TSTP Solution File: SEU656^2 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU656^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 : Mon Jun 24 15:09:50 EDT 2024
% Result : Theorem 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 79 equ; 0 cnn)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 855 ( 35 ~; 31 |; 27 &; 732 @)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 10 con; 0-2 aty)
% Number of variables : 167 ( 20 ^ 129 !; 18 ?; 167 :)
% 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,
theprop: $o ).
thf(decl_33,type,
kfst: $i > $i ).
thf(decl_34,type,
setukpairinjR: $o ).
thf(decl_35,type,
ksndsingleton: $o ).
thf(decl_36,type,
ksnd: $i > $i ).
thf(decl_37,type,
esk1_2: $i > $i > $i ).
thf(decl_38,type,
esk2_2: $i > $i > $i ).
thf(decl_39,type,
esk3_1: $i > $i ).
thf(decl_40,type,
esk4_0: $i ).
thf(decl_41,type,
esk5_0: $i ).
thf(decl_42,type,
epred1_1: $i > $i > $o ).
thf(decl_43,type,
esk6_1: $i > $i ).
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/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',iskpair) ).
thf(singleton,axiom,
( singleton
= ( ^ [X1: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ( X1
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',singleton) ).
thf(ksndsingleton,axiom,
( ksndsingleton
<=> ! [X7: $i] :
( ( iskpair @ X7 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X7 )
@ ^ [X3: $i] :
( X7
= ( kpair @ ( kfst @ X7 ) @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',ksndsingleton) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',dsetconstrER) ).
thf(kpairp,axiom,
( kpairp
<=> ! [X3: $i,X4: $i] : ( iskpair @ ( kpair @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',kpairp) ).
thf(theprop,axiom,
( theprop
<=> ! [X5: $i] :
( ( singleton @ X5 )
=> ( in @ ( setunion @ X5 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',theprop) ).
thf(ksndpairEq,conjecture,
( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [X3: $i,X4: $i] :
( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',ksndpairEq) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X3: $i,X4: $i,X6: $i,X7: $i] :
( ( ( kpair @ X3 @ X4 )
= ( kpair @ X6 @ X7 ) )
=> ( X4 = X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',setukpairinjR) ).
thf(kpair,axiom,
( kpair
= ( ^ [X3: $i,X4: $i] : ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',kpair) ).
thf(ksnd,axiom,
( ksnd
= ( ^ [X7: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X7 )
@ ^ [X3: $i] :
( X7
= ( kpair @ ( kfst @ X7 ) @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p',ksnd) ).
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,
( singleton
= ( ^ [Z0: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ( Z0
= ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_12,plain,
( ksndsingleton
<=> ! [X7: $i] :
( ( iskpair @ X7 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X7 )
@ ^ [Z0: $i] :
( X7
= ( kpair @ ( kfst @ X7 ) @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ksndsingleton]) ).
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] :
? [X21: $i] :
( ( in @ X21 @ ( setunion @ ( kpair @ X3 @ X4 ) ) )
& ? [X22: $i] :
( ( in @ X22 @ ( setunion @ ( kpair @ X3 @ X4 ) ) )
& ( ( kpair @ X3 @ X4 )
= ( setadjoin @ ( setadjoin @ X21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X21 @ ( setadjoin @ X22 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairp,c_0_10]) ).
thf(c_0_15,axiom,
( theprop
= ( ! [X5: $i] :
( ? [X23: $i] :
( ( in @ X23 @ X5 )
& ( X5
= ( setadjoin @ X23 @ emptyset ) ) )
=> ( in @ ( setunion @ X5 ) @ X5 ) ) ) ),
inference(apply_def,[status(thm)],[theprop,c_0_11]) ).
thf(c_0_16,plain,
( ksndsingleton
= ( ! [X7: $i] :
( ? [X24: $i] :
( ( in @ X24 @ ( setunion @ X7 ) )
& ? [X25: $i] :
( ( in @ X25 @ ( setunion @ X7 ) )
& ( X7
= ( setadjoin @ ( setadjoin @ X24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X24 @ ( setadjoin @ X25 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ ( setunion @ X7 )
@ ^ [Z0: $i] :
( X7
= ( kpair @ ( kfst @ X7 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X7 )
@ ^ [Z0: $i] :
( X7
= ( kpair @ ( kfst @ X7 ) @ Z0 ) ) )
= ( setadjoin @ X26 @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).
