TSTP Solution File: SYO881^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO881^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 08:50:18 EDT 2024
% Result : Theorem 122.13s 26.10s
% Output : CNFRefutation 122.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 37
% Syntax : Number of formulae : 108 ( 26 unt; 24 typ; 0 def)
% Number of atoms : 658 ( 24 equ; 0 cnn)
% Maximal formula atoms : 195 ( 7 avg)
% Number of connectives : 2178 ( 225 ~; 268 |; 79 &;1584 @)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 8 con; 0-2 aty)
% Number of variables : 180 ( 6 ^ 166 !; 8 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c_False: $o ).
thf(decl_25,type,
c_not: $o > $o ).
thf(decl_26,type,
c_and: $o > $o > $o ).
thf(decl_28,type,
c_iff: $o > $o > $o ).
thf(decl_29,type,
c_In: $i > $i > $o ).
thf(decl_30,type,
c_Subq: $i > $i > $o ).
thf(decl_31,type,
c_Empty: $i ).
thf(decl_32,type,
c_Union: $i > $i ).
thf(decl_33,type,
c_Power: $i > $i ).
thf(decl_47,type,
c_irreflexive_i: ( $i > $i > $o ) > $o ).
thf(decl_126,type,
epred1_2: $i > $i > $o ).
thf(decl_268,type,
esk1_0: $i ).
thf(decl_269,type,
esk2_2: $i > $i > $i ).
thf(decl_270,type,
esk3_2: $i > $i > $i ).
thf(decl_281,type,
epred144_2: $o > $o > $o ).
thf(decl_283,type,
esk13_2: $i > $i > $i ).
thf(decl_287,type,
esk17_1: ( $i > $i > $o ) > $i ).
thf(decl_288,type,
esk18_1: ( $i > $i > $o ) > $i ).
thf(decl_326,type,
esk52_0: $i > $i > $i ).
thf(decl_327,type,
esk53_0: $i > $i ).
thf(decl_328,type,
esk54_0: $i ).
thf(decl_329,type,
esk55_0: $i ).
thf(decl_330,type,
esk56_0: $i ).
thf(decl_504,type,
esk222_1: $i > $i > $i ).
thf(ax2,axiom,
! [X3: $o] :
( ( c_not @ ( c_not @ X3 ) )
=> X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(ax13,axiom,
( c_not
= ( ^ [X17: $o] :
( X17
=> c_False ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
thf(ax6,axiom,
! [X8: $i,X2: $i] :
( c_iff @ ( c_In @ X2 @ ( c_Union @ X8 ) )
@ ? [X9: $i] : ( c_and @ ( c_In @ X2 @ X9 ) @ ( c_In @ X9 @ X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(ax14,axiom,
( c_and
= ( ^ [X18: $o,X19: $o] :
! [X20: $o] :
( ( X18
=> ( X19
=> X20 ) )
=> X20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
thf(ax5,axiom,
( c_not
@ ? [X7: $i] : ( c_In @ X7 @ c_Empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(ax3,axiom,
! [X4: $o,X5: $o] :
( ( c_iff @ X4 @ X5 )
=> ( X4
<=> X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(ax17,axiom,
( c_Subq
= ( ^ [X26: $i,X2: $i] :
! [X9: $i] :
( ( c_In @ X9 @ X26 )
=> ( c_In @ X9 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
thf(conj,conjecture,
( c_not
@ ! [X201: $i > $i > $o,X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X206: $i,X83: $i,X207: $i] :
( ( X205 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ X207 @ ( X202 @ ( X202 @ ( X202 @ X206 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X202 @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ X206 @ X207 ) ) ) @ X206 ) ) @ X207 ) @ ( X202 @ ( X205 @ X83 ) @ X207 ) ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) @ ( X202 @ X83 @ X83 ) ) @ ( X202 @ X83 @ ( X202 @ X207 @ X206 ) ) ) @ X206 ) ) ) @ X207 ) ) ) @ X206 ) ) @ X83 ) @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ ( X202 @ ( X205 @ X206 ) @ ( X202 @ ( X202 @ X83 @ X83 ) @ X83 ) ) @ X206 ) ) ) ) @ ( X205 @ ( X205 @ X83 ) ) ) @ X206 ) )
= ( X205 @ ( X205 @ X207 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(ax4,axiom,
! [X6: $i,X2: $i] :
( ( c_Subq @ X6 @ X2 )
=> ( ( c_Subq @ X2 @ X6 )
=> ( X6 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(ax30,axiom,
( c_irreflexive_i
= ( ^ [X38: $i > $i > $o] :
! [X2: $i] : ( c_not @ ( X38 @ X2 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(ax7,axiom,
! [X10: $i,X2: $i] : ( c_iff @ ( c_In @ X2 @ ( c_Power @ X10 ) ) @ ( c_Subq @ X2 @ X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(c_0_11,plain,
! [X2: $i,X8: $i] :
( ( epred1_2 @ X8 @ X2 )
<=> ~ ? [X9: $i] :
( ( ~ ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $false ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_12,axiom,
! [X3: $o] :
( ( ( ~ ( c_not @ X3 )
| ( c_not @ $true ) )
& ( ( c_not @ X3 )
| ( c_not @ $false ) ) )
=> X3 ),
inference(fool_unroll,[status(thm)],[ax2]) ).
