%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU691^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:25:03 AM UTC 2026
% Result : Theorem 1.14s 0.42s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
subset: $i > $i > $o ).
thf(decl_28,type,
kpair: $i > $i > $i ).
thf(decl_29,type,
cartprod: $i > $i > $i ).
thf(decl_30,type,
singleton: $i > $o ).
thf(decl_31,type,
ex1: $i > ( $i > $o ) > $o ).
thf(decl_32,type,
breln: $i > $i > $i > $o ).
thf(decl_33,type,
func: $i > $i > $i > $o ).
thf(decl_34,type,
ap: $i > $i > $i > $i > $i ).
thf(decl_35,type,
funcGraphProp1: $o ).
thf(decl_36,type,
funcGraphProp2: $o ).
thf(decl_37,type,
eqbreln: $o ).
thf(decl_38,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_39,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_40,type,
esk3_4: $i > $i > $i > $i > $i ).
thf(decl_41,type,
esk4_4: $i > $i > $i > $i > $i ).
thf(decl_42,type,
esk5_4: $i > $i > $i > $i > $i ).
thf(decl_43,type,
esk6_4: $i > $i > $i > $i > $i ).
thf(decl_44,type,
esk7_0: $i ).
thf(decl_45,type,
esk8_0: $i ).
thf(decl_46,type,
esk9_0: $i ).
thf(decl_47,type,
esk10_1: $i > $i ).
thf(decl_48,type,
esk11_0: $i ).
thf(decl_49,type,
esk12_1: $i > $i ).
thf(ex1,axiom,
( ex1
= ( ^ [X1: $i,X3: $i > $o] :
( singleton
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.p',ex1) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.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/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.p',func) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.p',breln) ).
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/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.p',funcext) ).
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/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.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/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.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/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.p',eqbreln) ).
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,negated_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 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[funcext]) ).
thf(c_0_15,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_16,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_17,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_18,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)],[c_0_14,c_0_13]),c_0_15]),c_0_16]),c_0_17]) ).
thf(c_0_19,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_18])])])])])]) ).
thf(c_0_20,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_19]) ).
thf(c_0_21,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_19]) ).
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 @ ( esk3_4 @ X1 @ X2 @ X4 @ X5 ) @ X1 )
| ~ ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
subset @ esk9_0 @ ( cartprod @ esk7_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X5: $i,X7: $i,X6: $i] :
( ( ( ap @ X1 @ X2 @ X4 @ ( esk5_4 @ X5 @ X6 @ X7 @ X4 ) )
= ( esk6_4 @ X5 @ X6 @ X7 @ X4 ) )
| ( X7 = X4 )
| ( in @ ( esk3_4 @ X5 @ X6 @ X7 @ X4 ) @ X5 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ ( esk6_4 @ X5 @ X6 @ X7 @ X4 ) @ X2 )
| ~ ( in @ ( esk5_4 @ X5 @ X6 @ X7 @ X4 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X5 @ X6 ) )
| ~ ( subset @ X7 @ ( cartprod @ X5 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk8_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) )
| ( X2 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]) ).
thf(c_0_27,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_19]) ).
thf(c_0_28,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_19]) ).
thf(c_0_29,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_19]) ).
thf(c_0_30,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_19]) ).
thf(c_0_31,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_19]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
| ( X1 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23])]) ).
thf(c_0_33,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_19]) ).
thf(c_0_34,negated_conjecture,
subset @ esk11_0 @ ( cartprod @ esk7_0 @ esk8_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_35,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(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
| ( X1 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_37,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_33,c_0_34]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34])]) ).
thf(c_0_39,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_19]) ).
thf(c_0_40,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_19]) ).
thf(c_0_41,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_19]) ).
thf(c_0_42,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_19]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_38]) ).
thf(c_0_44,negated_conjecture,
esk9_0 != esk11_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_45,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_39,c_0_40]),c_0_41]) ).
thf(c_0_46,negated_conjecture,
( ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_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_42,c_0_43]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_47,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_23])]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk9_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk9_0 ) )
| ( X4 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk9_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk9_0 ) )
| ( X4 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_27]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
| ( X1 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_25]),c_0_23])]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) )
| ( X1 = esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_50]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_51]),c_0_34])]) ).
