TSTP Solution File: SEU691^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU691^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.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 03:29:10 EDT 2024
% Result : Theorem 1.36s 0.66s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 35
% Syntax : Number of formulae : 173 ( 28 unt; 27 typ; 0 def)
% Number of atoms : 674 ( 140 equ; 0 cnn)
% Maximal formula atoms : 119 ( 4 avg)
% Number of connectives : 4121 ( 213 ~; 347 |; 48 &;3439 @)
% ( 3 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 9 con; 0-4 aty)
% Number of variables : 294 ( 61 ^ 221 !; 12 ?; 294 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
kpair: $i > $i > $i ).
thf(decl_28,type,
cartprod: $i > $i > $i ).
thf(decl_29,type,
singleton: $i > $o ).
thf(decl_30,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_31,type,
breln: $i > $i > $i > $o ).
thf(decl_32,type,
func: $i > $i > $i > $o ).
thf(decl_33,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_34,type,
funcGraphProp1: $o ).
thf(decl_35,type,
funcGraphProp2: $o ).
thf(decl_36,type,
eqbreln: $o ).
thf(decl_37,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_38,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_39,type,
esk3_4: $i > $i > $i > $i > $i ).
thf(decl_40,type,
esk4_4: $i > $i > $i > $i > $i ).
thf(decl_41,type,
esk5_4: $i > $i > $i > $i > $i ).
thf(decl_42,type,
esk6_4: $i > $i > $i > $i > $i ).
thf(decl_43,type,
esk7_0: $i ).
thf(decl_44,type,
esk8_0: $i ).
thf(decl_45,type,
esk9_0: $i ).
thf(decl_46,type,
esk10_1: $i > $i ).
thf(decl_47,type,
esk11_0: $i ).
thf(decl_48,type,
esk12_1: $i > $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(func,axiom,
( func
= ( ^ [X1: $i,X4: $i,X6: $i] :
( ( breln @ X1 @ X4 @ X6 )
& ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ex1 @ X4
@ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( kpair @ X2 @ ( ap @ X1 @ X4 @ X8 @ X2 ) ) @ X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
<=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X8 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= X7 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(eqbreln,axiom,
( eqbreln
<=> ! [X1: $i,X4: $i,X6: $i] :
( ( breln @ X1 @ X4 @ X6 )
=> ! [X9: $i] :
( ( breln @ X1 @ X4 @ X9 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X6 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X9 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X9 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X6 ) ) ) )
=> ( X6 = X9 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(funcext,conjecture,
( funcGraphProp1
=> ( funcGraphProp2
=> ( eqbreln
=> ! [X1: $i,X4: $i,X8: $i] :
( ( func @ X1 @ X4 @ X8 )
=> ! [X10: $i] :
( ( func @ X1 @ X4 @ X10 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= ( ap @ X1 @ X4 @ X10 @ X2 ) ) )
=> ( X8 = X10 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(c_0_8,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X33: $i] :
( ( in @ X33
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X33 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ex1]) ).
thf(c_0_9,plain,
( singleton
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ Z0 )
& ( Z0
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_10,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X34: $i] :
( ( in @ X34
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X34 @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[func]) ).
thf(c_0_11,plain,
( ex1
= ( ^ [Z0: $i,Z1: $i > $o] :
? [X33: $i] :
( ( in @ X33
@ ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
& ( ( dsetconstr @ Z0
@ ^ [Z2: $i] : ( Z1 @ Z2 ) )
= ( setadjoin @ X33 @ emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_13,plain,
( func
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
& ! [X2: $i] :
( ( in @ X2 @ Z0 )
=> ? [X34: $i] :
( ( in @ X34
@ ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
& ( ( dsetconstr @ Z1
@ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
= ( setadjoin @ X34 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_14,axiom,
( funcGraphProp1
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X35: $i] :
( ( in @ X35 @ X1 )
=> ? [X36: $i] :
( ( in @ X36
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X35 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X35 @ Z0 ) @ X8 ) )
= ( setadjoin @ X36 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ ( kpair @ X2 @ ( ap @ X1 @ X4 @ X8 @ X2 ) ) @ X8 ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp1,c_0_13]) ).
