%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM768^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7O4aiWQCUI true
% Computer : n003.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 Oct 2 04:48:18 PM UTC 2025
% Result : Theorem 5.60s 1.90s
% Output : Refutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 230 ( 33 equ; 26 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1093 ( 40 ~; 23 |; 0 &; 937 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 17 usr; 7 con; 0-6 aty)
% ( 56 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 119 ( 27 ^; 92 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(frac_type,type,
frac: $tType ).
thf(ind_type,type,
ind: ( nat > $o ) > nat ).
thf(some_type,type,
some: ( nat > $o ) > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(y_type,type,
y: frac ).
thf(num_type,type,
num: frac > nat ).
thf(den_type,type,
den: frac > nat ).
thf(ts_type,type,
ts: nat > nat > nat ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(x_type,type,
x: frac ).
thf(fr_type,type,
fr: nat > nat > frac ).
thf(amone_type,type,
amone: ( nat > $o ) > $o ).
thf(s_comb_type,type,
'#S':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).
thf(c_comb_type,type,
'#C':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).
thf(b_comb_type,type,
'#B':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).
thf(k_comb_type,type,
'#K':
!>[A: $tType,B: $tType] : ( B > A > B ) ).
thf(i_comb_type,type,
'#I':
!>[A: $tType] : ( A > A ) ).
thf(satz8b,axiom,
! [Xx: nat,Xy: nat] :
( amone
@ ^ [Xz: nat] :
( Xx
= ( pl @ Xy @ Xz ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: nat] :
( !!
@ ^ [Y1: nat] :
( amone
@ ^ [Y2: nat] :
( Y0
= ( pl @ Y1 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[satz8b]) ).
thf(zip_derived_cl3,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ amone ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ (=) ) ) @ pl ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl26,plain,
! [X2: nat] : ( !! @ ( '#B' @ amone @ ( '#B' @ ( '#B' @ ( nat = X2 ) ) @ pl ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl27,plain,
! [X2: nat,X4: nat] : ( amone @ ( '#B' @ ( nat = X2 ) @ ( pl @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(oneax,axiom,
! [Xp: nat > $o] :
( ~ ( ( amone @ Xp )
=> ~ ( some @ Xp ) )
=> ( Xp @ ( ind @ Xp ) ) ) ).
thf(zip_derived_cl16,plain,
( !!
@ ^ [Y0: nat > $o] :
( ( (~)
@ ( ( amone @ Y0 )
=> ( (~) @ ( some @ Y0 ) ) ) )
=> ( Y0 @ ( ind @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[oneax]) ).
thf(zip_derived_cl17,plain,
!! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ (~) @ ( '#S' @ ( '#B' @ (=>) @ amone ) @ ( '#B' @ (~) @ some ) ) ) ) @ ( '#S' @ '#I' @ ind ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl30,plain,
! [X2: nat > $o] :
( ( (~)
@ ( ( amone @ X2 )
=> ( (~) @ ( some @ X2 ) ) ) )
=> ( X2 @ ( ind @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl31,plain,
! [X2: nat > $o] :
( ( ( amone @ X2 )
=> ( (~) @ ( some @ X2 ) ) )
| ( X2 @ ( ind @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl32,plain,
! [X2: nat > $o] :
( ~ ( amone @ X2 )
| ~ ( some @ X2 )
| ( X2 @ ( ind @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl51,plain,
! [X0: nat,X1: nat] :
( ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) @ ( ind @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) )
| ~ ( some @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl27,zip_derived_cl32]) ).
thf(zip_derived_cl61,plain,
! [X0: nat,X1: nat] :
( ( X1
= ( pl @ X0 @ ( ind @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ) )
| ~ ( some @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl62,plain,
! [X0: nat,X1: nat] :
( ( X1
= ( pl @ X0 @ ( ind @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ) )
| ~ ( some @ ( '#B' @ ( nat = X1 ) @ ( pl @ X0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl61]) ).
thf(satz56,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xz @ Xu )
=> ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: frac] :
( !!
@ ^ [Y1: frac] :
( !!
@ ^ [Y2: frac] :
( !!
@ ^ [Y3: frac] :
( ( eq @ Y0 @ Y1 )
=> ( ( eq @ Y2 @ Y3 )
=> ( eq @ ( pf @ Y0 @ Y2 ) @ ( pf @ Y1 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[satz56]) ).