thf(c_0_53,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_19]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_51]),c_0_52]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i] :
( ( in @ ( kpair @ X1 @ ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 ) ) @ esk9_0 )
| ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X5: $i,X7: $i,X6: $i] :
( ( ( ap @ X1 @ X2 @ X4 @ ( esk3_4 @ X5 @ X6 @ X4 @ X7 ) )
= ( esk4_4 @ X5 @ X6 @ X4 @ X7 ) )
| ( X4 = X7 )
| ( in @ ( esk6_4 @ X5 @ X6 @ X4 @ X7 ) @ X6 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ ( esk4_4 @ X5 @ X6 @ X4 @ X7 ) @ X2 )
| ~ ( in @ ( esk3_4 @ X5 @ X6 @ X4 @ X7 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X7 @ ( cartprod @ X5 @ X6 ) )
| ~ ( subset @ X4 @ ( cartprod @ X5 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
thf(c_0_57,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_19]) ).
thf(c_0_58,negated_conjecture,
( ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_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_42,c_0_54]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_59,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_28,c_0_40]),c_0_41]) ).
thf(c_0_60,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(spm,[status(thm)],[c_0_55,c_0_31]) ).
thf(c_0_61,negated_conjecture,
! [X1: $i,X6: $i,X5: $i,X4: $i,X2: $i] :
( ( ( ap @ X1 @ X2 @ X4 @ ( esk3_4 @ X5 @ X2 @ X4 @ X6 ) )
= ( esk4_4 @ X5 @ X2 @ X4 @ X6 ) )
| ( X4 = X6 )
| ( in @ ( esk6_4 @ X5 @ X2 @ X4 @ X6 ) @ X2 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ ( esk3_4 @ X5 @ X2 @ X4 @ X6 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X6 @ ( cartprod @ X5 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X5 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
thf(c_0_62,negated_conjecture,
in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_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_58,c_0_27]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_63,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_19]) ).
thf(c_0_64,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_19]) ).
thf(c_0_65,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_59,c_0_31]),c_0_23])]),c_0_60]) ).
thf(c_0_66,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_61,c_0_62]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_67,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X5: $i,X7: $i,X6: $i] :
( ( ( ap @ X1 @ X2 @ X4 @ ( esk3_4 @ X5 @ X6 @ X4 @ X7 ) )
= ( esk4_4 @ X5 @ X6 @ X4 @ X7 ) )
| ( X4 = X7 )
| ( in @ ( esk5_4 @ X5 @ X6 @ X4 @ X7 ) @ X5 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ ( esk4_4 @ X5 @ X6 @ X4 @ X7 ) @ X2 )
| ~ ( in @ ( esk3_4 @ X5 @ X6 @ X4 @ X7 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X7 @ ( cartprod @ X5 @ X6 ) )
| ~ ( subset @ X4 @ ( cartprod @ X5 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_63]) ).
thf(c_0_68,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_64,c_0_23]) ).
thf(c_0_69,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_19]) ).
thf(c_0_70,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk9_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_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_65,c_0_66]),c_0_62])]) ).
thf(c_0_71,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ X2 @ ( esk3_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) )
| ( X2 = esk9_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ X2 ) @ X1 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X2 @ esk9_0 ) @ X1 )
| ~ ( subset @ X2 @ ( cartprod @ esk7_0 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_23])]) ).
thf(c_0_72,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_39,c_0_29]),c_0_30]) ).
thf(c_0_73,negated_conjecture,
( ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_69,c_0_70]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_74,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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(spm,[status(thm)],[c_0_71,c_0_62]),c_0_34])]),c_0_44]) ).
thf(c_0_75,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 )
= X2 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_72,c_0_73]),c_0_34])]) ).
thf(c_0_76,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_19]) ).
thf(c_0_77,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk9_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_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_65,c_0_74]),c_0_62])]) ).
thf(c_0_78,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ X1 @ X2 @ esk11_0 @ X4 ) )
= ( esk4_4 @ X1 @ X2 @ esk11_0 @ X4 ) )
| ( esk11_0 = X4 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ X2 @ esk11_0 @ X4 ) @ X2 )
| ~ ( in @ ( esk4_4 @ X1 @ X2 @ esk11_0 @ X4 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ X2 @ esk11_0 @ X4 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_75,c_0_53]) ).
