TSTP Solution File: SEU645^2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU645^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:48 EDT 2024
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 32
% Syntax : Number of formulae : 72 ( 28 unt; 20 typ; 0 def)
% Number of atoms : 170 ( 52 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 860 ( 36 ~; 33 |; 27 &; 734 @)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 147 ( 20 ^ 109 !; 18 ?; 147 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
setunion: $i > $i ).
thf(decl_26,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_27,type,
dsetconstrER: $o ).
thf(decl_28,type,
iskpair: $i > $o ).
thf(decl_29,type,
kpair: $i > $i > $i ).
thf(decl_30,type,
kpairp: $o ).
thf(decl_31,type,
singleton: $i > $o ).
thf(decl_32,type,
setukpairinjL1: $o ).
thf(decl_33,type,
kfstsingleton: $o ).
thf(decl_34,type,
theprop: $o ).
thf(decl_35,type,
kfst: $i > $i ).
thf(decl_36,type,
esk1_2: $i > $i > $i ).
thf(decl_37,type,
esk2_2: $i > $i > $i ).
thf(decl_38,type,
esk3_1: $i > $i ).
thf(decl_39,type,
esk4_0: $i ).
thf(decl_40,type,
esk5_0: $i ).
thf(decl_41,type,
epred1_1: $i > $i > $o ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ? [X4: $i] :
( ( in @ X4 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(kfstsingleton,axiom,
( kfstsingleton
<=> ! [X6: $i] :
( ( iskpair @ X6 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X3: $i,X4: $i] : ( iskpair @ ( kpair @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(theprop,axiom,
( theprop
<=> ! [X7: $i] :
( ( singleton @ X7 )
=> ( in @ ( setunion @ X7 ) @ X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(kfstpairEq,conjecture,
( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X3: $i,X4: $i] :
( ( kfst @ ( kpair @ X3 @ X4 ) )
= X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(setukpairinjL1,axiom,
( setukpairinjL1
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( X3 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(kpair,axiom,
( kpair
= ( ^ [X3: $i,X4: $i] : ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(kfst,axiom,
( kfst
= ( ^ [X6: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfst) ).
thf(c_0_10,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ? [X4: $i] :
( ( in @ X4 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_11,plain,
( kfstsingleton
<=> ! [X6: $i] :
( ( iskpair @ X6 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X6 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[kfstsingleton]) ).
thf(c_0_12,plain,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_13,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_14,axiom,
( kpairp
= ( ! [X3: $i,X4: $i] :
? [X20: $i] :
( ( in @ X20 @ ( setunion @ ( kpair @ X3 @ X4 ) ) )
& ? [X21: $i] :
( ( in @ X21 @ ( setunion @ ( kpair @ X3 @ X4 ) ) )
& ( ( kpair @ X3 @ X4 )
= ( setadjoin @ ( setadjoin @ X20 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X20 @ ( setadjoin @ X21 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairp,c_0_10]) ).
thf(c_0_15,plain,
( kfstsingleton
= ( ! [X6: $i] :
( ? [X22: $i] :
( ( in @ X22 @ ( setunion @ X6 ) )
& ? [X23: $i] :
( ( in @ X23 @ ( setunion @ X6 ) )
& ( X6
= ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X23 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ ( setunion @ X6 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X6 ) ) )
& ( ( dsetconstr @ ( setunion @ X6 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X6 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_10]),c_0_12]) ).
thf(c_0_16,axiom,
( theprop
= ( ! [X7: $i] :
( ? [X25: $i] :
( ( in @ X25 @ X7 )
& ( X7
= ( setadjoin @ X25 @ emptyset ) ) )
=> ( in @ ( setunion @ X7 ) @ X7 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_12]) ).
