%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : KLE039+2 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2G4NuK9AZw true
% Computer : n008.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 04:40:10 PM UTC 2025
% Result : Theorem 262.09s 38.10s
% Output : Refutation 262.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 180 ( 150 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 142 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1199 ( 29 ~; 26 |; 2 &;1140 @)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 310 ( 0 ^; 310 !; 0 ?; 310 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(star_type,type,
star: $i > $i ).
thf(sk__type,type,
sk_: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(zero_type,type,
zero: $i ).
thf(goals,conjecture,
! [X0: $i] :
( ( leq @ ( star @ X0 ) @ ( star @ ( star @ X0 ) ) )
& ( leq @ ( star @ ( star @ X0 ) ) @ ( star @ X0 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i] :
( ( leq @ ( star @ X0 ) @ ( star @ ( star @ X0 ) ) )
& ( leq @ ( star @ ( star @ X0 ) ) @ ( star @ X0 ) ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl17,plain,
( ~ ( leq @ ( star @ sk_ ) @ ( star @ ( star @ sk_ ) ) )
| ~ ( leq @ ( star @ ( star @ sk_ ) ) @ ( star @ sk_ ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(star_unfold_right,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i] : ( leq @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) @ ( star @ X0 ) ),
inference(cnf,[status(esa)],[star_unfold_right]) ).
thf(order,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
= X0 )
| ~ ( leq @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl226,plain,
! [X0: $i] :
( ( addition @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl11]) ).
thf(additive_commutativity,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl24005,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) )
= ( star @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl0]) ).
thf(additive_associativity,axiom,
! [C: $i,B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ C ) )
= ( addition @ ( addition @ A @ B ) @ C ) ) ).
thf(zip_derived_cl1,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl0_001,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl0_002,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(additive_idempotence,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ) ).
thf(zip_derived_cl3,plain,
! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[additive_idempotence]) ).
thf(zip_derived_cl53_003,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl205,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X0 ) )
= ( addition @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl53]) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i] :
( ( leq @ X0 @ X1 )
| ( ( addition @ X0 @ X1 )
!= X1 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(multiplicative_left_identity,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ) ).
thf(zip_derived_cl6,plain,
! [X0: $i] :
( ( multiplication @ one @ X0 )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_left_identity]) ).
thf(additive_identity,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ) ).
thf(zip_derived_cl2,plain,
! [X0: $i] :
( ( addition @ X0 @ zero )
= X0 ),
inference(cnf,[status(esa)],[additive_identity]) ).
thf(star_induction_left,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ) ).
thf(zip_derived_cl15,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( leq @ ( multiplication @ ( star @ X0 ) @ X1 ) @ X2 )
| ~ ( leq @ ( addition @ ( multiplication @ X0 @ X2 ) @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[star_induction_left]) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ~ ( leq @ ( multiplication @ X1 @ X0 ) @ X0 )
| ( leq @ ( multiplication @ ( star @ X1 ) @ zero ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl15]) ).
thf(right_annihilation,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ) ).
thf(zip_derived_cl9,plain,
! [X0: $i] :
( ( multiplication @ X0 @ zero )
= zero ),
inference(cnf,[status(esa)],[right_annihilation]) ).
thf(zip_derived_cl28,plain,
! [X0: $i,X1: $i] :
( ~ ( leq @ ( multiplication @ X1 @ X0 ) @ X0 )
| ( leq @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl23,zip_derived_cl9]) ).
thf(zip_derived_cl33,plain,
! [X0: $i] :
( ~ ( leq @ X0 @ X0 )
| ( leq @ zero @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl28]) ).
thf(zip_derived_cl34,plain,
! [X0: $i] :
( ( ( addition @ X0 @ X0 )
!= X0 )
| ( leq @ zero @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl33]) ).
thf(zip_derived_cl3_004,plain,
! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[additive_idempotence]) ).