thf(c_0_13,plain,
! [X237: $o] :
( ( c_not @ X237 )
<=> ( X237
=> c_False ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax13])]) ).
thf(c_0_14,axiom,
! [X8: $i,X2: $i] :
( ( ~ ( c_In @ X2 @ ( c_Union @ X8 ) )
| ( ( ( epred1_2 @ X8 @ X2 )
| ( c_iff @ $true @ $true ) )
& ( ? [X9: $i] :
( ( ~ ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $false ) ) ) ) )
| ( c_iff @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ ( c_Union @ X8 ) )
| ( ( ( epred1_2 @ X8 @ X2 )
| ( c_iff @ $false @ $true ) )
& ( ? [X9: $i] :
( ( ~ ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $false ) ) ) ) )
| ( c_iff @ $false @ $false ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[ax6]),c_0_11]),c_0_11]) ).
thf(c_0_15,plain,
! [X238: $o,X239: $o] :
( ( c_and @ X238 @ X239 )
<=> ! [X20: $o] :
( ( X238
=> ( X239
=> X20 ) )
=> X20 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax14])]) ).
thf(c_0_16,axiom,
( ( ~ ? [X7: $i] : ( c_In @ X7 @ c_Empty )
| ( c_not @ $true ) )
& ( ? [X7: $i] : ( c_In @ X7 @ c_Empty )
| ( c_not @ $false ) ) ),
inference(fool_unroll,[status(thm)],[ax5]) ).
thf(c_0_17,plain,
! [X447: $o] :
( ( ~ ( c_not @ X447 )
| ( c_not @ X447 )
| X447 )
& ( ~ ( c_not @ $false )
| ( c_not @ X447 )
| X447 )
& ( ~ ( c_not @ X447 )
| ~ ( c_not @ $true )
| X447 )
& ( ~ ( c_not @ $false )
| ~ ( c_not @ $true )
| X447 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
thf(c_0_18,plain,
! [X485: $o] :
( ( ~ ( c_not @ X485 )
| ~ X485
| c_False )
& ( X485
| ( c_not @ X485 ) )
& ( ~ c_False
| ( c_not @ X485 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_19,plain,
! [X454: $i,X455: $i,X457: $i,X458: $i] :
( ( ( epred1_2 @ X454 @ X455 )
| ( c_iff @ $true @ $true )
| ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
& ( ~ ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
| ( c_and @ $true @ $true )
| ~ ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
& ( ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
| ( c_and @ $true @ $false )
| ~ ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
& ( ~ ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
| ( c_and @ $false @ $true )
| ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
& ( ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
| ( c_and @ $false @ $false )
| ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
& ( ( epred1_2 @ X457 @ X458 )
| ( c_iff @ $false @ $true )
| ( c_In @ X458 @ ( c_Union @ X457 ) ) )
& ( ~ ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
| ( c_and @ $true @ $true )
| ~ ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
| ( c_iff @ $false @ $false )
| ( c_In @ X458 @ ( c_Union @ X457 ) ) )
& ( ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
| ( c_and @ $true @ $false )
| ~ ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
| ( c_iff @ $false @ $false )
| ( c_In @ X458 @ ( c_Union @ X457 ) ) )
& ( ~ ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
| ( c_and @ $false @ $true )
| ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
| ( c_iff @ $false @ $false )
| ( c_In @ X458 @ ( c_Union @ X457 ) ) )
& ( ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
| ( c_and @ $false @ $false )
| ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
| ( c_iff @ $false @ $false )
| ( c_In @ X458 @ ( c_Union @ X457 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_14])])])])])]) ).
thf(c_0_20,plain,
! [X448: $o,X449: $o] :
( ( ~ X448
| X449
| ~ ( c_iff @ X448 @ X449 ) )
& ( ~ X449
| X448
| ~ ( c_iff @ X448 @ X449 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).
thf(c_0_21,plain,
! [X486: $o,X487: $o,X488: $o,X489: $o,X490: $o] :
( ( X486
| X488
| ~ ( c_and @ X486 @ X487 ) )
& ( X487
| X488
| ~ ( c_and @ X486 @ X487 ) )
& ( ~ X488
| X488
| ~ ( c_and @ X486 @ X487 ) )
& ( ~ X489
| ~ X490
| ( epred144_2 @ X489 @ X490 )
| ( c_and @ X489 @ X490 ) )
& ( ~ ( epred144_2 @ X489 @ X490 )
| ( c_and @ X489 @ X490 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])])]) ).
