1 @ X77 ) )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ~ ( in @ X80 @ ( esk3_2 @ X77 @ X80 ) )
| ~ ( in @ X80 @ ( esk2_1 @ X77 ) )
| ( in @ ( esk1_1 @ X77 ) @ ( esk1_1 @ X77 ) )
| ~ ( epred1_1 @ X77 )
| ~ ( transitiveset @ X77 )
| ~ ( in @ X83 @ X77 )
| ~ ( in @ X82 @ X83 )
| ( in @ X82 @ X77 ) )
& ( ( in @ ( esk5_1 @ X84 ) @ ( powerset @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ X84 )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( nonempty @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ X84 )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( in @ ( esk6_2 @ X84 @ X87 ) @ ( esk5_1 @ X84 ) )
| ~ ( in @ X87 @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ X84 )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( X87
!= ( esk6_2 @ X84 @ X87 ) )
| ~ ( in @ X87 @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ X84 )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ~ ( in @ X87 @ ( esk6_2 @ X84 @ X87 ) )
| ~ ( in @ X87 @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ X84 )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( in @ ( esk5_1 @ X84 ) @ ( powerset @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ ( esk4_1 @ X84 ) )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( nonempty @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ ( esk4_1 @ X84 ) )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( in @ ( esk6_2 @ X84 @ X87 ) @ ( esk5_1 @ X84 ) )
| ~ ( in @ X87 @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ ( esk4_1 @ X84 ) )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ( X87
!= ( esk6_2 @ X84 @ X87 ) )
| ~ ( in @ X87 @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ ( esk4_1 @ X84 ) )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( ~ ( in @ X87 @ ( esk6_2 @ X84 @ X87 ) )
| ~ ( in @ X87 @ ( esk5_1 @ X84 ) )
| ( in @ ( esk4_1 @ X84 ) @ ( esk4_1 @ X84 ) )
| ~ ( epred2_1 @ X84 )
| ~ ( transitiveset @ X84 )
| ~ ( in @ X89 @ X84 )
| ~ ( in @ X89 @ X89 ) )
& ( epred3_1 @ esk7_0 )
& ( in @ esk7_0 @ esk8_0 )
& ( in @ esk8_0 @ esk7_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_25])])])])])]) ).
thf(c_0_32,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( in @ X2 @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ~ ( in @ X3 @ ( esk11_1 @ X1 ) )
| ~ ( in @ X3 @ X1 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X2 @ X1 )
| ~ ( epred3_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
thf(c_0_33,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( in @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_34,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( in @ ( esk10_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_35,plain,
! [X1: $i] :
( ( in @ ( esk13_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( epred3_1 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]) ).
thf(c_0_36,negated_conjecture,
epred3_1 @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_37,plain,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( esk11_1 @ X2 ) )
| ( in @ ( esk12_1 @ X2 ) @ X2 )
| ( epred1_1 @ X2 )
| ~ ( in @ X1 @ ( esk10_1 @ X2 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( epred3_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_38,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( in @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_39,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( in @ ( esk9_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_40,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_41,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( X1 = X3 )
| ( in @ X1 @ X3 )
| ( in @ X3 @ X1 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( epred3_1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_42,negated_conjecture,
( ( in @ ( esk13_1 @ esk7_0 ) @ esk7_0 )
| ( epred1_1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_43,plain,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( epred3_1 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
thf(c_0_44,plain,
! [X1: $i] :
( ( X1
= ( esk13_1 @ esk7_0 ) )
| ( in @ ( esk13_1 @ esk7_0 ) @ X1 )
| ( in @ X1 @ ( esk13_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_36])]) ).
thf(c_0_45,negated_conjecture,
( ( in @ ( esk12_1 @ esk7_0 ) @ esk7_0 )
| ( epred1_1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
thf(c_0_46,plain,
! [X1: $i] :
( ( in @ ( esk11_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk13_1 @ X1 ) @ ( esk12_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_47,plain,
( ( ( esk13_1 @ esk7_0 )
= ( esk12_1 @ esk7_0 ) )
| ( in @ ( esk12_1 @ esk7_0 ) @ ( esk13_1 @ esk7_0 ) )
| ( in @ ( esk13_1 @ esk7_0 ) @ ( esk12_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_48,plain,
! [X1: $i] :
( ( in @ ( esk11_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_49,plain,
! [X1: $i] :
( ( in @ ( esk11_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ( ( esk12_1 @ X1 )
!= ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_50,plain,
( ( in @ ( esk11_1 @ esk7_0 ) @ esk7_0 )
| ( epred1_1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]) ).