thf(c_0_17,negated_conjecture,
~ ( ! [X27: $i,X28: $i > $o,X29: $i] :
( ( in @ X29 @ ( dsetconstr @ X27 @ X28 ) )
=> ( X28 @ X29 ) )
=> ( ! [X30: $i,X31: $i] :
? [X32: $i] :
( ( in @ X32 @ ( setunion @ ( kpair @ X30 @ X31 ) ) )
& ? [X33: $i] :
( ( in @ X33 @ ( setunion @ ( kpair @ X30 @ X31 ) ) )
& ( ( kpair @ X30 @ X31 )
= ( setadjoin @ ( setadjoin @ X32 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X32 @ ( setadjoin @ X33 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [X34: $i] :
( ? [X35: $i] :
( ( in @ X35 @ X34 )
& ( X34
= ( setadjoin @ X35 @ emptyset ) ) )
=> ( in @ ( setunion @ X34 ) @ X34 ) )
=> ( ! [X36: $i,X37: $i,X38: $i,X39: $i] :
( ( ( kpair @ X36 @ X37 )
= ( kpair @ X38 @ X39 ) )
=> ( X37 = X39 ) )
=> ( ! [X40: $i] :
( ? [X41: $i] :
( ( in @ X41 @ ( setunion @ X40 ) )
& ? [X42: $i] :
( ( in @ X42 @ ( setunion @ X40 ) )
& ( X40
= ( setadjoin @ ( setadjoin @ X41 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X41 @ ( setadjoin @ X42 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X43: $i] :
( ( in @ X43
@ ( dsetconstr @ ( setunion @ X40 )
@ ^ [Z0: $i] :
( X40
= ( kpair @ ( kfst @ X40 ) @ Z0 ) ) ) )
& ( ( dsetconstr @ ( setunion @ X40 )
@ ^ [Z0: $i] :
( X40
= ( kpair @ ( kfst @ X40 ) @ Z0 ) ) )
= ( setadjoin @ X43 @ emptyset ) ) ) )
=> ! [X3: $i,X4: $i] :
( ( ksnd @ ( kpair @ X3 @ X4 ) )
= X4 ) ) ) ) ) ),
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)],[ksndpairEq]),c_0_13]),c_0_14]),c_0_15]),setukpairinjR]),c_0_16])]) ).
thf(c_0_18,plain,
! [X44: $i,X45: $i] :
( ( kpair @ X44 @ X45 )
= ( setadjoin @ ( setadjoin @ X44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X44 @ ( setadjoin @ X45 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_19,negated_conjecture,
! [X50: $i,X51: $i > $o,X52: $i,X53: $i,X54: $i,X57: $i,X58: $i,X59: $i,X60: $i,X61: $i,X62: $i,X63: $i,X64: $i,X65: $i] :
( ( ~ ( in @ X52 @ ( dsetconstr @ X50 @ X51 ) )
| ( X51 @ X52 ) )
& ( in @ ( esk1_2 @ X53 @ X54 ) @ ( setunion @ ( kpair @ X53 @ X54 ) ) )
& ( in @ ( esk2_2 @ X53 @ X54 ) @ ( setunion @ ( kpair @ X53 @ X54 ) ) )
& ( ( kpair @ X53 @ X54 )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X53 @ X54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X53 @ X54 ) @ ( setadjoin @ ( esk2_2 @ X53 @ X54 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ X58 @ X57 )
| ( X57
!= ( setadjoin @ X58 @ emptyset ) )
| ( in @ ( setunion @ X57 ) @ X57 ) )
& ( ( ( kpair @ X59 @ X60 )
!= ( kpair @ X61 @ X62 ) )
| ( X60 = X62 ) )
& ( ( in @ ( esk3_1 @ X63 )
@ ( dsetconstr @ ( setunion @ X63 )
@ ^ [Z0: $i] :
( X63
= ( kpair @ ( kfst @ X63 ) @ Z0 ) ) ) )
| ~ ( in @ X64 @ ( setunion @ X63 ) )
| ~ ( in @ X65 @ ( setunion @ X63 ) )
| ( X63
!= ( setadjoin @ ( setadjoin @ X64 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X64 @ ( setadjoin @ X65 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ( dsetconstr @ ( setunion @ X63 )
@ ^ [Z0: $i] :
( X63
= ( kpair @ ( kfst @ X63 ) @ Z0 ) ) )
= ( setadjoin @ ( esk3_1 @ X63 ) @ emptyset ) )
| ~ ( in @ X64 @ ( setunion @ X63 ) )
| ~ ( in @ X65 @ ( setunion @ X63 ) )
| ( X63
!= ( setadjoin @ ( setadjoin @ X64 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X64 @ ( setadjoin @ X65 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( ksnd @ ( kpair @ esk4_0 @ esk5_0 ) )
!= esk5_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,
! [X47: $i,X48: $i] :
( ( kpair @ X47 @ X48 )
= ( setadjoin @ ( setadjoin @ X47 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X47 @ ( setadjoin @ X48 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ( ( kpair @ X1 @ X3 )
!= ( kpair @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,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_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_20]) ).