thf(zip_derived_cl36,plain,
! [X0: $i] :
( ( X0 != X0 )
| ( leq @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl3]) ).
thf(zip_derived_cl37,plain,
! [X0: $i] : ( leq @ zero @ X0 ),
inference(simplify,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl11_005,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
= X0 )
| ~ ( leq @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl42,plain,
! [X0: $i] :
( ( addition @ zero @ X0 )
= X0 ),
inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl53_006,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl200,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ zero @ ( addition @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl53]) ).
thf(zip_derived_cl602,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X0 )
= ( addition @ zero @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl205,zip_derived_cl200]) ).
thf(zip_derived_cl42_007,plain,
! [X0: $i] :
( ( addition @ zero @ X0 )
= X0 ),
inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl656,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X0 )
= ( addition @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl602,zip_derived_cl42]) ).
thf(zip_derived_cl1156,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X1 )
= ( addition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl656]) ).
thf(zip_derived_cl1386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ ( addition @ X2 @ ( addition @ X1 @ X0 ) ) @ X1 )
= ( addition @ ( addition @ X0 @ X2 ) @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl53,zip_derived_cl1156]) ).
thf(zip_derived_cl1_008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl1417,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ ( addition @ X2 @ ( addition @ X1 @ X0 ) ) @ X1 )
= ( addition @ X0 @ ( addition @ X2 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1386,zip_derived_cl1]) ).
thf(zip_derived_cl89100,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ one )
= ( addition @ ( multiplication @ X0 @ ( star @ X0 ) ) @ ( addition @ ( star @ X0 ) @ one ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl24005,zip_derived_cl1417]) ).
thf(zip_derived_cl0_009,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl0_010,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl0_011,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl53_012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X2 @ ( addition @ X1 @ X0 ) )
= ( addition @ X0 @ ( addition @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl53]) ).
thf(zip_derived_cl24005_013,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) )
= ( star @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl0]) ).
thf(zip_derived_cl89346,plain,
! [X0: $i] :
( ( addition @ one @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl89100,zip_derived_cl0,zip_derived_cl0,zip_derived_cl192,zip_derived_cl24005]) ).
thf(zip_derived_cl0_014,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(left_distributivity,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiplication @ ( addition @ X0 @ X2 ) @ X1 )
= ( addition @ ( multiplication @ X0 @ X1 ) @ ( multiplication @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[left_distributivity]) ).
thf(zip_derived_cl10046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiplication @ ( addition @ X1 @ X0 ) @ X2 )
= ( addition @ ( multiplication @ X0 @ X2 ) @ ( multiplication @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl8]) ).
thf(zip_derived_cl89479,plain,
! [X0: $i,X1: $i] :
( ( multiplication @ ( star @ X0 ) @ X1 )
= ( addition @ ( multiplication @ ( star @ X0 ) @ X1 ) @ ( multiplication @ one @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89346,zip_derived_cl10046]) ).
thf(zip_derived_cl6_015,plain,
! [X0: $i] :
( ( multiplication @ one @ X0 )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_left_identity]) ).
thf(zip_derived_cl0_016,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl89676,plain,
! [X0: $i,X1: $i] :
( ( multiplication @ ( star @ X0 ) @ X1 )
= ( addition @ X1 @ ( multiplication @ ( star @ X0 ) @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl89479,zip_derived_cl6,zip_derived_cl0]) ).
thf(zip_derived_cl24005_017,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) )
= ( star @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl0]) ).
thf(zip_derived_cl53_018,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl3_019,plain,
! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[additive_idempotence]) ).
thf(zip_derived_cl1_020,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl60,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X0 @ X1 ) )
= ( addition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1]) ).
thf(zip_derived_cl177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ ( addition @ X1 @ X0 ) ) )
= ( addition @ X0 @ ( addition @ X2 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl53,zip_derived_cl60]) ).