thf(c_0_17,negated_conjecture,
~ ( ! [X26: $i,X27: $i > $o,X28: $i] :
( ( in @ X28 @ ( dsetconstr @ X26 @ X27 ) )
=> ( X27 @ X28 ) )
=> ( ! [X29: $i,X30: $i] :
? [X31: $i] :
( ( in @ X31 @ ( setunion @ ( kpair @ X29 @ X30 ) ) )
& ? [X32: $i] :
( ( in @ X32 @ ( setunion @ ( kpair @ X29 @ X30 ) ) )
& ( ( kpair @ X29 @ X30 )
= ( setadjoin @ ( setadjoin @ X31 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X31 @ ( setadjoin @ X32 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X33: $i,X34: $i,X35: $i] :
( ( in @ ( setadjoin @ X35 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X33 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X33 @ ( setadjoin @ X34 @ emptyset ) ) @ emptyset ) ) )
=> ( X33 = X35 ) )
=> ( ! [X36: $i] :
( ? [X37: $i] :
( ( in @ X37 @ ( setunion @ X36 ) )
& ? [X38: $i] :
( ( in @ X38 @ ( setunion @ X36 ) )
& ( X36
= ( setadjoin @ ( setadjoin @ X37 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X37 @ ( setadjoin @ X38 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X39: $i] :
( ( in @ X39
@ ( dsetconstr @ ( setunion @ X36 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X36 ) ) )
& ( ( dsetconstr @ ( setunion @ X36 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X36 ) )
= ( setadjoin @ X39 @ emptyset ) ) ) )
=> ( ! [X40: $i] :
( ? [X41: $i] :
( ( in @ X41 @ X40 )
& ( X40
= ( setadjoin @ X41 @ emptyset ) ) )
=> ( in @ ( setunion @ X40 ) @ X40 ) )
=> ! [X3: $i,X4: $i] :
( ( kfst @ ( kpair @ X3 @ X4 ) )
= X3 ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[kfstpairEq]),c_0_13]),c_0_14]),setukpairinjL1]),c_0_15]),c_0_16])]) ).
thf(c_0_18,plain,
! [X42: $i,X43: $i] :
( ( kpair @ X42 @ X43 )
= ( setadjoin @ ( setadjoin @ X42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X42 @ ( setadjoin @ X43 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_19,negated_conjecture,
! [X48: $i,X49: $i > $o,X50: $i,X51: $i,X52: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i,X60: $i,X62: $i,X63: $i] :
( ( ~ ( in @ X50 @ ( dsetconstr @ X48 @ X49 ) )
| ( X49 @ X50 ) )
& ( in @ ( esk1_2 @ X51 @ X52 ) @ ( setunion @ ( kpair @ X51 @ X52 ) ) )
& ( in @ ( esk2_2 @ X51 @ X52 ) @ ( setunion @ ( kpair @ X51 @ X52 ) ) )
& ( ( kpair @ X51 @ X52 )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X51 @ X52 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X51 @ X52 ) @ ( setadjoin @ ( esk2_2 @ X51 @ X52 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ ( setadjoin @ X57 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X55 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X55 @ ( setadjoin @ X56 @ emptyset ) ) @ emptyset ) ) )
| ( X55 = X57 ) )
& ( ( in @ ( esk3_1 @ X58 )
@ ( dsetconstr @ ( setunion @ X58 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X58 ) ) )
| ~ ( in @ X59 @ ( setunion @ X58 ) )
| ~ ( in @ X60 @ ( setunion @ X58 ) )
| ( X58
!= ( setadjoin @ ( setadjoin @ X59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X59 @ ( setadjoin @ X60 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ( dsetconstr @ ( setunion @ X58 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X58 ) )
= ( setadjoin @ ( esk3_1 @ X58 ) @ emptyset ) )
| ~ ( in @ X59 @ ( setunion @ X58 ) )
| ~ ( in @ X60 @ ( setunion @ X58 ) )
| ( X58
!= ( setadjoin @ ( setadjoin @ X59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X59 @ ( setadjoin @ X60 @ emptyset ) ) @ emptyset ) ) ) )
& ( ~ ( in @ X63 @ X62 )
| ( X62
!= ( setadjoin @ X63 @ emptyset ) )
| ( in @ ( setunion @ X62 ) @ X62 ) )
& ( ( kfst @ ( kpair @ esk4_0 @ esk5_0 ) )
!= esk4_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])]) ).