thf(c_0_15,axiom,
( funcGraphProp2
= ( ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X37: $i] :
( ( in @ X37 @ X1 )
=> ? [X38: $i] :
( ( in @ X38
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X37 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X37 @ Z0 ) @ X8 ) )
= ( setadjoin @ X38 @ emptyset ) ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X8 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= X7 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[funcGraphProp2,c_0_13]) ).
thf(c_0_16,axiom,
( eqbreln
= ( ! [X1: $i,X4: $i,X6: $i] :
( ( subset @ X6 @ ( cartprod @ X1 @ X4 ) )
=> ! [X9: $i] :
( ( subset @ X9 @ ( cartprod @ X1 @ X4 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X6 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X9 ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X4 )
=> ( ( in @ ( kpair @ X2 @ X7 ) @ X9 )
=> ( in @ ( kpair @ X2 @ X7 ) @ X6 ) ) ) )
=> ( X6 = X9 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[eqbreln,c_0_12]) ).
thf(c_0_17,negated_conjecture,
~ ( ! [X39: $i,X40: $i,X41: $i] :
( ( ( subset @ X41 @ ( cartprod @ X39 @ X40 ) )
& ! [X42: $i] :
( ( in @ X42 @ X39 )
=> ? [X43: $i] :
( ( in @ X43
@ ( dsetconstr @ X40
@ ^ [Z0: $i] : ( in @ ( kpair @ X42 @ Z0 ) @ X41 ) ) )
& ( ( dsetconstr @ X40
@ ^ [Z0: $i] : ( in @ ( kpair @ X42 @ Z0 ) @ X41 ) )
= ( setadjoin @ X43 @ emptyset ) ) ) ) )
=> ! [X44: $i] :
( ( in @ X44 @ X39 )
=> ( in @ ( kpair @ X44 @ ( ap @ X39 @ X40 @ X41 @ X44 ) ) @ X41 ) ) )
=> ( ! [X45: $i,X46: $i,X47: $i] :
( ( ( subset @ X47 @ ( cartprod @ X45 @ X46 ) )
& ! [X48: $i] :
( ( in @ X48 @ X45 )
=> ? [X49: $i] :
( ( in @ X49
@ ( dsetconstr @ X46
@ ^ [Z0: $i] : ( in @ ( kpair @ X48 @ Z0 ) @ X47 ) ) )
& ( ( dsetconstr @ X46
@ ^ [Z0: $i] : ( in @ ( kpair @ X48 @ Z0 ) @ X47 ) )
= ( setadjoin @ X49 @ emptyset ) ) ) ) )
=> ! [X50: $i] :
( ( in @ X50 @ X45 )
=> ! [X51: $i] :
( ( in @ X51 @ X46 )
=> ( ( in @ ( kpair @ X50 @ X51 ) @ X47 )
=> ( ( ap @ X45 @ X46 @ X47 @ X50 )
= X51 ) ) ) ) )
=> ( ! [X52: $i,X53: $i,X54: $i] :
( ( subset @ X54 @ ( cartprod @ X52 @ X53 ) )
=> ! [X55: $i] :
( ( subset @ X55 @ ( cartprod @ X52 @ X53 ) )
=> ( ! [X56: $i] :
( ( in @ X56 @ X52 )
=> ! [X57: $i] :
( ( in @ X57 @ X53 )
=> ( ( in @ ( kpair @ X56 @ X57 ) @ X54 )
=> ( in @ ( kpair @ X56 @ X57 ) @ X55 ) ) ) )
=> ( ! [X58: $i] :
( ( in @ X58 @ X52 )
=> ! [X59: $i] :
( ( in @ X59 @ X53 )
=> ( ( in @ ( kpair @ X58 @ X59 ) @ X55 )
=> ( in @ ( kpair @ X58 @ X59 ) @ X54 ) ) ) )
=> ( X54 = X55 ) ) ) ) )
=> ! [X1: $i,X4: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
& ! [X60: $i] :
( ( in @ X60 @ X1 )
=> ? [X61: $i] :
( ( in @ X61
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X60 @ Z0 ) @ X8 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X60 @ Z0 ) @ X8 ) )
= ( setadjoin @ X61 @ emptyset ) ) ) ) )
=> ! [X10: $i] :
( ( ( subset @ X10 @ ( cartprod @ X1 @ X4 ) )
& ! [X62: $i] :
( ( in @ X62 @ X1 )
=> ? [X63: $i] :
( ( in @ X63
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X62 @ Z0 ) @ X10 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( in @ ( kpair @ X62 @ Z0 ) @ X10 ) )
= ( setadjoin @ X63 @ emptyset ) ) ) ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( ap @ X1 @ X4 @ X8 @ X2 )
= ( ap @ X1 @ X4 @ X10 @ X2 ) ) )
=> ( X8 = X10 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[funcext]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_18,negated_conjecture,
! [X64: $i,X65: $i,X66: $i,X68: $i,X69: $i,X70: $i,X71: $i,X72: $i,X74: $i,X75: $i,X76: $i,X77: $i,X78: $i,X79: $i,X80: $i,X88: $i,X91: $i,X93: $i] :
