TSTP Solution File: SEU818^2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU818^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.UswUCS9xkO true
% Computer : n010.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 : Thu Aug 31 19:18:23 EDT 2023
% Result : Theorem 1.37s 0.77s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 35 ( 20 unt; 11 typ; 0 def)
% Number of atoms : 313 ( 46 equ; 2 cnn)
% Maximal formula atoms : 80 ( 13 avg)
% Number of connectives : 723 ( 20 ~; 27 |; 54 &; 454 @)
% ( 0 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 11 usr; 7 con; 0-2 aty)
% ( 26 !!; 2 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 43 ^; 93 !; 7 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(stricttotalorderedByIn_type,type,
stricttotalorderedByIn: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subsetI1_type,type,
subsetI1: $o ).
thf(wellorderedByIn_type,type,
wellorderedByIn: $i > $o ).
thf(ordinalTransSet_type,type,
ordinalTransSet: $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(nonempty_type,type,
nonempty: $i > $o ).
thf(transitiveset_type,type,
transitiveset: $i > $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(ordinalTransSet,axiom,
( ordinalTransSet
= ( ! [X: $i] :
( ( ordinal @ X )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) ) ) ).
thf('0',plain,
( ordinalTransSet
= ( ! [X4: $i] :
( ( ordinal @ X4 )
=> ! [X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( in @ X6 @ X8 )
=> ( in @ X6 @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ordinal,axiom,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ) ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) )
& ( in @ Xx @ X ) ) ) ) ) ) ) ).
thf(stricttotalorderedByIn,axiom,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ) ).
thf('1',plain,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[stricttotalorderedByIn]) ).
thf('2',plain,
( stricttotalorderedByIn
= ( ^ [V_1: $i] :
( ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ! [X6: $i] :
( ( in @ X6 @ V_1 )
=> ! [X8: $i] :
( ( in @ X8 @ V_1 )
=> ( ( ( in @ X4 @ X6 )
& ( in @ X6 @ X8 ) )
=> ( in @ X4 @ X8 ) ) ) ) )
& ! [X10: $i] :
( ( in @ X10 @ V_1 )
=> ! [X12: $i] :
( ( in @ X12 @ V_1 )
=> ( ( X10 = X12 )
| ( in @ X10 @ X12 )
| ( in @ X12 @ X10 ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ V_1 )
=> ~ ( in @ X14 @ X14 ) ) ) ) ),
define([status(thm)]) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
thf('3',plain,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[nonempty]) ).
thf('4',plain,
( nonempty
= ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf('5',plain,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) )
& ( in @ Xx @ X ) ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[wellorderedByIn,'2','4']) ).
thf('6',plain,
( wellorderedByIn
= ( ^ [V_1: $i] :
( ( stricttotalorderedByIn @ V_1 )
& ! [X4: $i] :
( ( in @ X4 @ ( powerset @ V_1 ) )
=> ( ( nonempty @ X4 )
=> ? [X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 = X8 )
| ( in @ X6 @ X8 ) ) )
& ( in @ X6 @ X4 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf('7',plain,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ordinal,'6','2','4']) ).
thf('8',plain,
( ordinal
= ( ^ [V_1: $i] :
( ( transitiveset @ V_1 )
& ( wellorderedByIn @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ) ).
thf('9',plain,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitiveset]) ).
thf('10',plain,
( transitiveset
= ( ^ [V_1: $i] :
! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( subset @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(subsetI1,axiom,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf('11',plain,
( subsetI1
= ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(ordinalTransSet1,conjecture,
( subsetI1
=> ( ordinalTransSet
=> ! [X: $i] :
( ( ordinal @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ( subset @ A @ X ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) )
=> ( ! [X10: $i] :
( ( ! [X26: $i] :
( ( in @ X26 @ ( powerset @ X10 ) )
=> ( ( X26 != emptyset )
=> ? [X28: $i] :
( ( in @ X28 @ X26 )
& ! [X30: $i] :
( ( in @ X30 @ X26 )
=> ( ( in @ X28 @ X30 )
| ( X28 = X30 ) ) ) ) ) )
& ! [X24: $i] :
( ( in @ X24 @ X10 )
=> ~ ( in @ X24 @ X24 ) )