thf(c_0_79,negated_conjecture,
( ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_76,c_0_77]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_80,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ X1 @ esk8_0 @ esk11_0 @ X2 ) )
= ( esk4_4 @ X1 @ esk8_0 @ esk11_0 @ X2 ) )
| ( esk11_0 = X2 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ esk8_0 @ esk11_0 @ X2 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ esk8_0 @ esk11_0 @ X2 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_78,c_0_57]) ).
thf(c_0_81,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ X1 )
= X2 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_72,c_0_79]),c_0_34])]) ).
thf(c_0_82,negated_conjecture,
! [X1: $i,X2: $i] :
( ( esk11_0 = X1 )
| ( in @ ( kpair @ ( esk3_4 @ X2 @ esk8_0 @ esk11_0 @ X1 ) @ ( esk4_4 @ X2 @ esk8_0 @ esk11_0 @ X1 ) ) @ esk9_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X2 @ esk8_0 @ esk11_0 @ X1 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X2 @ esk8_0 @ esk11_0 @ X1 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X2 @ esk8_0 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_65,c_0_80]) ).
thf(c_0_83,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ X1 @ X2 @ esk11_0 @ X4 ) )
= ( esk4_4 @ X1 @ X2 @ esk11_0 @ X4 ) )
| ( esk11_0 = X4 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk5_4 @ X1 @ X2 @ esk11_0 @ X4 ) @ X1 )
| ~ ( in @ ( esk4_4 @ X1 @ X2 @ esk11_0 @ X4 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ X2 @ esk11_0 @ X4 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_81,c_0_63]) ).
thf(c_0_84,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_22,c_0_34]) ).
thf(c_0_85,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_19]) ).
thf(c_0_86,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_82]),c_0_44]) ).
thf(c_0_87,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_68]),c_0_62]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) )
| ( X2 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_84]),c_0_34])]) ).
thf(c_0_89,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X5: $i,X7: $i,X6: $i] :
( ( ( ap @ X1 @ X2 @ X4 @ ( esk5_4 @ X5 @ X6 @ X7 @ X4 ) )
= ( esk6_4 @ X5 @ X6 @ X7 @ X4 ) )
| ( X7 = X4 )
| ( in @ ( esk4_4 @ X5 @ X6 @ X7 @ X4 ) @ X6 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ ( esk6_4 @ X5 @ X6 @ X7 @ X4 ) @ X2 )
| ~ ( in @ ( esk5_4 @ X5 @ X6 @ X7 @ X4 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X5 @ X6 ) )
| ~ ( subset @ X7 @ ( cartprod @ X5 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_85]) ).
thf(c_0_90,negated_conjecture,
in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_62]),c_0_23]),c_0_34])]) ).
thf(c_0_91,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk9_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_87]),c_0_62])]) ).
thf(c_0_92,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) )
| ( X1 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_27]),c_0_34])]) ).
thf(c_0_93,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_94,negated_conjecture,
in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_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_76,c_0_91]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_95,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 ) ) @ esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ 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_65,c_0_92]) ).
thf(c_0_96,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_23])]) ).
thf(c_0_97,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 )
| ~ ( 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_42,c_0_95]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_98,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_96]),c_0_94])]) ).
thf(c_0_99,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 @ ( esk5_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_72,c_0_97]),c_0_34])]) ).
thf(c_0_100,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_19]) ).
thf(c_0_101,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_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_35,c_0_98]),c_0_34]),c_0_94])]) ).
thf(c_0_102,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
| ( X4 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_99,c_0_21]) ).
thf(c_0_103,negated_conjecture,
( ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_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_100,c_0_101]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_104,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
| ( X4 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk3_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_27]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_105,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_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(spm,[status(thm)],[c_0_37,c_0_98]),c_0_94])]),c_0_103]) ).
thf(c_0_106,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk11_0 ) )
| ( X1 = esk11_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_84]),c_0_34])]) ).
thf(c_0_107,negated_conjecture,
( ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_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_100,c_0_105]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_108,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 ) ) @ esk9_0 )
| ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_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_65,c_0_106]) ).
thf(c_0_109,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_107]),c_0_23])]) ).
thf(c_0_110,negated_conjecture,
( ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( 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_42,c_0_108]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_111,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_19]) ).