( ( ( in @ ( esk1_3 @ X64 @ X65 @ X66 ) @ X64 )
| ~ ( subset @ X66 @ ( cartprod @ X64 @ X65 ) )
| ~ ( in @ X69 @ X64 )
| ( in @ ( kpair @ X69 @ ( ap @ X64 @ X65 @ X66 @ X69 ) ) @ X66 ) )
& ( ~ ( in @ X68
@ ( dsetconstr @ X65
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X64 @ X65 @ X66 ) @ Z0 ) @ X66 ) ) )
| ( ( dsetconstr @ X65
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X64 @ X65 @ X66 ) @ Z0 ) @ X66 ) )
!= ( setadjoin @ X68 @ emptyset ) )
| ~ ( subset @ X66 @ ( cartprod @ X64 @ X65 ) )
| ~ ( in @ X69 @ X64 )
| ( in @ ( kpair @ X69 @ ( ap @ X64 @ X65 @ X66 @ X69 ) ) @ X66 ) )
& ( ( in @ ( esk2_3 @ X70 @ X71 @ X72 ) @ X70 )
| ~ ( subset @ X72 @ ( cartprod @ X70 @ X71 ) )
| ~ ( in @ X75 @ X70 )
| ~ ( in @ X76 @ X71 )
| ~ ( in @ ( kpair @ X75 @ X76 ) @ X72 )
| ( ( ap @ X70 @ X71 @ X72 @ X75 )
= X76 ) )
& ( ~ ( in @ X74
@ ( dsetconstr @ X71
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X70 @ X71 @ X72 ) @ Z0 ) @ X72 ) ) )
| ( ( dsetconstr @ X71
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X70 @ X71 @ X72 ) @ Z0 ) @ X72 ) )
!= ( setadjoin @ X74 @ emptyset ) )
| ~ ( subset @ X72 @ ( cartprod @ X70 @ X71 ) )
| ~ ( in @ X75 @ X70 )
| ~ ( in @ X76 @ X71 )
| ~ ( in @ ( kpair @ X75 @ X76 ) @ X72 )
| ( ( ap @ X70 @ X71 @ X72 @ X75 )
= X76 ) )
& ( ( in @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ( X79 = X80 )
| ( in @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ( X79 = X80 )
| ( in @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ( X79 = X80 )
| ( in @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ~ ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ( X79 = X80 )
| ( in @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ( X79 = X80 )
| ( in @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ( X79 = X80 )
| ( in @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ( X79 = X80 )
| ( in @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ~ ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ( X79 = X80 )
| ( in @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ( X79 = X80 )
| ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ( X79 = X80 )
| ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ( X79 = X80 )
| ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ~ ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ( X79 = X80 )
| ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ X77 )
| ( X79 = X80 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) @ X78 )
| ( X79 = X80 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ( X79 = X80 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( ~ ( in @ ( kpair @ ( esk5_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk6_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X79 )
| ( X79 = X80 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X77 @ X78 @ X79 @ X80 ) @ ( esk4_4 @ X77 @ X78 @ X79 @ X80 ) ) @ X80 )
| ~ ( subset @ X80 @ ( cartprod @ X77 @ X78 ) )
| ~ ( subset @ X79 @ ( cartprod @ X77 @ X78 ) ) )
& ( subset @ esk9_0 @ ( cartprod @ esk7_0 @ esk8_0 ) )
& ( ( in @ ( esk10_1 @ X88 )
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X88 @ Z0 ) @ esk9_0 ) ) )
| ~ ( in @ X88 @ esk7_0 ) )
& ( ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X88 @ Z0 ) @ esk9_0 ) )
= ( setadjoin @ ( esk10_1 @ X88 ) @ emptyset ) )
| ~ ( in @ X88 @ esk7_0 ) )
& ( subset @ esk11_0 @ ( cartprod @ esk7_0 @ esk8_0 ) )
& ( ( in @ ( esk12_1 @ X91 )
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X91 @ Z0 ) @ esk11_0 ) ) )