thf(c_0_51,plain,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk13_1 @ X1 ) @ ( esk12_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_52,plain,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_53,plain,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ( ( esk12_1 @ X1 )
!= ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_54,plain,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk13_1 @ X1 ) @ ( esk12_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_55,plain,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_56,plain,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ( ( esk12_1 @ X1 )
!= ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_57,negated_conjecture,
in @ esk8_0 @ esk7_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_58,plain,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( esk11_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 )
| ~ ( in @ X2 @ ( esk11_1 @ esk7_0 ) )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_50]),c_0_36])]) ).
thf(c_0_59,plain,
( ( in @ ( esk10_1 @ esk7_0 ) @ ( esk11_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_47]),c_0_52]),c_0_53]) ).
thf(c_0_60,plain,
( ( in @ ( esk10_1 @ esk7_0 ) @ esk7_0 )
| ( epred1_1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_47]),c_0_55]),c_0_56]) ).
thf(c_0_61,plain,
! [X1: $i] :
( ( in @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk13_1 @ X1 ) @ ( esk12_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_62,plain,
! [X1: $i] :
( ( in @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_63,plain,
! [X1: $i] :
( ( in @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( epred1_1 @ X1 )
| ( ( esk12_1 @ X1 )
!= ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_64,plain,
! [X1: $i] :
( ( in @ ( esk9_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk13_1 @ X1 ) @ ( esk12_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_65,plain,
! [X1: $i] :
( ( in @ ( esk9_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ~ ( in @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_66,plain,
! [X1: $i] :
( ( in @ ( esk9_1 @ X1 ) @ X1 )
| ( epred1_1 @ X1 )
| ( ( esk12_1 @ X1 )
!= ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_67,plain,
! [X1: $i,X2: $i] :
( ~ ( in @ X1 @ X2 )
| ~ ( in @ X1 @ X1 )
| ~ ( epred3_1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ esk8_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_57]),c_0_36])]) ).
thf(c_0_69,negated_conjecture,
in @ esk7_0 @ esk8_0,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_70,plain,
! [X1: $i] :
( ( in @ X1 @ ( esk11_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 )
| ~ ( in @ X1 @ ( esk10_1 @ esk7_0 ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
thf(c_0_71,plain,
( ( in @ ( esk9_1 @ esk7_0 ) @ ( esk10_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_62]),c_0_63]) ).
thf(c_0_72,plain,
( ( in @ ( esk9_1 @ esk7_0 ) @ esk7_0 )
| ( epred1_1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_47]),c_0_65]),c_0_66]) ).
thf(c_0_73,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ X3 @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( in @ X2 @ X1 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_74,plain,
! [X1: $i] :
( ( transitiveset @ X1 )
| ~ ( epred3_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_75,negated_conjecture,
~ ( in @ esk8_0 @ esk8_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_57]),c_0_36])]) ).
thf(c_0_76,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk8_0 )
| ~ ( in @ esk7_0 @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_77,plain,
! [X1: $i] :
( ( epred1_1 @ X1 )
| ~ ( in @ ( esk13_1 @ X1 ) @ ( esk12_1 @ X1 ) )
| ~ ( in @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_78,plain,
( ( in @ ( esk9_1 @ esk7_0 ) @ ( esk11_1 @ esk7_0 ) )
| ( epred1_1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
thf(c_0_79,plain,
! [X1: $i] :
( ( epred1_1 @ X1 )
| ~ ( in @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
| ~ ( in @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_80,plain,
! [X1: $i] :
( ( epred1_1 @ X1 )
| ( ( esk12_1 @ X1 )
!= ( esk13_1 @ X1 ) )
| ~ ( in @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_81,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ esk7_0 @ X1 )
| ~ ( in @ esk8_0 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_69]) ).
thf(c_0_82,negated_conjecture,
transitiveset @ esk7_0,
inference(spm,[status(thm)],[c_0_74,c_0_36]) ).
thf(c_0_83,negated_conjecture,
~ ( in @ esk7_0 @ esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_57])]) ).
thf(c_0_84,plain,
( ( epred1_1 @ esk7_0 )
| ~ ( in @ ( esk13_1 @ esk7_0 ) @ ( esk12_1 @ esk7_0 ) ) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
thf(c_0_85,plain,
( ( epred1_1 @ esk7_0 )
| ~ ( in @ ( esk12_1 @ esk7_0 ) @ ( esk13_1 @ esk7_0 ) ) ),
inference(spm,[status(thm)],[c_0_79,c_0_78]) ).