thf(c_0_24,plain,
! [X69: $i,X1: $i] :
( ( epred1_1 @ X1 @ X69 )
<=> ( X1
= ( kpair @ ( kfst @ X1 ) @ X69 ) ) ),
introduced(definition) ).
thf(c_0_25,negated_conjecture,
! [X1: $i,X3: $i] :
( ( esk6_1 @ ( kpair @ X1 @ X3 ) )
= X3 ),
inference(recognize_injectivity,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X3: $i] :
( ( kpair @ ( esk1_2 @ X1 @ X3 ) @ ( esk2_2 @ X1 @ X3 ) )
= ( kpair @ X1 @ X3 ) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_27,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_24]) ).
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] :
( ( esk2_2 @ X1 @ X3 )
= X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
thf(c_0_30,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_27,c_0_23])]) ).
thf(c_0_31,negated_conjecture,
! [X3: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( kpair @ X3 @ X1 ) ) ),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_32,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_24]) ).
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 ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ X1 @ X3 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X3: $i] :
( ( kpair @ ( esk1_2 @ X1 @ X3 ) @ X3 )
= ( kpair @ X1 @ X3 ) ),
inference(rw,[status(thm)],[c_0_26,c_0_29]) ).
thf(c_0_35,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_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_32]),c_0_23])]) ).
thf(c_0_37,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(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
thf(c_0_38,plain,
! [X46: $i] :
( ( ksnd @ X46 )
= ( setunion
@ ( dsetconstr @ ( setunion @ X46 )
@ ^ [Z0: $i] :
( X46
= ( kpair @ ( kfst @ X46 ) @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ksnd])]) ).
thf(c_0_39,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_40,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ X1 @ X3 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_31])]) ).
thf(c_0_41,plain,
! [X49: $i] :
( ( ksnd @ X49 )
= ( setunion
@ ( dsetconstr @ ( setunion @ X49 )
@ ^ [Z0: $i] :
( X49
= ( kpair @ ( kfst @ X49 ) @ Z0 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
thf(c_0_42,plain,
! [X72: $i,X73: $i] :
( ( ~ ( epred1_1 @ X73 @ X72 )
| ( X73
= ( kpair @ ( kfst @ X73 ) @ X72 ) ) )
& ( ( X73
!= ( kpair @ ( kfst @ X73 ) @ X72 ) )
| ( epred1_1 @ X73 @ X72 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).
thf(c_0_43,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_39,c_0_37]) ).
thf(c_0_44,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(spm,[status(thm)],[c_0_40,c_0_34]),c_0_35])]) ).
thf(c_0_45,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_46,plain,
! [X1: $i] :
( ( ksnd @ X1 )
= ( setunion @ ( dsetconstr @ ( setunion @ X1 ) @ ( epred1_1 @ X1 ) ) ) ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_41]),c_0_24]) ).
thf(c_0_47,plain,
! [X1: $i,X3: $i] :
( ( X1
= ( kpair @ ( kfst @ X1 ) @ X3 ) )
| ~ ( epred1_1 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i,X3: $i] : ( epred1_1 @ ( kpair @ X1 @ X3 ) @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_49,negated_conjecture,
! [X1: $i] :
( ( in @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ ( setadjoin @ X1 @ emptyset ) )
| ~ ( in @ X1 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(er,[status(thm)],[c_0_45]) ).