thf(c_0_112,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk9_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk9_0 ) )
| ( X4 = esk9_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 )
| ( in @ ( esk4_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ X2 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk9_0 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_85]) ).
thf(c_0_113,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_110,c_0_27]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_114,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_64,c_0_34]) ).
thf(c_0_115,negated_conjecture,
! [X1: $i] :
( ( X1 = esk9_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) ) @ esk9_0 )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ X1 @ esk9_0 ) ) @ X1 )
| ~ ( subset @ X1 @ ( cartprod @ esk7_0 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_111,c_0_23]) ).
thf(c_0_116,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_90]),c_0_94]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_117,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_113]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_118,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ X2 @ ( esk3_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) )
| ( X2 = esk11_0 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ X2 ) @ X1 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ X2 @ esk11_0 ) @ X1 )
| ~ ( subset @ X2 @ ( cartprod @ esk7_0 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_114]),c_0_34])]) ).
thf(c_0_119,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk9_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_34]),c_0_44]) ).
thf(c_0_120,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_116]),c_0_94])]) ).
thf(c_0_121,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 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_117]),c_0_113])]) ).
thf(c_0_122,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_113]),c_0_23])]),c_0_44]) ).
thf(c_0_123,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ X2 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk2_3 @ X1 @ X2 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X2 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_119]) ).
thf(c_0_124,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_35,c_0_120]),c_0_34]),c_0_94])]) ).
thf(c_0_125,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 @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_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_35,c_0_121]),c_0_34]),c_0_113])]) ).
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 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_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(spm,[status(thm)],[c_0_31,c_0_122]),c_0_113])]) ).
thf(c_0_127,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_123,c_0_90]) ).
thf(c_0_128,negated_conjecture,
( ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_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_100,c_0_124]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_129,negated_conjecture,
( ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_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_69,c_0_125]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_130,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 @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_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_35,c_0_126]),c_0_34]),c_0_113])]) ).
thf(c_0_131,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_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(spm,[status(thm)],[c_0_127,c_0_94]),c_0_23])]) ).
thf(c_0_132,negated_conjecture,
( ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ esk8_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_120]),c_0_94])]),c_0_128]) ).
thf(c_0_133,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 @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_121]),c_0_113])]),c_0_129]) ).
thf(c_0_134,negated_conjecture,
( ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_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_76,c_0_130]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_135,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ X1 @ X2 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ X2 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X2 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_131]) ).
thf(c_0_136,negated_conjecture,
in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_100,c_0_132]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_137,negated_conjecture,
( ( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_133]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_138,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 @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_126]),c_0_113])]),c_0_134]) ).
thf(c_0_139,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ X1 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
thf(c_0_140,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_137]),c_0_23])]) ).
thf(c_0_141,negated_conjecture,
( ( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_138]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_142,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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(spm,[status(thm)],[c_0_139,c_0_62]),c_0_34])]) ).
thf(c_0_143,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ X1 @ X2 @ esk9_0 @ X4 ) )
= ( esk4_4 @ X1 @ X2 @ esk9_0 @ X4 ) )
| ( esk9_0 = X4 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ X2 @ esk9_0 @ X4 ) @ X2 )
| ~ ( in @ ( esk4_4 @ X1 @ X2 @ esk9_0 @ X4 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ X2 @ esk9_0 @ X4 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_140,c_0_53]) ).
thf(c_0_144,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_141]),c_0_23])]) ).
thf(c_0_145,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_31,c_0_142]),c_0_94])]) ).
thf(c_0_146,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) )
= ( esk4_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) )
| ( esk9_0 = X2 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_143,c_0_57]) ).
thf(c_0_147,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk3_4 @ X1 @ X2 @ esk9_0 @ X4 ) )
= ( esk4_4 @ X1 @ X2 @ esk9_0 @ X4 ) )
| ( esk9_0 = X4 )
| ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk5_4 @ X1 @ X2 @ esk9_0 @ X4 ) @ X1 )
| ~ ( in @ ( esk4_4 @ X1 @ X2 @ esk9_0 @ X4 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ X2 @ esk9_0 @ X4 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_144,c_0_63]) ).
thf(c_0_148,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_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 )
| ~ ( 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_35,c_0_145]),c_0_34]),c_0_94])]) ).