thf(c_0_86,plain,
( ( epred1_1 @ esk7_0 )
| ( ( esk13_1 @ esk7_0 )
!= ( esk12_1 @ esk7_0 ) ) ),
inference(spm,[status(thm)],[c_0_80,c_0_78]) ).
thf(c_0_87,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( nonempty @ ( esk2_1 @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ X3 @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( in @ X2 @ X1 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk3_2 @ X1 @ X2 ) @ ( esk2_1 @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ X4 @ X1 )
| ~ ( in @ X2 @ ( esk2_1 @ X1 ) )
| ~ ( epred1_1 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( in @ X3 @ X1 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_89,plain,
! [X2: $i,X1: $i] :
( ( in @ ( esk19_2 @ X1 @ X2 ) @ X2 )
| ~ ( nonempty @ X2 )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( epred3_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_90,negated_conjecture,
( ( in @ ( esk2_1 @ esk7_0 ) @ ( powerset @ esk7_0 ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ~ ( epred1_1 @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_57]),c_0_82])]),c_0_83]) ).
thf(c_0_91,plain,
epred1_1 @ esk7_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_47]),c_0_85]),c_0_86]) ).
thf(c_0_92,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ esk7_0 @ X1 )
| ( nonempty @ ( esk2_1 @ X1 ) )
| ~ ( in @ esk8_0 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_87,c_0_69]) ).
thf(c_0_93,plain,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_2 @ X1 @ ( esk19_2 @ X2 @ ( esk2_1 @ X1 ) ) ) @ ( esk2_1 @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ X3 @ X1 )
| ~ ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X4 )
| ~ ( in @ X4 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( epred3_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_87]) ).
thf(c_0_94,negated_conjecture,
( ( in @ ( esk2_1 @ esk7_0 ) @ ( powerset @ esk7_0 ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
thf(c_0_95,negated_conjecture,
( ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( nonempty @ ( esk2_1 @ esk7_0 ) )
| ~ ( epred1_1 @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_57]),c_0_82])]),c_0_83]) ).
thf(c_0_96,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) @ ( esk2_1 @ esk7_0 ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_82]),c_0_91]),c_0_36])]) ).
thf(c_0_97,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( ( esk19_2 @ X3 @ X2 )
= X1 )
| ( in @ ( esk19_2 @ X3 @ X2 ) @ X1 )
| ~ ( in @ X1 @ X2 )
| ~ ( nonempty @ X2 )
| ~ ( in @ X2 @ ( powerset @ X3 ) )
| ~ ( epred3_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_98,negated_conjecture,
( ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( nonempty @ ( esk2_1 @ esk7_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_91])]) ).
thf(c_0_99,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) @ ( esk2_1 @ esk7_0 ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ X1 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_57]) ).
thf(c_0_100,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_1 @ X2 ) @ X2 )
| ( in @ X4 @ X2 )
| ( X1
!= ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X1 @ ( esk2_1 @ X2 ) )
| ~ ( epred1_1 @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_101,plain,
! [X1: $i] :
( ( ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) )
= X1 )
| ( in @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) @ X1 )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ~ ( in @ X1 @ ( esk2_1 @ esk7_0 ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_94]),c_0_36])]),c_0_98]) ).
thf(c_0_102,negated_conjecture,
( ( in @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) @ ( esk2_1 @ esk7_0 ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_69]),c_0_83]) ).
thf(c_0_103,plain,
! [X2: $i,X1: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( in @ X2 @ X1 )
| ( ( esk3_2 @ X1 @ ( esk19_2 @ X3 @ ( esk2_1 @ X1 ) ) )
!= ( esk19_2 @ X3 @ ( esk2_1 @ X1 ) ) )
| ~ ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X3 ) )
| ~ ( in @ X2 @ X4 )
| ~ ( in @ X4 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( epred3_1 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_89]),c_0_87]) ).
thf(c_0_104,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_1 @ X2 ) @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X1 @ ( esk2_1 @ X2 ) )
| ~ ( epred1_1 @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_105,plain,
( ( ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
= ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
| ( in @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
thf(c_0_106,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( in @ X1 @ esk7_0 )
| ( ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
!= ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_94]),c_0_82]),c_0_91]),c_0_36])]) ).