thf(c_0_20,plain,
! [X66: $i,X1: $i] :
( ( epred1_1 @ X1 @ X66 )
<=> ( in @ ( setadjoin @ X66 @ emptyset ) @ X1 ) ),
introduced(definition) ).
thf(c_0_21,plain,
! [X45: $i,X46: $i] :
( ( kpair @ X45 @ X46 )
= ( setadjoin @ ( setadjoin @ X45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X45 @ ( setadjoin @ X46 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( ( dsetconstr @ ( setunion @ X1 ) @ ( epred1_1 @ X1 ) )
= ( setadjoin @ ( esk3_1 @ X1 ) @ emptyset ) )
| ~ ( in @ X3 @ ( setunion @ X1 ) )
| ~ ( in @ X4 @ ( setunion @ X1 ) )
| ( X1
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_19]),c_0_20]) ).
thf(c_0_23,plain,
! [X1: $i,X3: $i] :
( ( kpair @ X1 @ X3 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i,X3: $i] :
( ( kpair @ X1 @ X3 )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X3 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X3 ) @ ( setadjoin @ ( esk2_2 @ X1 @ X3 ) @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X44: $i] :
( ( kfst @ X44 )
= ( setunion
@ ( dsetconstr @ ( setunion @ X44 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X44 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kfst])]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X3: $i] :
( ( ( dsetconstr @ ( setunion @ ( kpair @ X1 @ X3 ) ) @ ( epred1_1 @ ( kpair @ X1 @ X3 ) ) )
= ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) )
| ~ ( in @ X3 @ ( setunion @ ( kpair @ X1 @ X3 ) ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ X1 @ X3 ) ) ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X3: $i] :
( ( kpair @ ( esk1_2 @ X1 @ X3 ) @ ( esk2_2 @ X1 @ X3 ) )
= ( kpair @ X1 @ X3 ) ),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( esk2_2 @ X1 @ X3 ) @ ( setunion @ ( kpair @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( esk1_2 @ X1 @ X3 ) @ ( setunion @ ( kpair @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_30,plain,
! [X47: $i] :
( ( kfst @ X47 )
= ( setunion
@ ( dsetconstr @ ( setunion @ X47 )
@ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X47 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_25]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( ( in @ ( esk3_1 @ X1 ) @ ( dsetconstr @ ( setunion @ X1 ) @ ( epred1_1 @ X1 ) ) )
= $true )
| ~ ( in @ X3 @ ( setunion @ X1 ) )
| ~ ( in @ X4 @ ( setunion @ X1 ) )
| ( X1
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_19]),c_0_20]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i,X3: $i] :
( ( dsetconstr @ ( setunion @ ( kpair @ X1 @ X3 ) ) @ ( epred1_1 @ ( kpair @ X1 @ X3 ) ) )
= ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i,X1: $i] :
( ( in @ ( setunion @ X3 ) @ X3 )
| ~ ( in @ X1 @ X3 )
| ( X3
!= ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_35,plain,
! [X1: $i] :
( ( kfst @ X1 )
= ( setunion @ ( dsetconstr @ ( setunion @ X1 ) @ ( epred1_1 @ X1 ) ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_30]),c_0_20]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ ( dsetconstr @ ( setunion @ ( kpair @ X1 @ X3 ) ) @ ( epred1_1 @ ( kpair @ X1 @ X3 ) ) ) )
| ~ ( in @ X3 @ ( setunion @ ( kpair @ X1 @ X3 ) ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ X1 @ X3 ) ) ) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[c_0_31]),c_0_23])]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ( epred1_1 @ ( kpair @ X1 @ X3 ) @ X4 )
| ~ ( in @ X4 @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i] :
( ( in @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(er,[status(thm)],[c_0_34]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i,X3: $i] :
( ( setunion @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) )
= ( kfst @ ( kpair @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) )
| ~ ( in @ X3 @ ( setunion @ ( kpair @ X1 @ X3 ) ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ X1 @ X3 ) ) ) ),
inference(rw,[status(thm)],[c_0_36,c_0_33]) ).