thf(c_0_149,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) )
= ( esk4_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) )
| ( esk9_0 = X2 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ esk8_0 @ esk9_0 @ X2 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ X2 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_31,c_0_146]) ).
thf(c_0_150,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_114]),c_0_113]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_151,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_19]) ).
thf(c_0_152,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_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(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_145]),c_0_94])]),c_0_148]) ).
thf(c_0_153,negated_conjecture,
! [X1: $i,X2: $i] :
( ( esk9_0 = X1 )
| ( in @ ( kpair @ ( esk3_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) @ ( esk4_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) ) @ esk11_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) @ esk8_0 )
| ~ ( in @ ( esk1_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( esk3_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X2 @ esk8_0 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ esk8_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_149]),c_0_34])]) ).
thf(c_0_154,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_31,c_0_150]),c_0_113])]) ).
thf(c_0_155,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_156,negated_conjecture,
! [X1: $i,X2: $i] :
( ( esk9_0 = X1 )
| ( in @ ( kpair @ ( esk3_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) @ ( esk4_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) ) @ esk11_0 )
| ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X2 @ esk8_0 @ esk9_0 @ X1 ) @ esk7_0 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X2 @ esk8_0 ) )
| ~ ( subset @ X1 @ ( cartprod @ X2 @ esk8_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_149]),c_0_153]) ).
thf(c_0_157,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_35,c_0_154]),c_0_34]),c_0_113])]) ).
thf(c_0_158,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ X1 @ X2 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ X2 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X2 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_155]) ).
thf(c_0_159,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk6_4 @ X1 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk3_4 @ X1 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_156]),c_0_44]) ).
thf(c_0_160,negated_conjecture,
( ( 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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_157]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_161,negated_conjecture,
! [X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ X1 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_158,c_0_136]) ).
thf(c_0_162,negated_conjecture,
in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_113]),c_0_34]),c_0_23])]) ).
thf(c_0_163,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(spm,[status(thm)],[c_0_37,c_0_154]),c_0_113])]),c_0_160]) ).
thf(c_0_164,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_19]) ).
thf(c_0_165,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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(spm,[status(thm)],[c_0_161,c_0_62]),c_0_34])]) ).
thf(c_0_166,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ 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 @ X1 @ esk8_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_162]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_167,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_76,c_0_163]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_168,negated_conjecture,
! [X1: $i,X2: $i,X4: $i,X5: $i,X7: $i,X6: $i] :
( ( ( ap @ X1 @ X2 @ X4 @ ( esk5_4 @ X5 @ X6 @ X7 @ X4 ) )
= ( esk6_4 @ X5 @ X6 @ X7 @ X4 ) )
| ( X7 = X4 )
| ( in @ ( esk2_3 @ X1 @ X2 @ X4 ) @ X1 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X5 @ X6 @ X7 @ X4 ) @ ( esk4_4 @ X5 @ X6 @ X7 @ X4 ) ) @ X4 )
| ~ ( in @ ( esk6_4 @ X5 @ X6 @ X7 @ X4 ) @ X2 )
| ~ ( in @ ( esk5_4 @ X5 @ X6 @ X7 @ X4 ) @ X1 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X5 @ X6 ) )
| ~ ( subset @ X7 @ ( cartprod @ X5 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_164]) ).
thf(c_0_169,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk9_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_65,c_0_165]),c_0_62])]) ).
thf(c_0_170,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_34])]) ).
thf(c_0_171,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ X2 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ X2 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X2 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_172,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_170]),c_0_167])]) ).
thf(c_0_173,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_171,c_0_90]) ).
thf(c_0_174,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_100,c_0_172]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_175,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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(spm,[status(thm)],[c_0_173,c_0_94]),c_0_23])]) ).
thf(c_0_176,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_19]) ).
thf(c_0_177,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_111,c_0_34]) ).
thf(c_0_178,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_72,c_0_174]),c_0_34])]) ).
thf(c_0_179,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_31,c_0_175]),c_0_94])]) ).
thf(c_0_180,negated_conjecture,
( ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_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_176,c_0_169]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_181,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_177,c_0_23]),c_0_44]) ).
thf(c_0_182,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
| ( X4 = esk11_0 )
| ( in @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ esk8_0 )
| ( in @ ( esk4_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ X2 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_178,c_0_85]) ).