| ~ ( in @ X91 @ esk7_0 ) )
& ( ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X91 @ Z0 ) @ esk11_0 ) )
= ( setadjoin @ ( esk12_1 @ X91 ) @ emptyset ) )
| ~ ( in @ X91 @ esk7_0 ) )
& ( ~ ( in @ X93 @ esk7_0 )
| ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X93 )
= ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X93 ) ) )
& ( esk9_0 != esk11_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_17])])])])])]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ( X4 = X5 )
| ( in @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_20,negated_conjecture,
subset @ esk11_0 @ ( cartprod @ esk7_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ( X4 = X5 )
| ( in @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ( X4 = X5 )
| ( in @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i,X5: $i,X6: $i,X4: $i] :
( ( in @ ( kpair @ X6 @ ( ap @ X4 @ X2 @ X5 @ X6 ) ) @ X5 )
| ~ ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) ) )
| ( ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ~ ( subset @ X5 @ ( cartprod @ X4 @ X2 ) )
| ~ ( in @ X6 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk10_1 @ X1 )
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk9_0 ) ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk9_0 ) )
= ( setadjoin @ ( esk10_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X5: $i,X4: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X1 )
| ( in @ ( kpair @ X5 @ ( ap @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X5 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,negated_conjecture,
subset @ esk9_0 @ ( cartprod @ esk7_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X2: $i,X6: $i,X5: $i,X4: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ( ( ap @ X1 @ X2 @ X4 @ X5 )
= X6 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( in @ X5 @ X1 )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ ( kpair @ X5 @ X6 ) @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk8_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_31,negated_conjecture,
esk9_0 != esk11_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk8_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ( X4 = X5 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ( X4 = X5 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ( X4 = X5 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ X2 @ esk8_0 @ esk9_0 @ X1 ) ) @ esk9_0 )
| ~ ( in @ ( esk1_3 @ X2 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X2 @ esk8_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 ) ) @ esk9_0 )
| ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
thf(c_0_39,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 )
= X2 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk11_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
thf(c_0_40,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_31]) ).
thf(c_0_41,negated_conjecture,
( ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_31]) ).
thf(c_0_42,negated_conjecture,
( ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_31]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk8_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 ) ) @ esk9_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_28])]),c_0_38]) ).
thf(c_0_47,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]) ).
thf(c_0_48,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_28]),c_0_31]) ).
thf(c_0_49,negated_conjecture,
( ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_28]),c_0_31]) ).