thf(c_0_22,plain,
! [X452: $i] :
( ( ~ ( c_In @ X452 @ c_Empty )
| ( c_not @ $true ) )
& ( ( c_In @ esk1_0 @ c_Empty )
| ( c_not @ $false ) ) ),
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_16])])])])]) ).
thf(c_0_23,plain,
( ~ ( c_not @ ~ $true )
| ~ ( c_not @ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_17])])]) ).
thf(c_0_24,plain,
c_not @ ~ $true,
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_18])])]) ).
thf(c_0_25,plain,
! [X244: $i,X245: $i] :
( ( c_Subq @ X244 @ X245 )
<=> ! [X9: $i] :
( ( c_In @ X9 @ X244 )
=> ( c_In @ X9 @ X245 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax17])]) ).
thf(c_0_26,plain,
! [X6: $i,X2: $i] :
( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
| ( c_and @ ~ $true @ ~ $true )
| ( c_In @ X6 @ ( esk2_2 @ X2 @ X6 ) )
| ( c_iff @ $true @ ~ $true )
| ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,plain,
~ ( c_iff @ $true @ ~ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).
thf(c_0_28,plain,
! [X5: $o] :
~ ( c_and @ X5 @ ~ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21])])]) ).
thf(c_0_29,negated_conjecture,
~ ( ( ~ ! [X201: $i > $i > $o,X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X206: $i,X83: $i,X207: $i] :
( ( X205 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ X207 @ ( X202 @ ( X202 @ ( X202 @ X206 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X202 @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ X206 @ X207 ) ) ) @ X206 ) ) @ X207 ) @ ( X202 @ ( X205 @ X83 ) @ X207 ) ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) @ ( X202 @ X83 @ X83 ) ) @ ( X202 @ X83 @ ( X202 @ X207 @ X206 ) ) ) @ X206 ) ) ) @ X207 ) ) ) @ X206 ) ) @ X83 ) @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ ( X202 @ ( X205 @ X206 ) @ ( X202 @ ( X202 @ X83 @ X83 ) @ X83 ) ) @ X206 ) ) ) ) @ ( X205 @ ( X205 @ X83 ) ) ) @ X206 ) )
= ( X205 @ ( X205 @ X207 ) ) )
| ( c_not @ $true ) )
& ( ! [X201: $i > $i > $o,X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X206: $i,X83: $i,X207: $i] :
( ( X205 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ X207 @ ( X202 @ ( X202 @ ( X202 @ X206 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X202 @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ X206 @ X207 ) ) ) @ X206 ) ) @ X207 ) @ ( X202 @ ( X205 @ X83 ) @ X207 ) ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) @ ( X202 @ X83 @ X83 ) ) @ ( X202 @ X83 @ ( X202 @ X207 @ X206 ) ) ) @ X206 ) ) ) @ X207 ) ) ) @ X206 ) ) @ X83 ) @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ ( X202 @ ( X205 @ X206 ) @ ( X202 @ ( X202 @ X83 @ X83 ) @ X83 ) ) @ X206 ) ) ) ) @ ( X205 @ ( X205 @ X83 ) ) ) @ X206 ) )
= ( X205 @ ( X205 @ X207 ) ) )
| ( c_not @ $false ) ) ),
inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]) ).
thf(c_0_30,plain,
! [X2: $i] :
( ( c_not @ $true )
| ~ ( c_In @ X2 @ c_Empty ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_31,plain,
~ ( c_not @ $true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
thf(c_0_32,plain,
! [X500: $i,X501: $i,X502: $i,X503: $i,X504: $i] :
( ( ~ ( c_Subq @ X500 @ X501 )
| ~ ( c_In @ X502 @ X500 )
| ( c_In @ X502 @ X501 ) )
& ( ( c_In @ ( esk13_2 @ X503 @ X504 ) @ X503 )
| ( c_Subq @ X503 @ X504 ) )
& ( ~ ( c_In @ ( esk13_2 @ X503 @ X504 ) @ X504 )
| ( c_Subq @ X503 @ X504 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])])])]) ).