thf(c_0_107,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) @ ( esk2_1 @ esk7_0 ) )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_82]),c_0_91])]),c_0_106]) ).
thf(c_0_108,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ X3 @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( in @ X2 @ X1 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_109,plain,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_89]),c_0_36])]),c_0_98]),c_0_94]) ).
thf(c_0_110,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X1 ) )
| ( in @ esk7_0 @ X1 )
| ~ ( in @ esk8_0 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_108,c_0_69]) ).
thf(c_0_111,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_1 @ esk7_0 ) @ esk7_0 )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ X1 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_109,c_0_57]) ).
thf(c_0_112,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( nonempty @ ( esk2_1 @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ X3 @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( in @ X2 @ X1 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_113,negated_conjecture,
( ( in @ ( esk2_1 @ esk7_0 ) @ ( powerset @ esk7_0 ) )
| ( in @ ( esk1_1 @ esk7_0 ) @ ( esk1_1 @ esk7_0 ) )
| ~ ( epred1_1 @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_57]),c_0_82])]),c_0_83]) ).
thf(c_0_114,negated_conjecture,
in @ ( esk1_1 @ esk7_0 ) @ esk7_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_69]),c_0_83]) ).
thf(c_0_115,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ esk7_0 @ X1 )
| ( nonempty @ ( esk2_1 @ X1 ) )
| ~ ( in @ esk8_0 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_112,c_0_69]) ).
thf(c_0_116,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk3_2 @ X1 @ X2 ) @ ( esk2_1 @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ X4 @ X1 )
| ~ ( in @ X2 @ ( esk2_1 @ X1 ) )
| ~ ( epred1_1 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( in @ X3 @ X1 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_117,negated_conjecture,
( ( in @ ( esk1_1 @ esk7_0 ) @ ( esk1_1 @ esk7_0 ) )
| ( in @ ( esk2_1 @ esk7_0 ) @ ( powerset @ esk7_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_91])]) ).
thf(c_0_118,plain,
~ ( in @ ( esk1_1 @ esk7_0 ) @ ( esk1_1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_114]),c_0_36])]) ).
thf(c_0_119,negated_conjecture,
( ( in @ ( esk1_1 @ esk7_0 ) @ ( esk1_1 @ esk7_0 ) )
| ( nonempty @ ( esk2_1 @ esk7_0 ) )
| ~ ( epred1_1 @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_57]),c_0_82])]),c_0_83]) ).
thf(c_0_120,plain,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_2 @ X1 @ ( esk19_2 @ X2 @ ( esk2_1 @ X1 ) ) ) @ ( esk2_1 @ X1 ) )
| ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ X3 @ X1 )
| ~ ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ X4 )
| ~ ( in @ X4 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( epred3_1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_89]),c_0_112]) ).
thf(c_0_121,negated_conjecture,
in @ ( esk2_1 @ esk7_0 ) @ ( powerset @ esk7_0 ),
inference(sr,[status(thm)],[c_0_117,c_0_118]) ).
thf(c_0_122,negated_conjecture,
( ( in @ ( esk1_1 @ esk7_0 ) @ ( esk1_1 @ esk7_0 ) )
| ( nonempty @ ( esk2_1 @ esk7_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_91])]) ).
thf(c_0_123,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) @ ( esk2_1 @ esk7_0 ) )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_82]),c_0_91]),c_0_36])]),c_0_118]) ).
thf(c_0_124,negated_conjecture,
nonempty @ ( esk2_1 @ esk7_0 ),
inference(sr,[status(thm)],[c_0_122,c_0_118]) ).
thf(c_0_125,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) @ ( esk2_1 @ esk7_0 ) )
| ( in @ X1 @ esk7_0 )
| ~ ( in @ X1 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_123,c_0_57]) ).
thf(c_0_126,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_1 @ X2 ) @ ( esk1_1 @ X2 ) )
| ( in @ X4 @ X2 )
| ( X1
!= ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X1 @ ( esk2_1 @ X2 ) )
| ~ ( epred1_1 @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_127,plain,
! [X1: $i] :
( ( ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) )
= X1 )
| ( in @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) @ X1 )
| ~ ( in @ X1 @ ( esk2_1 @ esk7_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_121]),c_0_124]),c_0_36])]) ).
thf(c_0_128,negated_conjecture,
in @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) @ ( esk2_1 @ esk7_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_69]),c_0_83]) ).