thf(c_0_50,negated_conjecture,
( ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_28]),c_0_31]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X7: $i,X6: $i,X5: $i] :
( ( ( ap @ X4 @ X2 @ X5 @ X6 )
= X7 )
| ~ ( in @ X1
@ ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) ) )
| ( ( dsetconstr @ X2
@ ^ [Z0: $i] : ( in @ ( kpair @ ( esk2_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) )
!= ( setadjoin @ X1 @ emptyset ) )
| ~ ( subset @ X5 @ ( cartprod @ X4 @ X2 ) )
| ~ ( in @ X6 @ X4 )
| ~ ( in @ X7 @ X2 )
| ~ ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 )
@ ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk11_0 ) ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i] :
( ( ( dsetconstr @ esk8_0
@ ^ [Z0: $i] : ( in @ ( kpair @ X1 @ Z0 ) @ esk11_0 ) )
= ( setadjoin @ ( esk12_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( X4 = X5 )
| ( in @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ~ ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_55,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_41]) ).
thf(c_0_56,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_48]),c_0_49]),c_0_50]) ).
thf(c_0_57,negated_conjecture,
! [X4: $i,X2: $i,X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk11_0 @ X2 )
= X4 )
| ~ ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( in @ ( kpair @ X2 @ X4 ) @ esk11_0 )
| ~ ( in @ X4 @ esk8_0 )
| ~ ( in @ X2 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
thf(c_0_58,negated_conjecture,
( ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_59,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( X4 = X5 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ~ ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_60,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_56]),c_0_49]) ).
thf(c_0_61,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 )
= X2 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk11_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_20])]) ).
thf(c_0_62,negated_conjecture,
( ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_63,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ( X4 = X5 )
| ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_64,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_40]),c_0_41]),c_0_42]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 )
= X2 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk11_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_62]),c_0_20])]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ( X4 = X5 )
| ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) ) @ X1 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk8_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_63,c_0_20]) ).
thf(c_0_68,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_64]),c_0_41]) ).
thf(c_0_69,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_49]),c_0_50]) ).
thf(c_0_70,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) ) @ X1 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
thf(c_0_71,negated_conjecture,
! [X4: $i,X2: $i,X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ X2 )
= X4 )
| ~ ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( in @ ( kpair @ X2 @ X4 ) @ esk9_0 )
| ~ ( in @ X4 @ esk8_0 )
| ~ ( in @ X2 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_24]),c_0_25]) ).
thf(c_0_72,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_28]),c_0_31]) ).
thf(c_0_73,negated_conjecture,
in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_68]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_74,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_69]),c_0_49]) ).
thf(c_0_75,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
thf(c_0_76,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_28]),c_0_31]) ).
thf(c_0_77,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
thf(c_0_78,negated_conjecture,
in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_74]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_79,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_72]),c_0_50]),c_0_42]) ).
thf(c_0_80,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_76]),c_0_73])]) ).
thf(c_0_81,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_49]),c_0_41]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ X2 @ esk8_0 @ esk11_0 @ X1 ) ) @ esk11_0 )
| ( ( setadjoin @ ( esk12_1 @ ( esk1_3 @ X2 @ esk8_0 @ esk11_0 ) ) @ emptyset )
!= ( setadjoin @ X4 @ emptyset ) )
| ~ ( in @ X4 @ ( setadjoin @ ( esk12_1 @ ( esk1_3 @ X2 @ esk8_0 @ esk11_0 ) ) @ emptyset ) )
| ~ ( in @ ( esk1_3 @ X2 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X2 @ esk8_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_53]) ).
thf(c_0_83,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk12_1 @ X1 ) @ ( setadjoin @ ( esk12_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_84,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_28])]),c_0_79]) ).
thf(c_0_85,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_78]),c_0_28])]),c_0_81]) ).
thf(c_0_86,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ X2 @ esk8_0 @ esk11_0 @ X1 ) ) @ esk11_0 )
| ~ ( in @ ( esk1_3 @ X2 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X2 @ esk8_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_87,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_84]),c_0_78])]) ).