thf(zip_derived_cl89093,plain,
! [X0: $i] :
( ( addition @ ( multiplication @ X0 @ ( star @ X0 ) ) @ ( star @ X0 ) )
= ( addition @ ( multiplication @ X0 @ ( star @ X0 ) ) @ ( addition @ ( star @ X0 ) @ one ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl24005,zip_derived_cl177]) ).
thf(zip_derived_cl0_021,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl0_022,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl192_023,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X2 @ ( addition @ X1 @ X0 ) )
= ( addition @ X0 @ ( addition @ X1 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl53]) ).
thf(zip_derived_cl24005_024,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) )
= ( star @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl0]) ).
thf(zip_derived_cl89340,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ ( multiplication @ X0 @ ( star @ X0 ) ) )
= ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl89093,zip_derived_cl0,zip_derived_cl0,zip_derived_cl192,zip_derived_cl24005]) ).
thf(zip_derived_cl96113,plain,
! [X0: $i] :
( ( multiplication @ ( star @ X0 ) @ ( star @ ( star @ X0 ) ) )
= ( star @ ( star @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89676,zip_derived_cl89340]) ).
thf(zip_derived_cl89346_025,plain,
! [X0: $i] :
( ( addition @ one @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl89100,zip_derived_cl0,zip_derived_cl0,zip_derived_cl192,zip_derived_cl24005]) ).
thf(zip_derived_cl0_026,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(right_distributivity,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ) ).
thf(zip_derived_cl7,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiplication @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( multiplication @ X0 @ X1 ) @ ( multiplication @ X0 @ X2 ) ) ),
inference(cnf,[status(esa)],[right_distributivity]) ).
thf(zip_derived_cl8782,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiplication @ X2 @ ( addition @ X1 @ X0 ) )
= ( addition @ ( multiplication @ X2 @ X0 ) @ ( multiplication @ X2 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl7]) ).
thf(zip_derived_cl89478,plain,
! [X0: $i,X1: $i] :
( ( multiplication @ X1 @ ( star @ X0 ) )
= ( addition @ ( multiplication @ X1 @ ( star @ X0 ) ) @ ( multiplication @ X1 @ one ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89346,zip_derived_cl8782]) ).
thf(multiplicative_right_identity,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ) ).
thf(zip_derived_cl5,plain,
! [X0: $i] :
( ( multiplication @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_right_identity]) ).
thf(zip_derived_cl0_027,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl89675,plain,
! [X0: $i,X1: $i] :
( ( multiplication @ X1 @ ( star @ X0 ) )
= ( addition @ X1 @ ( multiplication @ X1 @ ( star @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl89478,zip_derived_cl5,zip_derived_cl0]) ).
thf(zip_derived_cl12_028,plain,
! [X0: $i,X1: $i] :
( ( leq @ X0 @ X1 )
| ( ( addition @ X0 @ X1 )
!= X1 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl60_029,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X0 @ X1 ) )
= ( addition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1]) ).
thf(zip_derived_cl0_030,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl6_031,plain,
! [X0: $i] :
( ( multiplication @ one @ X0 )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_left_identity]) ).
thf(zip_derived_cl15_032,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( leq @ ( multiplication @ ( star @ X0 ) @ X1 ) @ X2 )
| ~ ( leq @ ( addition @ ( multiplication @ X0 @ X2 ) @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[star_induction_left]) ).
thf(zip_derived_cl27,plain,
! [X0: $i,X1: $i] :
( ~ ( leq @ ( addition @ X0 @ X1 ) @ X0 )
| ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl15]) ).
thf(zip_derived_cl88,plain,
! [X0: $i,X1: $i] :
( ~ ( leq @ ( addition @ X1 @ X0 ) @ X0 )
| ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl27]) ).
thf(zip_derived_cl101,plain,
! [X0: $i,X1: $i] :
( ~ ( leq @ ( addition @ X1 @ X0 ) @ ( addition @ X1 @ X0 ) )
| ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ ( addition @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl88]) ).