thf(c_0_50,negated_conjecture,
! [X1: $i,X3: $i] :
( ( setunion @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) )
= ( ksnd @ ( kpair @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_46,c_0_37]) ).
thf(c_0_51,plain,
! [X1: $i,X3: $i] :
( ( kpair @ ( kfst @ ( kpair @ X1 @ X3 ) ) @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) )
= ( kpair @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_52,negated_conjecture,
! [X1: $i,X3: $i] : ( in @ ( ksnd @ ( kpair @ X1 @ X3 ) ) @ ( setadjoin @ ( esk3_1 @ ( kpair @ X1 @ X3 ) ) @ emptyset ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_50]) ).
thf(c_0_53,negated_conjecture,
! [X1: $i,X3: $i] :
( ( esk3_1 @ ( kpair @ X1 @ X3 ) )
= X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_51]),c_0_25]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i,X3: $i] : ( epred1_1 @ ( kpair @ X1 @ X3 ) @ ( ksnd @ ( kpair @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_52]) ).
thf(c_0_55,negated_conjecture,
! [X1: $i,X3: $i] :
( ( ksnd @ ( kpair @ X1 @ X3 ) )
= ( setunion @ ( setadjoin @ X3 @ emptyset ) ) ),
inference(spm,[status(thm)],[c_0_50,c_0_53]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i,X3: $i] : ( epred1_1 @ ( kpair @ X1 @ X3 ) @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) ),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_57,negated_conjecture,
( ( ksnd @ ( kpair @ esk4_0 @ esk5_0 ) )
!= esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_58,plain,
! [X1: $i,X3: $i] :
( ( kpair @ ( kfst @ ( kpair @ X1 @ X3 ) ) @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) )
= ( kpair @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
thf(c_0_59,negated_conjecture,
( ( setunion @ ( setadjoin @ esk5_0 @ emptyset ) )
!= esk5_0 ),
inference(rw,[status(thm)],[c_0_57,c_0_55]) ).
thf(c_0_60,negated_conjecture,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_58]),c_0_25]) ).
thf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU656^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 21 12:05:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.18/0.44 Running higher-order theorem proving
% 0.18/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.v1vIHjX3EI/E---3.1_19296.p
% 0.18/0.46 # Version: 3.2.0-ho
% 0.18/0.46 # Preprocessing class: HSSSSLSSMLMNSFA.
% 0.18/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.18/0.46 # Starting sh5l with 300s (1) cores
% 0.18/0.46 # Starting new_bool_1 with 300s (1) cores
% 0.18/0.46 # Starting new_bool_2 with 300s (1) cores
% 0.18/0.46 # new_ho_10 with pid 19375 completed with status 0
% 0.18/0.46 # Result found by new_ho_10
% 0.18/0.46 # Preprocessing class: HSSSSLSSMLMNSFA.
% 0.18/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.18/0.46 # No SInE strategy applied
% 0.18/0.46 # Search class: HHUSM-FFSF21-MSFSMFBN
% 0.18/0.46 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.46 # Starting new_ho_10 with 901s (1) cores
% 0.18/0.46 # Starting sh5l with 151s (1) cores
% 0.18/0.46 # Starting new_bool_1 with 151s (1) cores
% 0.18/0.46 # Starting new_bool_2 with 151s (1) cores
% 0.18/0.46 # Starting new_bool_9 with 146s (1) cores
% 0.18/0.46 # new_bool_9 with pid 19386 completed with status 0
% 0.18/0.46 # Result found by new_bool_9
% 0.18/0.46 # Preprocessing class: HSSSSLSSMLMNSFA.
% 0.18/0.46 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.46 # Starting new_ho_10 with 1500s (5) cores
% 0.18/0.46 # No SInE strategy applied
% 0.18/0.46 # Search class: HHUSM-FFSF21-MSFSMFBN
% 0.18/0.46 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.46 # Starting new_ho_10 with 901s (1) cores
% 0.18/0.46 # Starting sh5l with 151s (1) cores
% 0.18/0.46 # Starting new_bool_1 with 151s (1) cores
% 0.18/0.46 # Starting new_bool_2 with 151s (1) cores
% 0.18/0.46 # Starting new_bool_9 with 146s (1) cores
% 0.18/0.46 # Preprocessing time : 0.001 s
% 0.18/0.46 # Presaturation interreduction done
% 0.18/0.46
% 0.18/0.46 # Proof found!