& ! [X20: $i] :
( ( in @ X20 @ X10 )
=> ! [X22: $i] :
( ( in @ X22 @ X10 )
=> ( ( in @ X22 @ X20 )
| ( in @ X20 @ X22 )
| ( X20 = X22 ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ X10 )
=> ! [X16: $i] :
( ( in @ X16 @ X10 )
=> ! [X18: $i] :
( ( in @ X18 @ X10 )
=> ( ( ( in @ X16 @ X18 )
& ( in @ X14 @ X16 ) )
=> ( in @ X14 @ X18 ) ) ) ) )
& ! [X12: $i] :
( ( in @ X12 @ X10 )
=> ( subset @ X12 @ X10 ) ) )
=> ! [X32: $i,X34: $i] :
( ( in @ X34 @ X10 )
=> ( ( in @ X32 @ X34 )
=> ( in @ X32 @ X10 ) ) ) )
=> ! [X36: $i] :
( ( ! [X52: $i] :
( ( in @ X52 @ ( powerset @ X36 ) )
=> ( ( X52 != emptyset )
=> ? [X54: $i] :
( ( in @ X54 @ X52 )
& ! [X56: $i] :
( ( in @ X56 @ X52 )
=> ( ( in @ X54 @ X56 )
| ( X54 = X56 ) ) ) ) ) )
& ! [X50: $i] :
( ( in @ X50 @ X36 )
=> ~ ( in @ X50 @ X50 ) )
& ! [X46: $i] :
( ( in @ X46 @ X36 )
=> ! [X48: $i] :
( ( in @ X48 @ X36 )
=> ( ( in @ X48 @ X46 )
| ( in @ X46 @ X48 )
| ( X46 = X48 ) ) ) )
& ! [X40: $i] :
( ( in @ X40 @ X36 )
=> ! [X42: $i] :
( ( in @ X42 @ X36 )
=> ! [X44: $i] :
( ( in @ X44 @ X36 )
=> ( ( ( in @ X42 @ X44 )
& ( in @ X40 @ X42 ) )
=> ( in @ X40 @ X44 ) ) ) ) )
& ! [X38: $i] :
( ( in @ X38 @ X36 )
=> ( subset @ X38 @ X36 ) ) )
=> ! [X58: $i] :
( ( in @ X58 @ X36 )
=> ( subset @ X58 @ X36 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( in @ X8 @ X6 ) )
=> ( subset @ X4 @ X6 ) )
=> ( ! [X10: $i] :
( ( ! [X26: $i] :
( ( in @ X26 @ ( powerset @ X10 ) )
=> ( ( X26 != emptyset )
=> ? [X28: $i] :
( ( in @ X28 @ X26 )
& ! [X30: $i] :
( ( in @ X30 @ X26 )
=> ( ( in @ X28 @ X30 )
| ( X28 = X30 ) ) ) ) ) )
& ! [X24: $i] :
( ( in @ X24 @ X10 )
=> ~ ( in @ X24 @ X24 ) )
& ! [X20: $i] :
( ( in @ X20 @ X10 )
=> ! [X22: $i] :
( ( in @ X22 @ X10 )
=> ( ( in @ X22 @ X20 )
| ( in @ X20 @ X22 )
| ( X20 = X22 ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ X10 )
=> ! [X16: $i] :
( ( in @ X16 @ X10 )
=> ! [X18: $i] :
( ( in @ X18 @ X10 )
=> ( ( ( in @ X16 @ X18 )
& ( in @ X14 @ X16 ) )
=> ( in @ X14 @ X18 ) ) ) ) )
& ! [X12: $i] :
( ( in @ X12 @ X10 )
=> ( subset @ X12 @ X10 ) ) )
=> ! [X32: $i,X34: $i] :
( ( in @ X34 @ X10 )
=> ( ( in @ X32 @ X34 )
=> ( in @ X32 @ X10 ) ) ) )
=> ! [X36: $i] :
( ( ! [X52: $i] :
( ( in @ X52 @ ( powerset @ X36 ) )
=> ( ( X52 != emptyset )
=> ? [X54: $i] :
( ( in @ X54 @ X52 )
& ! [X56: $i] :
( ( in @ X56 @ X52 )
=> ( ( in @ X54 @ X56 )
| ( X54 = X56 ) ) ) ) ) )
& ! [X50: $i] :
( ( in @ X50 @ X36 )
=> ~ ( in @ X50 @ X50 ) )
& ! [X46: $i] :
( ( in @ X46 @ X36 )
=> ! [X48: $i] :
( ( in @ X48 @ X36 )
=> ( ( in @ X48 @ X46 )
| ( in @ X46 @ X48 )
| ( X46 = X48 ) ) ) )
& ! [X40: $i] :
( ( in @ X40 @ X36 )
=> ! [X42: $i] :
( ( in @ X42 @ X36 )
=> ! [X44: $i] :
( ( in @ X44 @ X36 )
=> ( ( ( in @ X42 @ X44 )
& ( in @ X40 @ X42 ) )
=> ( in @ X40 @ X44 ) ) ) ) )
& ! [X38: $i] :
( ( in @ X38 @ X36 )
=> ( subset @ X38 @ X36 ) ) )
=> ! [X58: $i] :
( ( in @ X58 @ X36 )
=> ( subset @ X58 @ X36 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( Y1 != emptyset )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( Y1 != emptyset )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl3,plain,
$false,
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU818^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.UswUCS9xkO true
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 15:25:36 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in HO mode
% 0.22/0.65 % Total configuration time : 828
% 0.22/0.65 % Estimated wc time : 1656
% 0.22/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.88/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.88/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.88/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.88/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.88/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.88/0.74 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.37/0.77 % Solved by lams/15_e_short1.sh.
% 1.37/0.77 % done 0 iterations in 0.012s
% 1.37/0.77 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.37/0.77 % SZS output start Refutation
% See solution above
% 1.37/0.78
% 1.37/0.78
% 1.37/0.78 % Terminating...
% 1.61/0.85 % Runner terminated.
% 1.61/0.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------