thf(zip_derived_cl7,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ eq ) @ pf ) ) ) ) @ pf ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl43,plain,
! [X2: frac] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( eq @ X2 ) ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ eq @ ( pf @ X2 ) ) ) ) @ pf ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl44,plain,
! [X2: frac,X4: frac] : ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ ( (=>) @ ( eq @ X2 @ X4 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ eq @ ( pf @ X2 ) ) ) @ ( pf @ X4 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl45,plain,
! [X2: frac,X4: frac,X6: frac] : ( !! @ ( '#B' @ ( (=>) @ ( eq @ X2 @ X4 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( eq @ X6 ) ) @ ( '#B' @ ( eq @ ( pf @ X2 @ X6 ) ) @ ( pf @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl46,plain,
! [X2: frac,X4: frac,X6: frac,X8: frac] :
( ( eq @ X2 @ X4 )
=> ( ( eq @ X6 @ X8 )
=> ( eq @ ( pf @ X2 @ X6 ) @ ( pf @ X4 @ X8 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl47,plain,
! [X2: frac,X4: frac,X6: frac,X8: frac] :
( ~ ( eq @ X2 @ X4 )
| ( ( eq @ X6 @ X8 )
=> ( eq @ ( pf @ X2 @ X6 ) @ ( pf @ X4 @ X8 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl48,plain,
! [X2: frac,X4: frac,X6: frac,X8: frac] :
( ~ ( eq @ X6 @ X8 )
| ( eq @ ( pf @ X2 @ X6 ) @ ( pf @ X4 @ X8 ) )
| ~ ( eq @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(satz39,axiom,
! [Xx: frac,Xy: frac,Xz: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xy @ Xz )
=> ( eq @ Xx @ Xz ) ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: frac] :
( !!
@ ^ [Y1: frac] :
( !!
@ ^ [Y2: frac] :
( ( eq @ Y0 @ Y1 )
=> ( ( eq @ Y1 @ Y2 )
=> ( eq @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf,[status(esa)],[satz39]) ).
thf(zip_derived_cl5,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) ) @ eq ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl35,plain,
! [X2: frac] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ (=>) @ ( eq @ X2 ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ eq ) ) @ ( eq @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl36,plain,
! [X2: frac,X4: frac] : ( !! @ ( '#B' @ ( (=>) @ ( eq @ X2 @ X4 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( eq @ X4 ) ) @ ( eq @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl37,plain,
! [X2: frac,X4: frac,X6: frac] :
( ( eq @ X2 @ X4 )
=> ( ( eq @ X4 @ X6 )
=> ( eq @ X2 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl38,plain,
! [X2: frac,X4: frac,X6: frac] :
( ~ ( eq @ X2 @ X4 )
| ( ( eq @ X4 @ X6 )
=> ( eq @ X2 @ X6 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl39,plain,
! [X2: frac,X4: frac,X6: frac] :
( ~ ( eq @ X4 @ X6 )
| ( eq @ X2 @ X6 )
| ~ ( eq @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(satz67c,conjecture,
( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference('cnf.neg',[status(esa)],[satz67c]) ).
thf(zip_derived_cl20,plain,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl21,plain,
~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
inference(lams2combs,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl148,plain,
! [X0: frac] :
( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ X0 )
| ~ ( eq @ X0 @ x ) ),
inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl21]) ).
thf(zip_derived_cl215,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ y @ X1 )
| ~ ( eq
@ ( fr
@ ( ind
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ X0 )
| ~ ( eq @ ( pf @ X1 @ X0 ) @ x ) ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl148]) ).
thf(satz37,axiom,
! [Xx: frac] : ( eq @ Xx @ Xx ) ).
thf(zip_derived_cl10,plain,
( !!
@ ^ [Y0: frac] : ( eq @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[satz37]) ).
thf(zip_derived_cl11,plain,
!! @ ( '#S' @ eq @ '#I' ),
inference(lams2combs,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl22,plain,
! [X2: frac] : ( eq @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl369,plain,
! [X0: frac] :
( ~ ( eq
@ ( pf @ X0
@ ( fr
@ ( ind
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x )
| ~ ( eq @ y @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl215,zip_derived_cl22]) ).
thf(zip_derived_cl39_001,plain,
! [X2: frac,X4: frac,X6: frac] :
( ~ ( eq @ X4 @ X6 )
| ( eq @ X2 @ X6 )
| ~ ( eq @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl387,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ y @ X0 )
| ~ ( eq
@ ( pf @ X0
@ ( fr
@ ( ind
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ X1 )
| ~ ( eq @ X1 @ x ) ),
inference('sup+',[status(thm)],[zip_derived_cl369,zip_derived_cl39]) ).
thf(satz57,axiom,
! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: nat] :
( !!
@ ^ [Y1: nat] :
( !!
@ ^ [Y2: nat] : ( eq @ ( pf @ ( fr @ Y0 @ Y2 ) @ ( fr @ Y1 @ Y2 ) ) @ ( fr @ ( pl @ Y0 @ Y1 ) @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[satz57]) ).
thf(zip_derived_cl15,plain,
!! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ eq ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ pf ) @ fr ) ) ) @ fr ) ) ) ) @ ( '#B' @ ( '#B' @ fr ) @ pl ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl40,plain,
! [X2: nat] : ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ eq ) @ ( '#B' @ ( '#S' @ ( '#B' @ pf @ ( fr @ X2 ) ) ) @ fr ) ) ) @ ( '#B' @ fr @ ( pl @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl41,plain,
! [X2: nat,X4: nat] : ( !! @ ( '#S' @ ( '#B' @ eq @ ( '#S' @ ( '#B' @ pf @ ( fr @ X2 ) ) @ ( fr @ X4 ) ) ) @ ( fr @ ( pl @ X2 @ X4 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
! [X2: nat,X4: nat,X6: nat] : ( eq @ ( pf @ ( fr @ X2 @ X6 ) @ ( fr @ X4 @ X6 ) ) @ ( fr @ ( pl @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl421,plain,
! [X0: nat] :
( ~ ( eq
@ ( fr
@ ( pl @ X0
@ ( ind
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ x )
| ~ ( eq @ y @ ( fr @ X0 @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl387,zip_derived_cl42]) ).
thf(zip_derived_cl561,plain,
( ~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ x )
| ~ ( some
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) )
| ~ ( eq @ y @ ( fr @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl421]) ).
thf(satz40a,axiom,
! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) ).
thf(zip_derived_cl18,plain,
( !!