thf(zip_derived_cl1464,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ ( addition @ X1 @ X0 ) @ ( addition @ X1 @ X0 ) )
!= ( addition @ X1 @ X0 ) )
| ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ ( addition @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl101]) ).
thf(zip_derived_cl1_033,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl205_034,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X0 ) )
= ( addition @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl53]) ).
thf(zip_derived_cl60_035,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X0 @ X1 ) )
= ( addition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1]) ).
thf(zip_derived_cl1531,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
!= ( addition @ X1 @ X0 ) )
| ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ ( addition @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1464,zip_derived_cl1,zip_derived_cl205,zip_derived_cl60]) ).
thf(zip_derived_cl1532,plain,
! [X0: $i,X1: $i] : ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ ( addition @ X1 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1531]) ).
thf(zip_derived_cl6_036,plain,
! [X0: $i] :
( ( multiplication @ one @ X0 )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_left_identity]) ).
thf(zip_derived_cl13_037,plain,
! [X0: $i] : ( leq @ ( addition @ one @ ( multiplication @ X0 @ ( star @ X0 ) ) ) @ ( star @ X0 ) ),
inference(cnf,[status(esa)],[star_unfold_right]) ).
thf(zip_derived_cl229,plain,
leq @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ),
inference('sup+',[status(thm)],[zip_derived_cl6,zip_derived_cl13]) ).
thf(zip_derived_cl11_038,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
= X0 )
| ~ ( leq @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl243,plain,
( ( addition @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ) )
= ( star @ one ) ),
inference('sup-',[status(thm)],[zip_derived_cl229,zip_derived_cl11]) ).
thf(zip_derived_cl200_039,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ zero @ ( addition @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl53]) ).
thf(zip_derived_cl398,plain,
( ( star @ one )
= ( addition @ zero @ ( addition @ ( star @ one ) @ ( addition @ one @ ( star @ one ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl243,zip_derived_cl200]) ).
thf(zip_derived_cl53_040,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl3_041,plain,
! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[additive_idempotence]) ).
thf(zip_derived_cl42_042,plain,
! [X0: $i] :
( ( addition @ zero @ X0 )
= X0 ),
inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl405,plain,
( ( star @ one )
= ( addition @ one @ ( star @ one ) ) ),
inference(demod,[status(thm)],[zip_derived_cl398,zip_derived_cl53,zip_derived_cl3,zip_derived_cl42]) ).
thf(zip_derived_cl60_043,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X0 @ X1 ) )
= ( addition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1]) ).
thf(zip_derived_cl200_044,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ zero @ ( addition @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl53]) ).
thf(zip_derived_cl347,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X1 )
= ( addition @ zero @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl60,zip_derived_cl200]) ).
thf(zip_derived_cl42_045,plain,
! [X0: $i] :
( ( addition @ zero @ X0 )
= X0 ),
inference('sup-',[status(thm)],[zip_derived_cl37,zip_derived_cl11]) ).
thf(zip_derived_cl357,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X1 )
= ( addition @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl347,zip_derived_cl42]) ).
thf(zip_derived_cl867,plain,
( ( addition @ ( star @ one ) @ one )
= ( addition @ one @ ( star @ one ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl405,zip_derived_cl357]) ).
thf(zip_derived_cl405_046,plain,
( ( star @ one )
= ( addition @ one @ ( star @ one ) ) ),
inference(demod,[status(thm)],[zip_derived_cl398,zip_derived_cl53,zip_derived_cl3,zip_derived_cl42]) ).
thf(zip_derived_cl888,plain,
( ( addition @ ( star @ one ) @ one )
= ( star @ one ) ),
inference(demod,[status(thm)],[zip_derived_cl867,zip_derived_cl405]) ).
thf(zip_derived_cl5_047,plain,
! [X0: $i] :
( ( multiplication @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_right_identity]) ).