% 0.18/0.46 # SZS status Theorem
% 0.18/0.46 # SZS output start CNFRefutation
% See solution above
% 0.18/0.46 # Parsed axioms : 25
% 0.18/0.46 # Removed by relevancy pruning/SinE : 0
% 0.18/0.46 # Initial clauses : 28
% 0.18/0.46 # Removed in clause preprocessing : 15
% 0.18/0.46 # Initial clauses in saturation : 13
% 0.18/0.46 # Processed clauses : 95
% 0.18/0.46 # ...of these trivial : 3
% 0.18/0.46 # ...subsumed : 12
% 0.18/0.46 # ...remaining for further processing : 80
% 0.18/0.46 # Other redundant clauses eliminated : 6
% 0.18/0.46 # Clauses deleted for lack of memory : 0
% 0.18/0.46 # Backward-subsumed : 1
% 0.18/0.46 # Backward-rewritten : 21
% 0.18/0.46 # Generated clauses : 220
% 0.18/0.46 # ...of the previous two non-redundant : 165
% 0.18/0.46 # ...aggressively subsumed : 0
% 0.18/0.46 # Contextual simplify-reflections : 0
% 0.18/0.46 # Paramodulations : 197
% 0.18/0.46 # Factorizations : 0
% 0.18/0.46 # NegExts : 3
% 0.18/0.46 # Equation resolutions : 7
% 0.18/0.46 # Disequality decompositions : 0
% 0.18/0.46 # Total rewrite steps : 145
% 0.18/0.46 # ...of those cached : 112
% 0.18/0.46 # Propositional unsat checks : 0
% 0.18/0.46 # Propositional check models : 0
% 0.18/0.46 # Propositional check unsatisfiable : 0
% 0.18/0.46 # Propositional clauses : 0
% 0.18/0.46 # Propositional clauses after purity: 0
% 0.18/0.46 # Propositional unsat core size : 0
% 0.18/0.46 # Propositional preprocessing time : 0.000
% 0.18/0.46 # Propositional encoding time : 0.000
% 0.18/0.46 # Propositional solver time : 0.000
% 0.18/0.46 # Success case prop preproc time : 0.000
% 0.18/0.46 # Success case prop encoding time : 0.000
% 0.18/0.46 # Success case prop solver time : 0.000
% 0.18/0.46 # Current number of processed clauses : 40
% 0.18/0.46 # Positive orientable unit clauses : 21
% 0.18/0.46 # Positive unorientable unit clauses: 0
% 0.18/0.46 # Negative unit clauses : 6
% 0.18/0.46 # Non-unit-clauses : 13
% 0.18/0.46 # Current number of unprocessed clauses: 77
% 0.18/0.46 # ...number of literals in the above : 90
% 0.18/0.46 # Current number of archived formulas : 0
% 0.18/0.46 # Current number of archived clauses : 37
% 0.18/0.46 # Clause-clause subsumption calls (NU) : 122
% 0.18/0.46 # Rec. Clause-clause subsumption calls : 117
% 0.18/0.46 # Non-unit clause-clause subsumptions : 11
% 0.18/0.46 # Unit Clause-clause subsumption calls : 8
% 0.18/0.46 # Rewrite failures with RHS unbound : 0
% 0.18/0.46 # BW rewrite match attempts : 22
% 0.18/0.46 # BW rewrite match successes : 12
% 0.18/0.46 # Condensation attempts : 0
% 0.18/0.46 # Condensation successes : 0
% 0.18/0.46 # Termbank termtop insertions : 10943
% 0.18/0.46 # Search garbage collected termcells : 547
% 0.18/0.46
% 0.18/0.46 # -------------------------------------------------
% 0.18/0.46 # User time : 0.008 s
% 0.18/0.46 # System time : 0.002 s
% 0.18/0.46 # Total time : 0.010 s
% 0.18/0.46 # Maximum resident set size: 1984 pages
% 0.18/0.46
% 0.18/0.46 # -------------------------------------------------
% 0.18/0.46 # User time : 0.036 s
% 0.18/0.46 # System time : 0.006 s
% 0.18/0.46 # Total time : 0.042 s
% 0.18/0.46 # Maximum resident set size: 1720 pages
% 0.18/0.46 % E---3.1 exiting
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------