TSTP Solution File: SEU664^2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU664^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.SSJmbUbtbq true
% Computer : n028.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 19:15:40 EDT 2023
% Result : Theorem 1.49s 0.81s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 83 ( 25 unt; 13 typ; 0 def)
% Number of atoms : 293 ( 76 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 958 ( 41 ~; 27 |; 24 &; 706 @)
% ( 0 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 9 con; 0-3 aty)
% ( 66 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 223 ( 80 ^; 135 !; 8 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
thf(cartprodfstpairEq_type,type,
cartprodfstpairEq: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(cartprodsndpairEq_type,type,
cartprodsndpairEq: $o ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(kfst_type,type,
kfst: $i > $i ).
thf('#sk5_type',type,
'#sk5': $i > $i > $i > $i ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf('#sk3_type',type,
'#sk3': $i > $i > $i > $i ).
thf(ksnd_type,type,
ksnd: $i > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf('#sk4_type',type,
'#sk4': $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ) ).
thf('0',plain,
( cartprodsndpairEq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( ( ksnd @ ( kpair @ X8 @ X10 ) )
= X10 ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ) ).
thf('1',plain,
( cartprodfstpairEq
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X6 )
=> ( ( kfst @ ( kpair @ X8 @ X10 ) )
= X8 ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ? [Xy: $i] :
( ( Xu
= ( kpair @ Xx @ Xy ) )
& ( in @ Xy @ B ) )
& ( in @ Xx @ A ) ) ) ) ) ).
thf('2',plain,
( cartprodmempair1
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ? [X10: $i] :
( ? [X12: $i] :
( ( X8
= ( kpair @ X10 @ X12 ) )
& ( in @ X12 @ X6 ) )
& ( in @ X10 @ X4 ) ) ) ) ),
define([status(thm)]) ).
thf(cartprodpairsurjEq,conjecture,
( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ? [X10: $i] :
( ( in @ X10 @ X4 )
& ? [X12: $i] :
( ( in @ X12 @ X6 )
& ( X8
= ( kpair @ X10 @ X12 ) ) ) ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( in @ X18 @ X14 )
=> ! [X20: $i] :
( ( in @ X20 @ X16 )
=> ( ( kfst @ ( kpair @ X18 @ X20 ) )
= X18 ) ) )
=> ( ! [X22: $i,X24: $i,X26: $i] :
( ( in @ X26 @ X22 )
=> ! [X28: $i] :
( ( in @ X28 @ X24 )
=> ( ( ksnd @ ( kpair @ X26 @ X28 ) )
= X28 ) ) )
=> ! [X30: $i,X32: $i,X34: $i] :
( ( in @ X34 @ ( cartprod @ X30 @ X32 ) )
=> ( ( kpair @ ( kfst @ X34 ) @ ( ksnd @ X34 ) )
= X34 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i,X8: $i] :
( ( in @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ? [X10: $i] :
( ( in @ X10 @ X4 )
& ? [X12: $i] :
( ( in @ X12 @ X6 )
& ( X8
= ( kpair @ X10 @ X12 ) ) ) ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( in @ X18 @ X14 )
=> ! [X20: $i] :
( ( in @ X20 @ X16 )
=> ( ( kfst @ ( kpair @ X18 @ X20 ) )
= X18 ) ) )
=> ( ! [X22: $i,X24: $i,X26: $i] :
( ( in @ X26 @ X22 )
=> ! [X28: $i] :
( ( in @ X28 @ X24 )
=> ( ( ksnd @ ( kpair @ X26 @ X28 ) )
= X28 ) ) )
=> ! [X30: $i,X32: $i,X34: $i] :
( ( in @ X34 @ ( cartprod @ X30 @ X32 ) )
=> ( ( kpair @ ( kfst @ X34 ) @ ( ksnd @ X34 ) )
= X34 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y2
= ( kpair @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( kfst @ ( kpair @ Y2 @ Y3 ) )
= Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ksnd @ ( kpair @ Y2 @ Y3 ) )
= Y3 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( kpair @ ( kfst @ Y2 ) @ ( ksnd @ Y2 ) )
= Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( ??
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
& ( Y2
= ( kpair @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( cartprod @ X2 @ Y0 ) )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
& ( Y1
= ( kpair @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( cartprod @ X2 @ X4 ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ X4 )
& ( Y0
= ( kpair @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ X6 @ ( cartprod @ X2 @ X4 ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
& ( X6
= ( kpair @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
& ( X6
= ( kpair @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ ( '#sk3' @ X2 @ X4 @ X6 ) @ X2 )
& ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
& ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ Y0 ) ) ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
& ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ Y0 ) ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 )
& ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk5' @ X2 @ X4 @ X6 ) ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk5' @ X2 @ X4 @ X6 ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk5' @ X2 @ X4 @ X6 ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( kfst @ ( kpair @ Y2 @ Y3 ) )
= Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ksnd @ ( kpair @ Y2 @ Y3 ) )
= Y3 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( kpair @ ( kfst @ Y2 ) @ ( ksnd @ Y2 ) )
= Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ksnd @ ( kpair @ Y2 @ Y3 ) )
= Y3 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( kpair @ ( kfst @ Y2 ) @ ( ksnd @ Y2 ) )
= Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl9,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( kpair @ ( kfst @ Y2 ) @ ( ksnd @ Y2 ) )
= Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( cartprod @ '#sk1' @ Y0 ) )
=> ( ( kpair @ ( kfst @ Y1 ) @ ( ksnd @ Y1 ) )
= Y1 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) )
=> ( ( kpair @ ( kfst @ Y0 ) @ ( ksnd @ Y0 ) )
= Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl21,plain,
~ ( ( in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ) )
=> ( ( kpair @ ( kfst @ '#sk4' ) @ ( ksnd @ '#sk4' ) )
= '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl27,plain,
( ( kpair @ ( kfst @ '#sk4' ) @ ( ksnd @ '#sk4' ) )
!= '#sk4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl31,plain,
( ( kpair @ ( kfst @ '#sk4' ) @ ( ksnd @ '#sk4' ) )
!= '#sk4' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl36_001,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk5' @ X2 @ X4 @ X6 ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl26,plain,
in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk3' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl38,plain,
in @ ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) @ '#sk1',
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl22]) ).