thf(zip_derived_cl3_048,plain,
! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
inference(cnf,[status(esa)],[additive_idempotence]) ).
thf(zip_derived_cl1532_049,plain,
! [X0: $i,X1: $i] : ( leq @ ( multiplication @ ( star @ one ) @ X1 ) @ ( addition @ X1 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1531]) ).
thf(zip_derived_cl5459,plain,
! [X0: $i] : ( leq @ ( multiplication @ ( star @ one ) @ X0 ) @ X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1532]) ).
thf(zip_derived_cl5652,plain,
leq @ ( star @ one ) @ one,
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl5459]) ).
thf(zip_derived_cl11_050,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
= X0 )
| ~ ( leq @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl5654,plain,
( ( addition @ ( star @ one ) @ one )
= one ),
inference('sup-',[status(thm)],[zip_derived_cl5652,zip_derived_cl11]) ).
thf(zip_derived_cl5655,plain,
( one
= ( star @ one ) ),
inference(demod,[status(thm)],[zip_derived_cl888,zip_derived_cl5654]) ).
thf(zip_derived_cl6_051,plain,
! [X0: $i] :
( ( multiplication @ one @ X0 )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_left_identity]) ).
thf(zip_derived_cl5764,plain,
! [X0: $i,X1: $i] : ( leq @ X1 @ ( addition @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1532,zip_derived_cl5655,zip_derived_cl6]) ).
thf(zip_derived_cl94555,plain,
! [X0: $i,X1: $i] : ( leq @ X1 @ ( multiplication @ X1 @ ( star @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89675,zip_derived_cl5764]) ).
thf(zip_derived_cl96703,plain,
! [X0: $i] : ( leq @ ( star @ X0 ) @ ( star @ ( star @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl96113,zip_derived_cl94555]) ).
thf(zip_derived_cl96771,plain,
~ ( leq @ ( star @ ( star @ sk_ ) ) @ ( star @ sk_ ) ),
inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl96703]) ).
thf(zip_derived_cl89340_052,plain,
! [X0: $i] :
( ( addition @ ( star @ X0 ) @ ( multiplication @ X0 @ ( star @ X0 ) ) )
= ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl89093,zip_derived_cl0,zip_derived_cl0,zip_derived_cl192,zip_derived_cl24005]) ).
thf(zip_derived_cl0_053,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl15_054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( leq @ ( multiplication @ ( star @ X0 ) @ X1 ) @ X2 )
| ~ ( leq @ ( addition @ ( multiplication @ X0 @ X2 ) @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[star_induction_left]) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( leq @ ( addition @ X2 @ ( multiplication @ X1 @ X0 ) ) @ X0 )
| ( leq @ ( multiplication @ ( star @ X1 ) @ X2 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl0,zip_derived_cl15]) ).
thf(zip_derived_cl90720,plain,
! [X0: $i] :
( ~ ( leq @ ( star @ X0 ) @ ( star @ X0 ) )
| ( leq @ ( multiplication @ ( star @ X0 ) @ ( star @ X0 ) ) @ ( star @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl89340,zip_derived_cl43]) ).
thf(zip_derived_cl5459_055,plain,
! [X0: $i] : ( leq @ ( multiplication @ ( star @ one ) @ X0 ) @ X0 ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl1532]) ).
thf(zip_derived_cl5655_056,plain,
( one
= ( star @ one ) ),
inference(demod,[status(thm)],[zip_derived_cl888,zip_derived_cl5654]) ).
thf(zip_derived_cl6_057,plain,
! [X0: $i] :
( ( multiplication @ one @ X0 )
= X0 ),
inference(cnf,[status(esa)],[multiplicative_left_identity]) ).
thf(zip_derived_cl5777,plain,
! [X0: $i] : ( leq @ X0 @ X0 ),
inference(demod,[status(thm)],[zip_derived_cl5459,zip_derived_cl5655,zip_derived_cl6]) ).