thf(c_0_88,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_85]),c_0_78])]) ).
thf(c_0_89,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ( X4 = X5 )
| ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_90,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_20]),c_0_78])]) ).
thf(c_0_91,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_88]),c_0_20]),c_0_78])]) ).
thf(c_0_92,negated_conjecture,
! [X1: $i] :
( ( X1 = esk11_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) ) @ X1 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_89,c_0_20]) ).
thf(c_0_93,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) @ X2 )
| ( X4 = X5 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_94,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_87]),c_0_20]),c_0_78])]),c_0_90]) ).
thf(c_0_95,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ( X4 = X5 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_96,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_88]),c_0_20]),c_0_78])]),c_0_91]) ).
thf(c_0_97,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_28]),c_0_31]) ).
thf(c_0_98,negated_conjecture,
in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_99,negated_conjecture,
in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_100,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_97]),c_0_98]),c_0_99])]) ).
thf(c_0_101,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_100]),c_0_73]),c_0_78])]) ).
thf(c_0_102,negated_conjecture,
! [X2: $i,X1: $i] :
( ( X1
= ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X2 ) )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ esk9_0 )
| ~ ( in @ X2 @ esk7_0 )
| ~ ( in @ X1 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_71]),c_0_28])]) ).
thf(c_0_103,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_101]),c_0_78])]) ).
thf(c_0_104,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_100]),c_0_78]),c_0_73])]),c_0_103]) ).
thf(c_0_105,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( X4 = X5 )
| ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_106,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_104]),c_0_99])]) ).
thf(c_0_107,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_108,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_107]),c_0_78]),c_0_73])]) ).
thf(c_0_109,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_107]),c_0_73]),c_0_78])]),c_0_108]) ).
thf(c_0_110,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_109]),c_0_78])]) ).
thf(c_0_111,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_110]),c_0_20]),c_0_78])]) ).
thf(c_0_112,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ( X4 = X5 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_113,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_110]),c_0_20]),c_0_78])]),c_0_111]) ).
thf(c_0_114,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_115,negated_conjecture,
! [X1: $i,X5: $i,X4: $i,X2: $i] :
( ( X4 = X5 )
| ~ ( in @ ( kpair @ ( esk5_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk6_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X4 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ X5 ) ) @ X5 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_116,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_114]),c_0_98]),c_0_99])]) ).
thf(c_0_117,negated_conjecture,
( ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_113]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_118,negated_conjecture,
in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_116]),c_0_99])]),c_0_117]) ).
thf(c_0_119,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 )
= X2 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk11_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_118]),c_0_20])]) ).
thf(c_0_120,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_97]),c_0_98]),c_0_99])]) ).
thf(c_0_121,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_120]),c_0_73]),c_0_78])]) ).
thf(c_0_122,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_120]),c_0_78]),c_0_73])]) ).
thf(c_0_123,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_121]),c_0_78])]),c_0_122]) ).
thf(c_0_124,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_123]),c_0_99])]) ).
thf(c_0_125,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_124]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_126,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_125]),c_0_78]),c_0_73])]) ).
thf(c_0_127,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_126]),c_0_20]),c_0_78])]) ).
thf(c_0_128,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_126]),c_0_20]),c_0_78])]),c_0_127]) ).
thf(c_0_129,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk11_0 )
| ~ ( in @ X1 @ esk7_0 )
| ~ ( in @ X2 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_20])]) ).
thf(c_0_130,negated_conjecture,
( ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_128]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_131,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk11_0 )
| ~ ( in @ X1 @ esk7_0 )
| ~ ( in @ X2 @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_118])]) ).
thf(c_0_132,negated_conjecture,
( ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_99]),c_0_98])]) ).
thf(c_0_133,negated_conjecture,
~ ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ),
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_112,c_0_128]),c_0_20]),c_0_28])]),c_0_31]),c_0_132]) ).
thf(c_0_134,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_125]),c_0_73]),c_0_78])]),c_0_133]) ).