thf(c_0_183,negated_conjecture,
( ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk1_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_35,c_0_179]),c_0_34]),c_0_94])]),c_0_180]) ).
thf(c_0_184,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ X2 @ 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 @ X1 @ X2 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X2 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_181]) ).
thf(c_0_185,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_162]),c_0_167]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_186,negated_conjecture,
( ( in @ ( esk2_3 @ esk7_0 @ esk8_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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_179]),c_0_94])]),c_0_183]),c_0_180]) ).
thf(c_0_187,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ 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 @ X1 @ esk8_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_184,c_0_162]) ).
thf(c_0_188,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_185]),c_0_167])]) ).
thf(c_0_189,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk11_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_186]),c_0_23])]) ).
thf(c_0_190,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(spm,[status(thm)],[c_0_187,c_0_167]),c_0_34])]) ).
thf(c_0_191,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_100,c_0_188]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_192,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 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]),c_0_113])]) ).
thf(c_0_193,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_192]),c_0_113])]) ).
thf(c_0_194,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_65,c_0_193]),c_0_167])]) ).
thf(c_0_195,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_151,c_0_194]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_196,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_195]),c_0_191]),c_0_113])]) ).
thf(c_0_197,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_31,c_0_196]),c_0_113])]) ).
thf(c_0_198,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_35,c_0_197]),c_0_34]),c_0_113])]) ).
thf(c_0_199,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(spm,[status(thm)],[c_0_37,c_0_197]),c_0_113])]),c_0_198]) ).
thf(c_0_200,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ X2 @ 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 )
| ( in @ ( esk2_3 @ X1 @ X2 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X2 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_199]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_201,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ 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 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk11_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk9_0 @ esk11_0 ) @ X1 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_200,c_0_162]) ).
thf(c_0_202,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(spm,[status(thm)],[c_0_201,c_0_167]),c_0_34])]) ).
thf(c_0_203,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_176,c_0_199]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_204,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_65,c_0_202]),c_0_167])]),c_0_203]) ).
thf(c_0_205,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_72,c_0_204]),c_0_34])]) ).
thf(c_0_206,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_205,c_0_131]),c_0_136]),c_0_62])]) ).
thf(c_0_207,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_206]),c_0_94])]) ).
thf(c_0_208,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_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_35,c_0_207]),c_0_34]),c_0_94])]) ).
thf(c_0_209,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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(spm,[status(thm)],[c_0_37,c_0_207]),c_0_94])]),c_0_208]) ).
thf(c_0_210,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk11_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_151,c_0_209]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_211,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_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_205,c_0_210]),c_0_136]),c_0_62])]) ).
thf(c_0_212,negated_conjecture,
( ( in @ ( kpair @ ( esk3_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk4_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) ) @ esk9_0 )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_211]),c_0_62])]) ).
thf(c_0_213,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ap @ X1 @ X2 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ X2 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X2 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_212]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_214,negated_conjecture,
! [X1: $i] :
( ( ( ap @ X1 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ( in @ ( esk2_3 @ X1 @ esk8_0 @ esk9_0 ) @ X1 )
| ~ ( in @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ X1 )
| ~ ( subset @ esk9_0 @ ( cartprod @ X1 @ esk8_0 ) ) ),
inference(spm,[status(thm)],[c_0_213,c_0_90]) ).
thf(c_0_215,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_94]),c_0_23])]) ).
thf(c_0_216,negated_conjecture,
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
= ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) )
| ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_215]),c_0_94])]) ).
thf(c_0_217,negated_conjecture,
( ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( kpair @ ( esk5_4 @ esk7_0 @ esk8_0 @ esk11_0 @ esk9_0 ) @ ( esk6_4 @ esk7_0 @ esk8_0 @ esk11_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_176,c_0_212]),c_0_23]),c_0_34])]),c_0_44]) ).
thf(c_0_218,negated_conjecture,
( ( in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0 )
| ~ ( in @ ( esk1_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_35,c_0_216]),c_0_34]),c_0_94])]),c_0_217]) ).
thf(c_0_219,negated_conjecture,
in @ ( esk2_3 @ esk7_0 @ esk8_0 @ esk9_0 ) @ esk7_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_216]),c_0_94])]),c_0_218]),c_0_217]) ).