thf(c_0_41,plain,
! [X69: $i,X70: $i] :
( ( ~ ( epred1_1 @ X70 @ X69 )
| ( in @ ( setadjoin @ X69 @ emptyset ) @ X70 ) )
& ( ~ ( in @ ( setadjoin @ X69 @ emptyset ) @ X70 )
| ( epred1_1 @ X70 @ X69 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_1 @ ( kpair @ X1 @ X3 ) @ ( kfst @ ( kpair @ X1 @ X3 ) ) )
| ~ ( in @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_28]),c_0_29])]) ).
thf(c_0_44,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( X3 = X1 )
| ~ ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_45,plain,
! [X1: $i,X3: $i] :
( ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 )
| ~ ( epred1_1 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i,X3: $i] : ( epred1_1 @ ( kpair @ X1 @ X3 ) @ ( kfst @ ( kpair @ X1 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
thf(c_0_47,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( X1 = X3 )
| ~ ( in @ ( setadjoin @ X1 @ emptyset ) @ ( kpair @ X3 @ X4 ) ) ),
inference(rw,[status(thm)],[c_0_44,c_0_23]) ).
thf(c_0_48,plain,
! [X1: $i,X3: $i] : ( in @ ( setadjoin @ ( kfst @ ( kpair @ X1 @ X3 ) ) @ emptyset ) @ ( kpair @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_49,negated_conjecture,
( ( kfst @ ( kpair @ esk4_0 @ esk5_0 ) )
!= esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_50,negated_conjecture,
! [X3: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X3 ) )
= X1 ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU645^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun May 19 18:17:52 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.18/0.46 Running higher-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 # Version: 3.1.0-ho
% 0.18/0.47 # Preprocessing class: HSSSSLSSMLMNSFA.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting new_ho_10 with 1500s (5) cores
% 0.18/0.47 # Starting sh5l with 300s (1) cores
% 0.18/0.47 # Starting new_bool_1 with 300s (1) cores
% 0.18/0.47 # Starting new_bool_2 with 300s (1) cores
% 0.18/0.47 # new_ho_10 with pid 25155 completed with status 0
% 0.18/0.47 # Result found by new_ho_10
% 0.18/0.47 # Preprocessing class: HSSSSLSSMLMNSFA.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting new_ho_10 with 1500s (5) cores
% 0.18/0.47 # No SInE strategy applied
% 0.18/0.47 # Search class: HHUSM-FFSF21-MSFSMFBN
% 0.18/0.47 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.47 # Starting new_ho_10 with 901s (1) cores
% 0.18/0.47 # Starting sh5l with 151s (1) cores
% 0.18/0.47 # Starting new_bool_1 with 151s (1) cores
% 0.18/0.47 # Starting new_bool_2 with 151s (1) cores
% 0.18/0.47 # Starting new_bool_9 with 146s (1) cores
% 0.18/0.47 # sh5l with pid 25163 completed with status 0
% 0.18/0.47 # Result found by sh5l
% 0.18/0.47 # Preprocessing class: HSSSSLSSMLMNSFA.
% 0.18/0.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.47 # Starting new_ho_10 with 1500s (5) cores
% 0.18/0.47 # No SInE strategy applied
% 0.18/0.47 # Search class: HHUSM-FFSF21-MSFSMFBN
% 0.18/0.47 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.47 # Starting new_ho_10 with 901s (1) cores
% 0.18/0.47 # Starting sh5l with 151s (1) cores
% 0.18/0.47 # Preprocessing time : 0.001 s
% 0.18/0.47 # Presaturation interreduction done
% 0.18/0.47
% 0.18/0.47 # Proof found!