thf(zip_derived_cl90911,plain,
! [X0: $i] : ( leq @ ( multiplication @ ( star @ X0 ) @ ( star @ X0 ) ) @ ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl90720,zip_derived_cl5777]) ).
thf(zip_derived_cl11_058,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
= X0 )
| ~ ( leq @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl100361,plain,
! [X0: $i] :
( ( addition @ ( multiplication @ ( star @ X0 ) @ ( star @ X0 ) ) @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl90911,zip_derived_cl11]) ).
thf(zip_derived_cl15_059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( leq @ ( multiplication @ ( star @ X0 ) @ X1 ) @ X2 )
| ~ ( leq @ ( addition @ ( multiplication @ X0 @ X2 ) @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[star_induction_left]) ).
thf(zip_derived_cl156210,plain,
! [X0: $i] :
( ~ ( leq @ ( star @ X0 ) @ ( star @ X0 ) )
| ( leq @ ( multiplication @ ( star @ ( star @ X0 ) ) @ ( star @ X0 ) ) @ ( star @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl100361,zip_derived_cl15]) ).
thf(zip_derived_cl5777_060,plain,
! [X0: $i] : ( leq @ X0 @ X0 ),
inference(demod,[status(thm)],[zip_derived_cl5459,zip_derived_cl5655,zip_derived_cl6]) ).
thf(zip_derived_cl89346_061,plain,
! [X0: $i] :
( ( addition @ one @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl89100,zip_derived_cl0,zip_derived_cl0,zip_derived_cl192,zip_derived_cl24005]) ).
thf(zip_derived_cl357_062,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X1 )
= ( addition @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl347,zip_derived_cl42]) ).
thf(zip_derived_cl53_063,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X2 @ X1 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl357_064,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X1 )
= ( addition @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl347,zip_derived_cl42]) ).
thf(zip_derived_cl852,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ ( addition @ X2 @ ( addition @ X1 @ X0 ) ) @ X1 )
= ( addition @ X1 @ ( addition @ X0 @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl53,zip_derived_cl357]) ).
thf(zip_derived_cl0_065,plain,
! [X0: $i,X1: $i] :
( ( addition @ X1 @ X0 )
= ( addition @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[additive_commutativity]) ).
thf(zip_derived_cl1_066,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X1 @ X0 ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1]) ).
thf(zip_derived_cl27239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ ( addition @ X2 @ X1 ) @ ( addition @ X0 @ X2 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl852,zip_derived_cl58]) ).
thf(zip_derived_cl43385,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ ( addition @ X1 @ X2 ) @ ( addition @ X1 @ X0 ) )
= ( addition @ X1 @ ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl357,zip_derived_cl27239]) ).
thf(zip_derived_cl205_067,plain,
! [X0: $i,X1: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X0 ) )
= ( addition @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl3,zip_derived_cl53]) ).
thf(zip_derived_cl1_068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ ( addition @ X1 @ X0 ) @ X2 ) )
= ( addition @ ( addition @ X1 @ X0 ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl205,zip_derived_cl1]) ).
thf(zip_derived_cl1_069,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl1_070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ X2 ) )
= ( addition @ ( addition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[additive_associativity]) ).
thf(zip_derived_cl654,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ X0 @ ( addition @ X1 @ ( addition @ X0 @ X2 ) ) )
= ( addition @ X1 @ ( addition @ X0 @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl598,zip_derived_cl1,zip_derived_cl1]) ).
thf(zip_derived_cl43605,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition @ ( addition @ X1 @ X2 ) @ ( addition @ X1 @ X0 ) )
= ( addition @ X2 @ ( addition @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl43385,zip_derived_cl654]) ).
thf(zip_derived_cl89509,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ one @ X1 ) @ ( star @ X0 ) )
= ( addition @ X1 @ ( addition @ one @ ( star @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89346,zip_derived_cl43605]) ).