thf(c_0_220,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk9_0 @ X1 )
= X2 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk9_0 )
| ~ ( in @ X2 @ esk8_0 )
| ~ ( in @ X1 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_219]),c_0_23])]) ).
thf(c_0_221,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_205,c_0_181]),c_0_162]),c_0_167])]) ).
thf(c_0_222,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 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_191]),c_0_113])]) ).
thf(c_0_223,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_222]),c_0_113])]) ).
thf(c_0_224,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_65,c_0_223]),c_0_167])]) ).
thf(c_0_225,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_151,c_0_224]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_226,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_225]),c_0_191]),c_0_113])]) ).
thf(c_0_227,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_31,c_0_226]),c_0_113])]) ).
thf(c_0_228,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_35,c_0_227]),c_0_34]),c_0_113])]) ).
thf(c_0_229,negated_conjecture,
! [X1: $i,X4: $i,X2: $i] :
( ( ( ap @ esk7_0 @ esk8_0 @ esk11_0 @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
= ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) )
| ( X4 = esk11_0 )
| ~ ( in @ ( kpair @ ( esk3_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ ( esk4_4 @ X1 @ X2 @ X4 @ esk11_0 ) ) @ esk11_0 )
| ~ ( in @ ( esk6_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk8_0 )
| ~ ( in @ ( esk5_4 @ X1 @ X2 @ X4 @ esk11_0 ) @ esk7_0 )
| ~ ( subset @ esk11_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_205,c_0_164]) ).
thf(c_0_230,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(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_227]),c_0_113])]),c_0_228]) ).
thf(c_0_231,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 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_162]),c_0_167]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_232,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_176,c_0_230]),c_0_34]),c_0_23])]),c_0_44]) ).
thf(c_0_233,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_231]),c_0_167])]),c_0_232]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU691^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n026.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 14:13:28 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.PIpjfJWZYH/E---3.1_658698.p
% 1.14/0.42 % Version: 3.5.1-ho
% 1.14/0.42 % Preprocessing class: HSSSSLSSSLMNHFN.
% 1.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.14/0.42 % Starting ho_unfolding_6 with 1500s (5) cores
% 1.14/0.42 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 1.14/0.42 % Starting pre_casc_5 with 300s (1) cores
% 1.14/0.42 % Starting ehoh_best_sine with 300s (1) cores
% 1.14/0.42 % ho_unfolding_6 with pid 658711 completed with status 0
% 1.14/0.42 % Result found by ho_unfolding_6
% 1.14/0.42 % Preprocessing class: HSSSSLSSSLMNHFN.
% 1.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.14/0.42 % Starting ho_unfolding_6 with 1500s (5) cores
% 1.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 1.14/0.42 % No SInE strategy applied
% 1.14/0.42 % Search class: HGUSF-FFMF32-MHFFMFNN
% 1.14/0.42 % partial match(1): HGUSF-FFSF32-MHFFMFNN
% 1.14/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.14/0.42 % Starting SubtermCWHack with 136s (1) cores
% 1.14/0.42 % Starting ho_unfolding_6 with 151s (1) cores
% 1.14/0.42 % Starting sh5l with 136s (1) cores
% 1.14/0.42 % Starting new_bool_1 with 136s (1) cores
% 1.14/0.42 % Starting new_bool_2 with 136s (1) cores
% 1.14/0.42 % SubtermCWHack with pid 658716 completed with status 0
% 1.14/0.42 % Result found by SubtermCWHack
% 1.14/0.42 % Preprocessing class: HSSSSLSSSLMNHFN.
% 1.14/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.14/0.42 % Starting ho_unfolding_6 with 1500s (5) cores
% 1.14/0.42 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 1.14/0.42 % No SInE strategy applied
% 1.14/0.42 % Search class: HGUSF-FFMF32-MHFFMFNN
% 1.14/0.42 % partial match(1): HGUSF-FFSF32-MHFFMFNN
% 1.14/0.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.14/0.42 % Starting SubtermCWHack with 136s (1) cores
% 1.14/0.42 % Preprocessing time : 0.001 s
% 1.14/0.42
% 1.14/0.42 % Proof found!