thf(c_0_33,plain,
! [X6: $i,X2: $i] :
( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
| ( c_and @ $true @ ~ $true )
| ( c_iff @ $true @ ~ $true )
| ~ ( c_In @ X6 @ ( esk2_2 @ X2 @ X6 ) )
| ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_34,plain,
! [X6: $i,X2: $i] :
( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
| ( c_In @ X6 @ ( esk2_2 @ X2 @ X6 ) )
| ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_35,negated_conjecture,
! [X816: $i > $i > $i,X817: $i > $i,X818: $i,X819: $i,X820: $i] :
( ( ( ( esk53_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ esk56_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ esk54_0 @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk56_0 ) @ ( esk52_0 @ ( esk53_0 @ esk55_0 ) @ esk56_0 ) ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk53_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ ( esk52_0 @ esk55_0 @ esk55_0 ) ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ esk54_0 ) ) ) @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk55_0 ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ ( esk53_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk55_0 ) @ esk55_0 ) ) @ esk54_0 ) ) ) ) @ ( esk53_0 @ ( esk53_0 @ esk55_0 ) ) ) @ esk54_0 ) )
!= ( esk53_0 @ ( esk53_0 @ esk56_0 ) ) )
| ( ( X817 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ X820 @ ( X816 @ ( X816 @ ( X816 @ X818 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X816 @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ X818 @ X820 ) ) ) @ X818 ) ) @ X820 ) @ ( X816 @ ( X817 @ X819 ) @ X820 ) ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X817 @ ( X816 @ X820 @ X818 ) ) ) @ ( X816 @ X819 @ X819 ) ) @ ( X816 @ X819 @ ( X816 @ X820 @ X818 ) ) ) @ X818 ) ) ) @ X820 ) ) ) @ X818 ) ) @ X819 ) @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ ( X816 @ ( X817 @ X818 ) @ ( X816 @ ( X816 @ X819 @ X819 ) @ X819 ) ) @ X818 ) ) ) ) @ ( X817 @ ( X817 @ X819 ) ) ) @ X818 ) )
= ( X817 @ ( X817 @ X820 ) ) ) )
& ( ~ ( c_not @ $false )
| ( ( X817 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ X820 @ ( X816 @ ( X816 @ ( X816 @ X818 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X816 @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ X818 @ X820 ) ) ) @ X818 ) ) @ X820 ) @ ( X816 @ ( X817 @ X819 ) @ X820 ) ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X817 @ ( X816 @ X820 @ X818 ) ) ) @ ( X816 @ X819 @ X819 ) ) @ ( X816 @ X819 @ ( X816 @ X820 @ X818 ) ) ) @ X818 ) ) ) @ X820 ) ) ) @ X818 ) ) @ X819 ) @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ ( X816 @ ( X817 @ X818 ) @ ( X816 @ ( X816 @ X819 @ X819 ) @ X819 ) ) @ X818 ) ) ) ) @ ( X817 @ ( X817 @ X819 ) ) ) @ X818 ) )
= ( X817 @ ( X817 @ X820 ) ) ) )
& ( ( ( esk53_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ esk56_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ esk54_0 @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk56_0 ) @ ( esk52_0 @ ( esk53_0 @ esk55_0 ) @ esk56_0 ) ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk53_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ ( esk52_0 @ esk55_0 @ esk55_0 ) ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ esk54_0 ) ) ) @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk55_0 ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ ( esk53_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk55_0 ) @ esk55_0 ) ) @ esk54_0 ) ) ) ) @ ( esk53_0 @ ( esk53_0 @ esk55_0 ) ) ) @ esk54_0 ) )
!= ( esk53_0 @ ( esk53_0 @ esk56_0 ) ) )
| ~ ( c_not @ $true ) )
& ( ~ ( c_not @ $false )
| ~ ( c_not @ $true ) ) ),
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)],[inference(fof_simplification,[status(thm)],[c_0_29])])])])])])]) ).
thf(c_0_36,plain,
! [X450: $i,X451: $i] :
( ~ ( c_Subq @ X450 @ X451 )
| ~ ( c_Subq @ X451 @ X450 )
| ( X450 = X451 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
thf(c_0_37,plain,
! [X2: $i] :
~ ( c_In @ X2 @ c_Empty ),
inference(sr,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_38,plain,
! [X2: $i,X6: $i] :
( ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X2 )
| ( c_Subq @ X2 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_39,plain,
! [X6: $i,X2: $i] :
( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
| ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_33,c_0_28]),c_0_27]),c_0_34]) ).
thf(c_0_40,negated_conjecture,
! [X2: $i,X6: $i,X12: $i > $i,X89: $i > $i > $i,X7: $i] :
( ( ( X12 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ X7 @ ( X89 @ ( X89 @ ( X89 @ X6 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X89 @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ X6 @ X7 ) ) ) @ X6 ) ) @ X7 ) @ ( X89 @ ( X12 @ X2 ) @ X7 ) ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X12 @ ( X89 @ X7 @ X6 ) ) ) @ ( X89 @ X2 @ X2 ) ) @ ( X89 @ X2 @ ( X89 @ X7 @ X6 ) ) ) @ X6 ) ) ) @ X7 ) ) ) @ X6 ) ) @ X2 ) @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ ( X89 @ ( X12 @ X6 ) @ ( X89 @ ( X89 @ X2 @ X2 ) @ X2 ) ) @ X6 ) ) ) ) @ ( X12 @ ( X12 @ X2 ) ) ) @ X6 ) )
= ( X12 @ ( X12 @ X7 ) ) )
| ~ ( c_not @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_41,plain,
! [X1967: $i,X1968: $i] :
( ( esk222_1 @ X1968 @ X1967 )
= X1968 ),
inference(variable_rename,[status(thm)],]) ).