thf(zip_derived_cl26_002,plain,
in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl40,plain,
in @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) @ '#sk2',
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl32]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( kfst @ ( kpair @ Y2 @ Y3 ) )
= Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( kfst @ ( kpair @ Y1 @ Y2 ) )
= Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( kfst @ ( kpair @ Y0 @ Y1 ) )
= Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ X6 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( kfst @ ( kpair @ X6 @ Y0 ) )
= X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( kfst @ ( kpair @ X6 @ Y0 ) )
= X6 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X4 )
=> ( ( kfst @ ( kpair @ X6 @ X8 ) )
= X6 ) )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X4 )
| ( ( kfst @ ( kpair @ X6 @ X8 ) )
= X6 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X4 )
| ( ( kfst @ ( kpair @ X6 @ X8 ) )
= X6 )
| ~ ( in @ X6 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl42,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( ( kfst @ ( kpair @ X1 @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ) )
= X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl34]) ).
thf(zip_derived_cl78,plain,
( ( kfst @ ( kpair @ ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ) )
= ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl42]) ).
thf(zip_derived_cl94,plain,
( ( ( kfst @ '#sk4' )
= ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) )
| ~ ( in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl36,zip_derived_cl78]) ).
thf(zip_derived_cl26_003,plain,
in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl96,plain,
( ( kfst @ '#sk4' )
= ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl26]) ).
thf(zip_derived_cl98,plain,
( ( kpair @ ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) @ ( ksnd @ '#sk4' ) )
!= '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl31,zip_derived_cl96]) ).
thf(zip_derived_cl36_004,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( X6
= ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk5' @ X2 @ X4 @ X6 ) ) )
| ~ ( in @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl38_005,plain,
in @ ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) @ '#sk1',
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl22]) ).
thf(zip_derived_cl40_006,plain,
in @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) @ '#sk2',
inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl32]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( ksnd @ ( kpair @ Y2 @ Y3 ) )
= Y3 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( ksnd @ ( kpair @ Y1 @ Y2 ) )
= Y2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( ksnd @ ( kpair @ Y0 @ Y1 ) )
= Y1 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ X6 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( ksnd @ ( kpair @ X6 @ Y0 ) )
= Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( ksnd @ ( kpair @ X6 @ Y0 ) )
= Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X4 )
=> ( ( ksnd @ ( kpair @ X6 @ X8 ) )
= X8 ) )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X4 )
| ( ( ksnd @ ( kpair @ X6 @ X8 ) )
= X8 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X4 )
| ( ( ksnd @ ( kpair @ X6 @ X8 ) )
= X8 )
| ~ ( in @ X6 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl56,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( ( ksnd @ ( kpair @ X1 @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ) )
= ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl37]) ).
thf(zip_derived_cl101,plain,
( ( ksnd @ ( kpair @ ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ) )
= ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl56]) ).
thf(zip_derived_cl111,plain,
( ( ( ksnd @ '#sk4' )
= ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) )
| ~ ( in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl36,zip_derived_cl101]) ).
thf(zip_derived_cl26_007,plain,
in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl113,plain,
( ( ksnd @ '#sk4' )
= ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl111,zip_derived_cl26]) ).
thf(zip_derived_cl115,plain,
( ( kpair @ ( '#sk3' @ '#sk1' @ '#sk2' @ '#sk4' ) @ ( '#sk5' @ '#sk1' @ '#sk2' @ '#sk4' ) )
!= '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl98,zip_derived_cl113]) ).
thf(zip_derived_cl116,plain,
( ( '#sk4' != '#sk4' )
| ~ ( in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl115]) ).
thf(zip_derived_cl26_008,plain,
in @ '#sk4' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl118,plain,
'#sk4' != '#sk4',
inference(demod,[status(thm)],[zip_derived_cl116,zip_derived_cl26]) ).
thf(zip_derived_cl119,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU664^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.SSJmbUbtbq true
% 0.17/0.35 % Computer : n028.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Wed Aug 23 14:50:34 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.17/0.35 % Running portfolio for 300 s
% 0.17/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.35 % Number of cores: 8
% 0.17/0.36 % Python version: Python 3.6.8
% 0.17/0.36 % Running in HO mode
% 0.21/0.63 % Total configuration time : 828
% 0.21/0.63 % Estimated wc time : 1656
% 0.21/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.49/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.49/0.81 % Solved by lams/35_full_unif4.sh.
% 1.49/0.81 % done 74 iterations in 0.035s
% 1.49/0.81 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.49/0.81 % SZS output start Refutation
% See solution above
% 1.49/0.81
% 1.49/0.81
% 1.49/0.81 % Terminating...
% 1.49/0.86 % Runner terminated.
% 1.79/0.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------