% 1.14/0.42 % SZS status Theorem
% 1.14/0.42 % SZS output start CNFRefutation
% See solution above
% 1.14/0.42 % Parsed axioms : 23
% 1.14/0.42 % Removed by relevancy pruning/SinE : 0
% 1.14/0.42 % Initial clauses : 43
% 1.14/0.42 % Removed in clause preprocessing : 15
% 1.14/0.42 % Initial clauses in saturation : 28
% 1.14/0.42 % Processed clauses : 881
% 1.14/0.42 % ...of these trivial : 0
% 1.14/0.42 % ...subsumed : 241
% 1.14/0.42 % ...remaining for further processing : 640
% 1.14/0.42 % Other redundant clauses eliminated : 0
% 1.14/0.42 % Clauses deleted for lack of memory : 0
% 1.14/0.42 % Backward-subsumed : 251
% 1.14/0.42 % Backward-rewritten : 248
% 1.14/0.42 % Generated clauses : 2540
% 1.14/0.42 % ...of the previous two non-redundant : 2255
% 1.14/0.42 % ...aggressively subsumed : 0
% 1.14/0.42 % Contextual simplify-reflections : 109
% 1.14/0.42 % Paramodulations : 2540
% 1.14/0.42 % Factorizations : 0
% 1.14/0.42 % NegExts : 0
% 1.14/0.42 % Equation resolutions : 0
% 1.14/0.42 % Disequality decompositions : 0
% 1.14/0.42 % Total rewrite steps : 2796
% 1.14/0.42 % ...of those cached : 2775
% 1.14/0.42 % Propositional unsat checks : 0
% 1.14/0.42 % Propositional check models : 0
% 1.14/0.42 % Propositional check unsatisfiable : 0
% 1.14/0.42 % Propositional clauses : 0
% 1.14/0.42 % Propositional clauses after purity: 0
% 1.14/0.42 % Propositional unsat core size : 0
% 1.14/0.42 % Propositional preprocessing time : 0.000
% 1.14/0.42 % Propositional encoding time : 0.000
% 1.14/0.42 % Propositional solver time : 0.000
% 1.14/0.42 % Success case prop preproc time : 0.000
% 1.14/0.42 % Success case prop encoding time : 0.000
% 1.14/0.42 % Success case prop solver time : 0.000
% 1.14/0.42 % Current number of processed clauses : 141
% 1.14/0.42 % Positive orientable unit clauses : 21
% 1.14/0.42 % Positive unorientable unit clauses: 0
% 1.14/0.42 % Negative unit clauses : 3
% 1.14/0.42 % Non-unit-clauses : 117
% 1.14/0.42 % Current number of unprocessed clauses: 265
% 1.14/0.42 % ...number of literals in the above : 2830
% 1.14/0.42 % Current number of archived formulas : 0
% 1.14/0.42 % Current number of archived clauses : 499
% 1.14/0.42 % Clause-clause subsumption calls (NU) : 66200
% 1.14/0.42 % Rec. Clause-clause subsumption calls : 3107
% 1.14/0.42 % Non-unit clause-clause subsumptions : 591
% 1.14/0.42 % Unit Clause-clause subsumption calls : 484
% 1.14/0.42 % Rewrite failures with RHS unbound : 0
% 1.14/0.42 % BW rewrite match attempts : 104
% 1.14/0.42 % BW rewrite match successes : 16
% 1.14/0.42 % Condensation attempts : 0
% 1.14/0.42 % Condensation successes : 0
% 1.14/0.42 % Termbank termtop insertions : 170094
% 1.14/0.42 % Search garbage collected termcells : 1265
% 1.14/0.42
% 1.14/0.42 % -------------------------------------------------
% 1.14/0.42 % User time : 0.163 s
% 1.14/0.42 % System time : 0.007 s
% 1.14/0.42 % Total time : 0.170 s
% 1.14/0.42 % Maximum resident set size: 3856 pages
% 1.14/0.42
% 1.14/0.42 % -------------------------------------------------
% 1.14/0.42 % User time : 0.602 s
% 1.14/0.42 % System time : 0.029 s
% 1.14/0.42 % Total time : 0.631 s
% 1.14/0.42 % Maximum resident set size: 4864 pages
% 1.14/0.42 % E exiting
%------------------------------------------------------------------------------