thf(c_0_42,plain,
! [X6: $i,X2: $i] :
( ( X2 = X6 )
| ~ ( c_Subq @ X2 @ X6 )
| ~ ( c_Subq @ X6 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_43,plain,
! [X2: $i] : ( c_Subq @ c_Empty @ X2 ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_44,plain,
! [X2: $i] :
~ ( c_In @ X2 @ ( c_Union @ c_Empty ) ),
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
thf(c_0_45,plain,
! [X2: $i,X8: $i] :
( ( epred1_2 @ X8 @ X2 )
=> ~ ? [X9: $i] :
( ( ~ ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ X9 )
| ( ( ~ ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $true ) )
& ( ( c_In @ X9 @ X8 )
| ( c_and @ $false @ $false ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_11]) ).
thf(c_0_46,negated_conjecture,
! [X2: $i,X6: $i,X12: $i > $i,X89: $i > $i > $i,X7: $i] :
( ( X12 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ X7 @ ( X89 @ ( X89 @ ( X89 @ X6 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X89 @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ X6 @ X7 ) ) ) @ X6 ) ) @ X7 ) @ ( X89 @ ( X12 @ X2 ) @ X7 ) ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X12 @ ( X89 @ X7 @ X6 ) ) ) @ ( X89 @ X2 @ X2 ) ) @ ( X89 @ X2 @ ( X89 @ X7 @ X6 ) ) ) @ X6 ) ) ) @ X7 ) ) ) @ X6 ) ) @ X2 ) @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ ( X89 @ ( X12 @ X6 ) @ ( X89 @ ( X89 @ X2 @ X2 ) @ X2 ) ) @ X6 ) ) ) ) @ ( X12 @ ( X12 @ X2 ) ) ) @ X6 ) )
= ( X12 @ ( X12 @ X7 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_24])]) ).
thf(c_0_47,plain,
! [X6: $i,X2: $i] :
( ( esk222_1 @ X2 @ X6 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_48,plain,
! [X2: $i] :
( ( X2 = c_Empty )
| ~ ( c_Subq @ X2 @ c_Empty ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_49,plain,
! [X2: $i] : ( c_Subq @ ( c_Union @ c_Empty ) @ X2 ),
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
thf(c_0_50,plain,
! [X826: $i,X827: $i,X828: $i] :
( ( ~ ( c_In @ X826 @ X828 )
| ( c_In @ X826 @ X828 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ( c_In @ X826 @ X828 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ( c_In @ X828 @ X827 )
| ( c_In @ X826 @ X828 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $false @ $true )
| ( c_In @ X826 @ X828 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ~ ( c_and @ $false @ $true )
| ( c_In @ X826 @ X828 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X826 @ X828 )
| ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $false @ $true )
| ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ~ ( c_and @ $false @ $true )
| ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X826 @ X828 )
| ~ ( c_and @ $true @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $false @ $true )
| ~ ( c_and @ $true @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ~ ( c_and @ $false @ $true )
| ~ ( c_and @ $true @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X826 @ X828 )
| ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $false @ $true )
| ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ~ ( c_and @ $false @ $true )
| ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X826 @ X828 )
| ~ ( c_and @ $true @ $false )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $false )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ( c_In @ X828 @ X827 )
| ~ ( c_and @ $true @ $false )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_In @ X828 @ X827 )
| ~ ( c_and @ $false @ $true )
| ~ ( c_and @ $true @ $false )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) )
& ( ~ ( c_and @ $false @ $false )
| ~ ( c_and @ $false @ $true )
| ~ ( c_and @ $true @ $false )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X827 @ X826 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
thf(c_0_51,plain,
! [X3: $o,X4: $o] :
( ( c_and @ X3 @ X4 )
| ~ ( epred144_2 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_52,plain,
( ( epred144_2 @ $true @ $true )
| ( c_and @ $true @ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21])])]) ).
thf(c_0_53,plain,
! [X6: $i,X2: $i] :
( ( epred1_2 @ X2 @ X6 )
| ( c_iff @ ~ $true @ $true )
| ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_54,plain,
~ ( c_iff @ ~ $true @ $true ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).
thf(c_0_55,plain,
! [X2: $i,X12: $i > $i,X6: $i] :
( ( X12 @ X2 )
= ( X12 @ ( X12 @ X6 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]) ).
thf(c_0_56,plain,
( ( c_Union @ c_Empty )
= c_Empty ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_57,plain,
! [X258: $i > $i > $o] :
( ( c_irreflexive_i @ X258 )
<=> ! [X2: $i] :
( ( ~ ( X258 @ X2 @ X2 )
| ( c_not @ $true ) )
& ( ( X258 @ X2 @ X2 )
| ( c_not @ $false ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax30])])]) ).