thf(c_0_135,negated_conjecture,
( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_134]),c_0_78])]) ).
thf(c_0_136,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_135]),c_0_20]),c_0_78])]) ).
thf(c_0_137,negated_conjecture,
( ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_136]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_138,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 ) ) @ esk11_0 )
| ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
thf(c_0_139,negated_conjecture,
( ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_131]),c_0_99]),c_0_98])]) ).
thf(c_0_140,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) ) @ esk11_0 )
| ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_78]) ).
thf(c_0_141,negated_conjecture,
~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 ),
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_112,c_0_136]),c_0_20]),c_0_28])]),c_0_31]),c_0_139]) ).
thf(c_0_142,negated_conjecture,
in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_135]),c_0_141]) ).
thf(c_0_143,negated_conjecture,
~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk9_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_142]),c_0_20]),c_0_28])]),c_0_31]) ).
thf(c_0_144,negated_conjecture,
~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) ) @ esk11_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_131]),c_0_99]),c_0_98])]) ).
thf(c_0_145,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_142]),c_0_20]),c_0_28])]),c_0_31]),c_0_144]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU691^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.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 18:20:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 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
% 1.36/0.66 # Version: 3.1.0-ho
% 1.36/0.66 # Preprocessing class: HSSSSLSSSLMNHFN.
% 1.36/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.66 # Starting ho_unfolding_6 with 1500s (5) cores
% 1.36/0.66 # Starting ehoh_best_sine_rwall with 300s (1) cores
% 1.36/0.66 # Starting pre_casc_5 with 300s (1) cores
% 1.36/0.66 # Starting ehoh_best_sine with 300s (1) cores
% 1.36/0.66 # ho_unfolding_6 with pid 11933 completed with status 0
% 1.36/0.66 # Result found by ho_unfolding_6
% 1.36/0.66 # Preprocessing class: HSSSSLSSSLMNHFN.
% 1.36/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.66 # Starting ho_unfolding_6 with 1500s (5) cores
% 1.36/0.66 # No SInE strategy applied
% 1.36/0.66 # Search class: HGUSF-FFMF32-MHFFMFNN
% 1.36/0.66 # partial match(1): HGUSF-FFSF32-MHFFMFNN
% 1.36/0.66 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.36/0.66 # Starting new_ho_10 with 811s (1) cores
% 1.36/0.66 # Starting ho_unfolding_6 with 151s (1) cores
% 1.36/0.66 # Starting new_bool_1 with 136s (1) cores
% 1.36/0.66 # Starting new_bool_2 with 136s (1) cores
% 1.36/0.66 # Starting new_bool_9 with 136s (1) cores
% 1.36/0.66 # ho_unfolding_6 with pid 11941 completed with status 0
% 1.36/0.66 # Result found by ho_unfolding_6
% 1.36/0.66 # Preprocessing class: HSSSSLSSSLMNHFN.
% 1.36/0.66 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.66 # Starting ho_unfolding_6 with 1500s (5) cores
% 1.36/0.66 # No SInE strategy applied
% 1.36/0.66 # Search class: HGUSF-FFMF32-MHFFMFNN
% 1.36/0.66 # partial match(1): HGUSF-FFSF32-MHFFMFNN
% 1.36/0.66 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.36/0.66 # Starting new_ho_10 with 811s (1) cores
% 1.36/0.66 # Starting ho_unfolding_6 with 151s (1) cores
% 1.36/0.66 # Preprocessing time : 0.002 s
% 1.36/0.66
% 1.36/0.66 # Proof found!