thf(zip_derived_cl89346_071,plain,
! [X0: $i] :
( ( addition @ one @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl89100,zip_derived_cl0,zip_derived_cl0,zip_derived_cl192,zip_derived_cl24005]) ).
thf(zip_derived_cl89696,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ one @ X1 ) @ ( star @ X0 ) )
= ( addition @ X1 @ ( star @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl89509,zip_derived_cl89346]) ).
thf(star_unfold_left,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ) ).
thf(zip_derived_cl14,plain,
! [X0: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ X0 ) @ X0 ) ) @ ( star @ X0 ) ),
inference(cnf,[status(esa)],[star_unfold_left]) ).
thf(zip_derived_cl11_072,plain,
! [X0: $i,X1: $i] :
( ( ( addition @ X1 @ X0 )
= X0 )
| ~ ( leq @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[order]) ).
thf(zip_derived_cl745,plain,
! [X0: $i] :
( ( addition @ ( addition @ one @ ( multiplication @ ( star @ X0 ) @ X0 ) ) @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl11]) ).
thf(zip_derived_cl98292,plain,
! [X0: $i] :
( ( addition @ ( multiplication @ ( star @ X0 ) @ X0 ) @ ( star @ X0 ) )
= ( star @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl89696,zip_derived_cl745]) ).
thf(zip_derived_cl89675_073,plain,
! [X0: $i,X1: $i] :
( ( multiplication @ X1 @ ( star @ X0 ) )
= ( addition @ X1 @ ( multiplication @ X1 @ ( star @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl89478,zip_derived_cl5,zip_derived_cl0]) ).
thf(zip_derived_cl357_074,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( addition @ X1 @ X0 ) @ X1 )
= ( addition @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl347,zip_derived_cl42]) ).
thf(zip_derived_cl94540,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( multiplication @ X1 @ ( star @ X0 ) ) @ X1 )
= ( addition @ X1 @ ( multiplication @ X1 @ ( star @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl89675,zip_derived_cl357]) ).
thf(zip_derived_cl89675_075,plain,
! [X0: $i,X1: $i] :
( ( multiplication @ X1 @ ( star @ X0 ) )
= ( addition @ X1 @ ( multiplication @ X1 @ ( star @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl89478,zip_derived_cl5,zip_derived_cl0]) ).
thf(zip_derived_cl94838,plain,
! [X0: $i,X1: $i] :
( ( addition @ ( multiplication @ X1 @ ( star @ X0 ) ) @ X1 )
= ( multiplication @ X1 @ ( star @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl94540,zip_derived_cl89675]) ).
thf(zip_derived_cl110889,plain,
! [X0: $i] :
( ( star @ ( star @ X0 ) )
= ( multiplication @ ( star @ ( star @ X0 ) ) @ ( star @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl98292,zip_derived_cl94838]) ).
thf(zip_derived_cl156448,plain,
! [X0: $i] : ( leq @ ( star @ ( star @ X0 ) ) @ ( star @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl156210,zip_derived_cl5777,zip_derived_cl110889]) ).
thf(zip_derived_cl156889,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl96771,zip_derived_cl156448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : KLE039+2 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2G4NuK9AZw true
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 14:00:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.39/0.59 % Total configuration time : 435
% 0.39/0.59 % Estimated wc time : 1092
% 0.39/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.47/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.47/0.69 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.47/0.70 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.47/0.71 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.47/0.71 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.47/0.71 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.47/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 262.09/38.10 % Solved by fo/fo7.sh.
% 262.09/38.10 % done 28464 iterations in 37.360s
% 262.09/38.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 262.09/38.10 % SZS output start Refutation
% See solution above
% 262.09/38.10
% 262.09/38.10
% 262.09/38.10 % Terminating...
% 262.57/38.20 % Runner terminated.
% 262.57/38.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------