thf(c_0_58,plain,
! [X7: $i,X6: $i,X2: $i] :
( ~ ( c_In @ X2 @ X6 )
| ~ ( c_In @ X6 @ X7 )
| ~ ( c_and @ $true @ $true )
| ~ ( epred1_2 @ X7 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_59,plain,
c_and @ $true @ $true,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_60,plain,
! [X6: $i,X2: $i] :
( ( c_In @ X2 @ ( c_Union @ X6 ) )
| ( epred1_2 @ X6 @ X2 ) ),
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_61,plain,
! [X2: $i] :
( ( c_Union @ X2 )
= c_Empty ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).
thf(c_0_62,plain,
! [X527: $i > $i > $o,X528: $i,X529: $i,X530: $i > $i > $o] :
( ( ~ ( X527 @ X528 @ X528 )
| ( c_not @ $true )
| ~ ( c_irreflexive_i @ X527 ) )
& ( ( X527 @ X529 @ X529 )
| ( c_not @ $false )
| ~ ( c_irreflexive_i @ X527 ) )
& ( ~ ( X530 @ ( esk18_1 @ X530 ) @ ( esk18_1 @ X530 ) )
| ( X530 @ ( esk17_1 @ X530 ) @ ( esk17_1 @ X530 ) )
| ( c_irreflexive_i @ X530 ) )
& ( ~ ( c_not @ $false )
| ( X530 @ ( esk17_1 @ X530 ) @ ( esk17_1 @ X530 ) )
| ( c_irreflexive_i @ X530 ) )
& ( ~ ( X530 @ ( esk18_1 @ X530 ) @ ( esk18_1 @ X530 ) )
| ~ ( c_not @ $true )
| ( c_irreflexive_i @ X530 ) )
& ( ~ ( c_not @ $false )
| ~ ( c_not @ $true )
| ( c_irreflexive_i @ X530 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])])])]) ).
thf(c_0_63,plain,
! [X2: $i,X6: $i,X7: $i] :
( ~ ( c_In @ X2 @ X6 )
| ~ ( c_In @ X7 @ X2 )
| ~ ( epred1_2 @ X6 @ X7 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
thf(c_0_64,plain,
! [X2: $i,X6: $i] : ( epred1_2 @ X2 @ X6 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_37]) ).
thf(c_0_65,plain,
! [X37: $i > $i > $o] :
( ( X37 @ ( esk17_1 @ X37 ) @ ( esk17_1 @ X37 ) )
| ( c_irreflexive_i @ X37 )
| ~ ( c_not @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_66,plain,
! [X7: $i,X6: $i,X2: $i] :
( ~ ( c_In @ X2 @ X6 )
| ~ ( c_In @ X7 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
thf(c_0_67,plain,
! [X37: $i > $i > $o] :
( ( X37 @ ( esk17_1 @ X37 ) @ ( esk17_1 @ X37 ) )
| ( c_irreflexive_i @ X37 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_24])]) ).
thf(c_0_68,axiom,
! [X10: $i,X2: $i] :
( ( ~ ( c_In @ X2 @ ( c_Power @ X10 ) )
| ( ( ~ ( c_Subq @ X2 @ X10 )
| ( c_iff @ $true @ $true ) )
& ( ( c_Subq @ X2 @ X10 )
| ( c_iff @ $true @ $false ) ) ) )
& ( ( c_In @ X2 @ ( c_Power @ X10 ) )
| ( ( ~ ( c_Subq @ X2 @ X10 )
| ( c_iff @ $false @ $true ) )
& ( ( c_Subq @ X2 @ X10 )
| ( c_iff @ $false @ $false ) ) ) ) ),
inference(fool_unroll,[status(thm)],[ax7]) ).
thf(c_0_69,plain,
! [X2: $i,X37: $i > $i > $o] :
( ( c_not @ $true )
| ~ ( X37 @ X2 @ X2 )
| ~ ( c_irreflexive_i @ X37 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_70,plain,
! [X2: $i] :
( ( c_irreflexive_i @ c_In )
| ~ ( c_In @ X2 @ ( esk17_1 @ c_In ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_71,plain,
! [X460: $i,X461: $i] :
( ( ~ ( c_Subq @ X461 @ X460 )
| ( c_iff @ $true @ $true )
| ~ ( c_In @ X461 @ ( c_Power @ X460 ) ) )
& ( ( c_Subq @ X461 @ X460 )
| ( c_iff @ $true @ $false )
| ~ ( c_In @ X461 @ ( c_Power @ X460 ) ) )
& ( ~ ( c_Subq @ X461 @ X460 )
| ( c_iff @ $false @ $true )
| ( c_In @ X461 @ ( c_Power @ X460 ) ) )
& ( ( c_Subq @ X461 @ X460 )
| ( c_iff @ $false @ $false )
| ( c_In @ X461 @ ( c_Power @ X460 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])])]) ).