% 1.36/0.66 # SZS status Theorem
% 1.36/0.66 # SZS output start CNFRefutation
% See solution above
% 1.36/0.66 # Parsed axioms : 23
% 1.36/0.66 # Removed by relevancy pruning/SinE : 0
% 1.36/0.66 # Initial clauses : 43
% 1.36/0.66 # Removed in clause preprocessing : 15
% 1.36/0.66 # Initial clauses in saturation : 28
% 1.36/0.66 # Processed clauses : 553
% 1.36/0.66 # ...of these trivial : 2
% 1.36/0.66 # ...subsumed : 145
% 1.36/0.66 # ...remaining for further processing : 405
% 1.36/0.66 # Other redundant clauses eliminated : 16
% 1.36/0.66 # Clauses deleted for lack of memory : 0
% 1.36/0.66 # Backward-subsumed : 106
% 1.36/0.66 # Backward-rewritten : 120
% 1.36/0.66 # Generated clauses : 4241
% 1.36/0.66 # ...of the previous two non-redundant : 4087
% 1.36/0.66 # ...aggressively subsumed : 0
% 1.36/0.66 # Contextual simplify-reflections : 81
% 1.36/0.66 # Paramodulations : 4121
% 1.36/0.66 # Factorizations : 0
% 1.36/0.66 # NegExts : 51
% 1.36/0.66 # Equation resolutions : 25
% 1.36/0.66 # Disequality decompositions : 0
% 1.36/0.66 # Total rewrite steps : 2624
% 1.36/0.66 # ...of those cached : 2610
% 1.36/0.66 # Propositional unsat checks : 0
% 1.36/0.66 # Propositional check models : 0
% 1.36/0.66 # Propositional check unsatisfiable : 0
% 1.36/0.66 # Propositional clauses : 0
% 1.36/0.66 # Propositional clauses after purity: 0
% 1.36/0.66 # Propositional unsat core size : 0
% 1.36/0.66 # Propositional preprocessing time : 0.000
% 1.36/0.66 # Propositional encoding time : 0.000
% 1.36/0.66 # Propositional solver time : 0.000
% 1.36/0.66 # Success case prop preproc time : 0.000
% 1.36/0.66 # Success case prop encoding time : 0.000
% 1.36/0.66 # Success case prop solver time : 0.000
% 1.36/0.66 # Current number of processed clauses : 162
% 1.36/0.66 # Positive orientable unit clauses : 16
% 1.36/0.66 # Positive unorientable unit clauses: 0
% 1.36/0.66 # Negative unit clauses : 5
% 1.36/0.66 # Non-unit-clauses : 141
% 1.36/0.66 # Current number of unprocessed clauses: 3268
% 1.36/0.66 # ...number of literals in the above : 26393
% 1.36/0.66 # Current number of archived formulas : 0
% 1.36/0.66 # Current number of archived clauses : 243
% 1.36/0.66 # Clause-clause subsumption calls (NU) : 17454
% 1.36/0.66 # Rec. Clause-clause subsumption calls : 4190
% 1.36/0.66 # Non-unit clause-clause subsumptions : 288
% 1.36/0.66 # Unit Clause-clause subsumption calls : 621
% 1.36/0.66 # Rewrite failures with RHS unbound : 0
% 1.36/0.66 # BW rewrite match attempts : 64
% 1.36/0.66 # BW rewrite match successes : 12
% 1.36/0.66 # Condensation attempts : 553
% 1.36/0.66 # Condensation successes : 0
% 1.36/0.66 # Termbank termtop insertions : 307058
% 1.36/0.66 # Search garbage collected termcells : 1266
% 1.36/0.66
% 1.36/0.66 # -------------------------------------------------
% 1.36/0.66 # User time : 0.162 s
% 1.36/0.66 # System time : 0.005 s
% 1.36/0.66 # Total time : 0.167 s
% 1.36/0.66 # Maximum resident set size: 2088 pages
% 1.36/0.66
% 1.36/0.66 # -------------------------------------------------
% 1.36/0.66 # User time : 0.823 s
% 1.36/0.66 # System time : 0.024 s
% 1.36/0.66 # Total time : 0.847 s
% 1.36/0.66 # Maximum resident set size: 1764 pages
% 1.36/0.66 % E---3.1 exiting
% 1.36/0.66 % E exiting
%------------------------------------------------------------------------------