% 0.18/0.47 # SZS status Theorem
% 0.18/0.47 # SZS output start CNFRefutation
% See solution above
% 0.18/0.47 # Parsed axioms : 24
% 0.18/0.47 # Removed by relevancy pruning/SinE : 0
% 0.18/0.47 # Initial clauses : 27
% 0.18/0.47 # Removed in clause preprocessing : 14
% 0.18/0.47 # Initial clauses in saturation : 13
% 0.18/0.47 # Processed clauses : 55
% 0.18/0.47 # ...of these trivial : 2
% 0.18/0.47 # ...subsumed : 3
% 0.18/0.47 # ...remaining for further processing : 50
% 0.18/0.47 # Other redundant clauses eliminated : 3
% 0.18/0.47 # Clauses deleted for lack of memory : 0
% 0.18/0.47 # Backward-subsumed : 2
% 0.18/0.47 # Backward-rewritten : 7
% 0.18/0.47 # Generated clauses : 84
% 0.18/0.47 # ...of the previous two non-redundant : 70
% 0.18/0.47 # ...aggressively subsumed : 0
% 0.18/0.47 # Contextual simplify-reflections : 0
% 0.18/0.47 # Paramodulations : 81
% 0.18/0.47 # Factorizations : 0
% 0.18/0.47 # NegExts : 0
% 0.18/0.47 # Equation resolutions : 3
% 0.18/0.47 # Disequality decompositions : 0
% 0.18/0.47 # Total rewrite steps : 42
% 0.18/0.47 # ...of those cached : 26
% 0.18/0.47 # Propositional unsat checks : 0
% 0.18/0.47 # Propositional check models : 0
% 0.18/0.47 # Propositional check unsatisfiable : 0
% 0.18/0.47 # Propositional clauses : 0
% 0.18/0.47 # Propositional clauses after purity: 0
% 0.18/0.47 # Propositional unsat core size : 0
% 0.18/0.47 # Propositional preprocessing time : 0.000
% 0.18/0.47 # Propositional encoding time : 0.000
% 0.18/0.47 # Propositional solver time : 0.000
% 0.18/0.47 # Success case prop preproc time : 0.000
% 0.18/0.47 # Success case prop encoding time : 0.000
% 0.18/0.47 # Success case prop solver time : 0.000
% 0.18/0.47 # Current number of processed clauses : 25
% 0.18/0.47 # Positive orientable unit clauses : 16
% 0.18/0.47 # Positive unorientable unit clauses: 0
% 0.18/0.47 # Negative unit clauses : 0
% 0.18/0.47 # Non-unit-clauses : 9
% 0.18/0.47 # Current number of unprocessed clauses: 32
% 0.18/0.47 # ...number of literals in the above : 46
% 0.18/0.47 # Current number of archived formulas : 0
% 0.18/0.47 # Current number of archived clauses : 22
% 0.18/0.47 # Clause-clause subsumption calls (NU) : 73
% 0.18/0.47 # Rec. Clause-clause subsumption calls : 70
% 0.18/0.47 # Non-unit clause-clause subsumptions : 3
% 0.18/0.47 # Unit Clause-clause subsumption calls : 3
% 0.18/0.47 # Rewrite failures with RHS unbound : 0
% 0.18/0.47 # BW rewrite match attempts : 8
% 0.18/0.47 # BW rewrite match successes : 5
% 0.18/0.47 # Condensation attempts : 55
% 0.18/0.47 # Condensation successes : 0
% 0.18/0.47 # Termbank termtop insertions : 6449
% 0.18/0.47 # Search garbage collected termcells : 546
% 0.18/0.47
% 0.18/0.47 # -------------------------------------------------
% 0.18/0.47 # User time : 0.007 s
% 0.18/0.47 # System time : 0.002 s
% 0.18/0.47 # Total time : 0.009 s
% 0.18/0.47 # Maximum resident set size: 1952 pages
% 0.18/0.47
% 0.18/0.47 # -------------------------------------------------
% 0.18/0.47 # User time : 0.030 s
% 0.18/0.47 # System time : 0.009 s
% 0.18/0.47 # Total time : 0.040 s
% 0.18/0.47 # Maximum resident set size: 1720 pages
% 0.18/0.48 % E---3.1 exiting
% 0.18/0.48 % E exiting
%------------------------------------------------------------------------------