thf(c_0_72,plain,
! [X37: $i > $i > $o,X2: $i] :
( ~ ( c_irreflexive_i @ X37 )
| ~ ( X37 @ X2 @ X2 ) ),
inference(sr,[status(thm)],[c_0_69,c_0_31]) ).
thf(c_0_73,plain,
c_irreflexive_i @ c_In,
inference(spm,[status(thm)],[c_0_70,c_0_67]) ).
thf(c_0_74,plain,
! [X2: $i,X6: $i] :
( ( c_iff @ ~ $true @ $true )
| ( c_In @ X2 @ ( c_Power @ X6 ) )
| ~ ( c_Subq @ X2 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_75,plain,
! [X2: $i] :
~ ( c_In @ X2 @ X2 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_76,plain,
! [X2: $i,X6: $i] :
( ( c_In @ X2 @ ( c_Power @ X6 ) )
| ~ ( c_Subq @ X2 @ X6 ) ),
inference(sr,[status(thm)],[c_0_74,c_0_54]) ).
thf(c_0_77,plain,
! [X2: $i,X12: $i > $i] :
( ( X12 @ X2 )
= ( X12 @ c_Empty ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_55]),c_0_55]) ).
thf(c_0_78,plain,
! [X2: $i] :
~ ( c_Subq @ ( c_Power @ X2 ) @ X2 ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
thf(c_0_79,plain,
! [X2: $i,X12: $i > $i,X6: $i] :
( ( X12 @ X2 )
= ( X12 @ X6 ) ),
inference(spm,[status(thm)],[c_0_77,c_0_77]) ).
thf(c_0_80,plain,
! [X2: $i,X6: $i] :
( ( c_Subq @ X2 @ X6 )
| ~ ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_81,plain,
! [X2: $i,X6: $i] :
~ ( c_Subq @ ( c_Power @ X2 ) @ X6 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_82,plain,
! [X2: $i] : ( c_Subq @ X2 @ X2 ),
inference(spm,[status(thm)],[c_0_80,c_0_38]) ).
thf(c_0_83,plain,
$false,
inference(spm,[status(thm)],[c_0_81,c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SYO881^1 : TPTP v8.2.0. Released v7.5.0.
% 0.04/0.09 % Command : run_E %s %d THM
% 0.09/0.28 % Computer : n022.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon May 20 11:02:22 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.14/0.38 Running higher-order theorem proving
% 0.14/0.38 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
% 122.13/26.10 # Version: 3.1.0-ho
% 122.13/26.10 # partial match(1): HSLMSMSSSSLCHSA
% 122.13/26.10 # Preprocessing class: HSLMSLSSSSLCHSA.
% 122.13/26.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/26.10 # Starting pre_casc_6 with 1500s (5) cores
% 122.13/26.10 # Starting ehoh_best7 with 300s (1) cores
% 122.13/26.10 # Starting new_bool_8 with 300s (1) cores
% 122.13/26.10 # Starting new_ho_11 with 300s (1) cores
% 122.13/26.10 # new_ho_11 with pid 14694 completed with status 0
% 122.13/26.10 # Result found by new_ho_11
% 122.13/26.10 # partial match(1): HSLMSMSSSSLCHSA
% 122.13/26.10 # Preprocessing class: HSLMSLSSSSLCHSA.
% 122.13/26.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/26.10 # Starting pre_casc_6 with 1500s (5) cores
% 122.13/26.10 # Starting ehoh_best7 with 300s (1) cores
% 122.13/26.10 # Starting new_bool_8 with 300s (1) cores
% 122.13/26.10 # Starting new_ho_11 with 300s (1) cores
% 122.13/26.10 # No SInE strategy applied
% 122.13/26.10 # Search class: HGHSM-SMLM33-DHSFFSBC
% 122.13/26.10 # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 122.13/26.10 # Scheduled 6 strats onto 1 cores with 280 seconds (280 total)
% 122.13/26.10 # Starting new_ho_10 with 84s (1) cores
% 122.13/26.10 # new_ho_10 with pid 15781 completed with status 0
% 122.13/26.10 # Result found by new_ho_10
% 122.13/26.10 # partial match(1): HSLMSMSSSSLCHSA
% 122.13/26.10 # Preprocessing class: HSLMSLSSSSLCHSA.