@ ^ [Y0: frac] :
( !!
@ ^ [Y1: nat] : ( eq @ ( fr @ ( ts @ ( num @ Y0 ) @ Y1 ) @ ( ts @ ( den @ Y0 ) @ Y1 ) ) @ Y0 ) ) ),
inference(cnf,[status(esa)],[satz40a]) ).
thf(zip_derived_cl19,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ eq ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ fr ) @ ( '#B' @ ts @ num ) ) ) @ ( '#B' @ ts @ den ) ) ) ) @ '#I' ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl33,plain,
! [X2: frac] : ( !! @ ( '#C' @ ( '#B' @ eq @ ( '#S' @ ( '#B' @ fr @ ( ts @ ( num @ X2 ) ) ) @ ( ts @ ( den @ X2 ) ) ) ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl34,plain,
! [X2: frac,X4: nat] : ( eq @ ( fr @ ( ts @ ( num @ X2 ) @ X4 ) @ ( ts @ ( den @ X2 ) @ X4 ) ) @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(m,axiom,
( some
@ ^ [Xu: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ) ).
thf(zip_derived_cl0,plain,
( some
@ ^ [Y0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Y0 ) ) ),
inference(cnf,[status(esa)],[m]) ).
thf(zip_derived_cl1,plain,
( some
@ ( '#B'
@ ( nat
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
@ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).
thf(satz29,axiom,
! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: nat] :
( !!
@ ^ [Y1: nat] :
( ( ts @ Y0 @ Y1 )
= ( ts @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[satz29]) ).
thf(zip_derived_cl13,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ts ) ) @ ( '#C' @ ts ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl23,plain,
! [X2: nat] : ( !! @ ( '#S' @ ( '#B' @ (=) @ ( ts @ X2 ) ) @ ( '#C' @ ts @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl24,plain,
! [X2: nat,X4: nat] :
( ( ts @ X2 @ X4 )
= ( ts @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl25,plain,
! [X2: nat,X4: nat] :
( ( ts @ X2 @ X4 )
= ( ts @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl24]) ).
thf(satz40,axiom,
! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: frac] :
( !!
@ ^ [Y1: nat] : ( eq @ Y0 @ ( fr @ ( ts @ ( num @ Y0 ) @ Y1 ) @ ( ts @ ( den @ Y0 ) @ Y1 ) ) ) ) ),
inference(cnf,[status(esa)],[satz40]) ).
thf(zip_derived_cl9,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#B' @ eq ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ fr ) @ ( '#B' @ ts @ num ) ) ) @ ( '#B' @ ts @ den ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl28,plain,
! [X2: frac] : ( !! @ ( '#B' @ ( eq @ X2 ) @ ( '#S' @ ( '#B' @ fr @ ( ts @ ( num @ X2 ) ) ) @ ( ts @ ( den @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl29,plain,
! [X2: frac,X4: nat] : ( eq @ X2 @ ( fr @ ( ts @ ( num @ X2 ) @ X4 ) @ ( ts @ ( den @ X2 ) @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl129,plain,
! [X0: frac,X1: nat] : ( eq @ X0 @ ( fr @ ( ts @ ( num @ X0 ) @ X1 ) @ ( ts @ X1 @ ( den @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl25,zip_derived_cl29]) ).
thf(zip_derived_cl565,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl561,zip_derived_cl34,zip_derived_cl1,zip_derived_cl129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM768^1 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7O4aiWQCUI true
% 0.09/0.31 % Computer : n003.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Wed Oct 1 16:16:38 EDT 2025
% 0.13/0.31 % CPUTime :
% 0.13/0.31 % Running portfolio for 300 s
% 0.13/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.31 % Number of cores: 8
% 0.13/0.32 % Python version: Python 3.6.8
% 0.13/0.32 % Running in HO mode
% 0.48/0.67 % Total configuration time : 828
% 0.48/0.67 % Estimated wc time : 1656
% 0.48/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.48/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.48/0.85 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.48/0.86 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.48/0.87 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.48/0.87 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.49/0.93 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.49/0.95 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.49/0.96 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 5.60/1.90 % Solved by lams/40_b.comb.sh.
% 5.60/1.90 % done 74 iterations in 0.809s
% 5.60/1.90 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.60/1.90 % SZS output start Refutation
% See solution above
% 5.60/1.90
% 5.60/1.90
% 5.60/1.90 % Terminating...
% 6.02/2.07 % Runner terminated.
% 6.02/2.10 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------