thf(c_0_129,plain,
! [X2: $i,X1: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_1 @ X1 ) @ ( esk1_1 @ X1 ) )
| ( in @ X2 @ X1 )
| ( ( esk3_2 @ X1 @ ( esk19_2 @ X3 @ ( esk2_1 @ X1 ) ) )
!= ( esk19_2 @ X3 @ ( esk2_1 @ X1 ) ) )
| ~ ( in @ ( esk2_1 @ X1 ) @ ( powerset @ X3 ) )
| ~ ( in @ X2 @ X4 )
| ~ ( in @ X4 @ X1 )
| ~ ( transitiveset @ X1 )
| ~ ( epred1_1 @ X1 )
| ~ ( epred3_1 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_89]),c_0_112]) ).
thf(c_0_130,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X3: $i] :
( ( in @ ( esk1_1 @ X2 ) @ ( esk1_1 @ X2 ) )
| ( in @ X4 @ X2 )
| ~ ( in @ X1 @ ( esk3_2 @ X2 @ X1 ) )
| ~ ( in @ X1 @ ( esk2_1 @ X2 ) )
| ~ ( epred1_1 @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( in @ X3 @ X2 )
| ~ ( in @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_131,plain,
( ( ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
= ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
| ( in @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) @ ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
thf(c_0_132,plain,
! [X1: $i,X2: $i] :
( ( in @ X1 @ esk7_0 )
| ( ( esk3_2 @ esk7_0 @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
!= ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_121]),c_0_82]),c_0_91]),c_0_36])]),c_0_118]) ).
thf(c_0_133,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ esk7_0 )
| ~ ( in @ ( esk19_2 @ esk7_0 @ ( esk2_1 @ esk7_0 ) ) @ ( esk2_1 @ esk7_0 ) )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_82]),c_0_91])]),c_0_118]),c_0_132]) ).
thf(c_0_134,plain,
! [X1: $i,X2: $i] :
( ( in @ X1 @ esk7_0 )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_89]),c_0_121]),c_0_124]),c_0_36])]) ).
thf(c_0_135,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk7_0 )
| ~ ( in @ X1 @ esk8_0 ) ),
inference(spm,[status(thm)],[c_0_134,c_0_57]) ).
thf(c_0_136,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_69]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU823^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:56:37 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 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
% 4.44/1.03 # Version: 3.1.0-ho
% 4.44/1.03 # Preprocessing class: HSSSSLSSSLSNSFN.
% 4.44/1.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.44/1.03 # Starting new_ho_10 with 1500s (5) cores
% 4.44/1.03 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 4.44/1.03 # Starting lpo1_def_fix with 300s (1) cores
% 4.44/1.03 # Starting ehoh_best8_lambda with 300s (1) cores
% 4.44/1.03 # new_ho_10 with pid 6154 completed with status 0
% 4.44/1.03 # Result found by new_ho_10
% 4.44/1.03 # Preprocessing class: HSSSSLSSSLSNSFN.
% 4.44/1.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.44/1.03 # Starting new_ho_10 with 1500s (5) cores
% 4.44/1.03 # No SInE strategy applied
% 4.44/1.03 # Search class: HGHSF-FFMS21-SSFFMFNN
% 4.44/1.03 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 4.44/1.03 # Starting new_ho_10 with 901s (1) cores
% 4.44/1.03 # Starting ehoh_best_sine_rwall with 151s (1) cores
% 4.44/1.03 # Starting lpo1_def_fix with 151s (1) cores
% 4.44/1.03 # Starting sh4l with 151s (1) cores
% 4.44/1.03 # Starting ehoh_best_sine with 146s (1) cores
% 4.44/1.03 # sh4l with pid 6163 completed with status 0
% 4.44/1.03 # Result found by sh4l
% 4.44/1.03 # Preprocessing class: HSSSSLSSSLSNSFN.
% 4.44/1.03 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.44/1.03 # Starting new_ho_10 with 1500s (5) cores
% 4.44/1.03 # No SInE strategy applied
% 4.44/1.03 # Search class: HGHSF-FFMS21-SSFFMFNN
% 4.44/1.03 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 4.44/1.03 # Starting new_ho_10 with 901s (1) cores
% 4.44/1.03 # Starting ehoh_best_sine_rwall with 151s (1) cores
% 4.44/1.03 # Starting lpo1_def_fix with 151s (1) cores
% 4.44/1.03 # Starting sh4l with 151s (1) cores
% 4.44/1.03 # Preprocessing time : 0.003 s
% 4.44/1.03
% 4.44/1.03 # Proof found!