% 122.13/26.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/26.10 # Starting pre_casc_6 with 1500s (5) cores
% 122.13/26.10 # Starting ehoh_best7 with 300s (1) cores
% 122.13/26.10 # Starting new_bool_8 with 300s (1) cores
% 122.13/26.10 # Starting new_ho_11 with 300s (1) cores
% 122.13/26.10 # No SInE strategy applied
% 122.13/26.10 # Search class: HGHSM-SMLM33-DHSFFSBC
% 122.13/26.10 # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 122.13/26.10 # Scheduled 6 strats onto 1 cores with 280 seconds (280 total)
% 122.13/26.10 # Starting new_ho_10 with 84s (1) cores
% 122.13/26.10 # Preprocessing time : 0.130 s
% 122.13/26.10 # Presaturation interreduction done
% 122.13/26.10
% 122.13/26.10 # Proof found!
% 122.13/26.10 # SZS status Theorem
% 122.13/26.10 # SZS output start CNFRefutation
% See solution above
% 122.13/26.10 # Parsed axioms : 213
% 122.13/26.10 # Removed by relevancy pruning/SinE : 0
% 122.13/26.10 # Initial clauses : 468687
% 122.13/26.10 # Removed in clause preprocessing : 463862
% 122.13/26.10 # Initial clauses in saturation : 4825
% 122.13/26.10 # Processed clauses : 7679
% 122.13/26.10 # ...of these trivial : 330
% 122.13/26.10 # ...subsumed : 3956
% 122.13/26.10 # ...remaining for further processing : 3393
% 122.13/26.10 # Other redundant clauses eliminated : 130
% 122.13/26.10 # Clauses deleted for lack of memory : 0
% 122.13/26.10 # Backward-subsumed : 202
% 122.13/26.10 # Backward-rewritten : 509
% 122.13/26.10 # Generated clauses : 42532
% 122.13/26.10 # ...of the previous two non-redundant : 41057
% 122.13/26.10 # ...aggressively subsumed : 0
% 122.13/26.10 # Contextual simplify-reflections : 281
% 122.13/26.10 # Paramodulations : 42376
% 122.13/26.10 # Factorizations : 0
% 122.13/26.10 # NegExts : 0
% 122.13/26.10 # Equation resolutions : 130
% 122.13/26.10 # Disequality decompositions : 0
% 122.13/26.10 # Total rewrite steps : 16329
% 122.13/26.10 # ...of those cached : 14684
% 122.13/26.10 # Propositional unsat checks : 0
% 122.13/26.10 # Propositional check models : 0
% 122.13/26.10 # Propositional check unsatisfiable : 0
% 122.13/26.10 # Propositional clauses : 0
% 122.13/26.10 # Propositional clauses after purity: 0
% 122.13/26.10 # Propositional unsat core size : 0
% 122.13/26.10 # Propositional preprocessing time : 0.000
% 122.13/26.10 # Propositional encoding time : 0.000
% 122.13/26.10 # Propositional solver time : 0.000
% 122.13/26.10 # Success case prop preproc time : 0.000
% 122.13/26.10 # Success case prop encoding time : 0.000
% 122.13/26.10 # Success case prop solver time : 0.000
% 122.13/26.10 # Current number of processed clauses : 1402
% 122.13/26.10 # Positive orientable unit clauses : 154
% 122.13/26.10 # Positive unorientable unit clauses: 5
% 122.13/26.10 # Negative unit clauses : 86
% 122.13/26.10 # Non-unit-clauses : 1157
% 122.13/26.10 # Current number of unprocessed clauses: 39285
% 122.13/26.10 # ...number of literals in the above : 193099
% 122.13/26.10 # Current number of archived formulas : 0
% 122.13/26.10 # Current number of archived clauses : 1933
% 122.13/26.10 # Clause-clause subsumption calls (NU) : 1774000
% 122.13/26.10 # Rec. Clause-clause subsumption calls : 395059
% 122.13/26.10 # Non-unit clause-clause subsumptions : 1777
% 122.13/26.10 # Unit Clause-clause subsumption calls : 103342
% 122.13/26.10 # Rewrite failures with RHS unbound : 0
% 122.13/26.10 # BW rewrite match attempts : 14865
% 122.13/26.10 # BW rewrite match successes : 1230
% 122.13/26.10 # Condensation attempts : 7888
% 122.13/26.10 # Condensation successes : 221
% 122.13/26.10 # Termbank termtop insertions : 21204624
% 122.13/26.10 # Search garbage collected termcells : 2011264
% 122.13/26.10
% 122.13/26.10 # -------------------------------------------------
% 122.13/26.10 # User time : 23.238 s
% 122.13/26.10 # System time : 1.521 s
% 122.13/26.10 # Total time : 24.759 s
% 122.13/26.10 # Maximum resident set size: 1254296 pages
% 122.13/26.10
% 122.13/26.10 # -------------------------------------------------
% 122.13/26.10 # User time : 23.246 s
% 122.13/26.10 # System time : 1.678 s
% 122.13/26.10 # Total time : 24.924 s
% 122.13/26.10 # Maximum resident set size: 2188 pages
% 122.13/26.10 % E---3.1 exiting
% 122.13/26.10 % E exiting
%------------------------------------------------------------------------------