% 4.44/1.03 # SZS status Theorem
% 4.44/1.03 # SZS output start CNFRefutation
% See solution above
% 4.44/1.03 # Parsed axioms : 15
% 4.44/1.03 # Removed by relevancy pruning/SinE : 0
% 4.44/1.03 # Initial clauses : 98
% 4.44/1.03 # Removed in clause preprocessing : 9
% 4.44/1.03 # Initial clauses in saturation : 89
% 4.44/1.03 # Processed clauses : 1562
% 4.44/1.03 # ...of these trivial : 24
% 4.44/1.03 # ...subsumed : 363
% 4.44/1.03 # ...remaining for further processing : 1175
% 4.44/1.03 # Other redundant clauses eliminated : 0
% 4.44/1.03 # Clauses deleted for lack of memory : 0
% 4.44/1.03 # Backward-subsumed : 211
% 4.44/1.03 # Backward-rewritten : 330
% 4.44/1.03 # Generated clauses : 7741
% 4.44/1.03 # ...of the previous two non-redundant : 7104
% 4.44/1.03 # ...aggressively subsumed : 0
% 4.44/1.03 # Contextual simplify-reflections : 113
% 4.44/1.03 # Paramodulations : 7665
% 4.44/1.03 # Factorizations : 62
% 4.44/1.03 # NegExts : 0
% 4.44/1.03 # Equation resolutions : 0
% 4.44/1.03 # Disequality decompositions : 0
% 4.44/1.03 # Total rewrite steps : 980
% 4.44/1.03 # ...of those cached : 971
% 4.44/1.03 # Propositional unsat checks : 0
% 4.44/1.03 # Propositional check models : 0
% 4.44/1.03 # Propositional check unsatisfiable : 0
% 4.44/1.03 # Propositional clauses : 0
% 4.44/1.03 # Propositional clauses after purity: 0
% 4.44/1.03 # Propositional unsat core size : 0
% 4.44/1.03 # Propositional preprocessing time : 0.000
% 4.44/1.03 # Propositional encoding time : 0.000
% 4.44/1.03 # Propositional solver time : 0.000
% 4.44/1.03 # Success case prop preproc time : 0.000
% 4.44/1.03 # Success case prop encoding time : 0.000
% 4.44/1.03 # Success case prop solver time : 0.000
% 4.44/1.03 # Current number of processed clauses : 620
% 4.44/1.03 # Positive orientable unit clauses : 10
% 4.44/1.03 # Positive unorientable unit clauses: 0
% 4.44/1.03 # Negative unit clauses : 3
% 4.44/1.03 # Non-unit-clauses : 607
% 4.44/1.03 # Current number of unprocessed clauses: 4252
% 4.44/1.03 # ...number of literals in the above : 41046
% 4.44/1.03 # Current number of archived formulas : 0
% 4.44/1.03 # Current number of archived clauses : 555
% 4.44/1.03 # Clause-clause subsumption calls (NU) : 326552
% 4.44/1.03 # Rec. Clause-clause subsumption calls : 5575
% 4.44/1.03 # Non-unit clause-clause subsumptions : 679
% 4.44/1.03 # Unit Clause-clause subsumption calls : 2261
% 4.44/1.03 # Rewrite failures with RHS unbound : 0
% 4.44/1.03 # BW rewrite match attempts : 4
% 4.44/1.03 # BW rewrite match successes : 4
% 4.44/1.03 # Condensation attempts : 1562
% 4.44/1.03 # Condensation successes : 0
% 4.44/1.03 # Termbank termtop insertions : 492890
% 4.44/1.03 # Search garbage collected termcells : 1705
% 4.44/1.03
% 4.44/1.03 # -------------------------------------------------
% 4.44/1.03 # User time : 0.535 s
% 4.44/1.03 # System time : 0.009 s
% 4.44/1.03 # Total time : 0.544 s
% 4.44/1.03 # Maximum resident set size: 2120 pages
% 4.44/1.03
% 4.44/1.03 # -------------------------------------------------
% 4.44/1.03 # User time : 2.622 s
% 4.44/1.03 # System time : 0.042 s
% 4.44/1.03 # Total time : 2.664 s
% 4.44/1.03 # Maximum resident set size: 1760 pages
% 4.44/1.03 % E---3.1 exiting
% 4.44/1.03 % E exiting
%------------------------------------------------------------------------------