%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fMmRZiZjcY true
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:36:11 PM UTC 2026
% Result : Theorem 11.43s 2.29s
% Output : Refutation 11.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 34
% Syntax : Number of formulae : 143 ( 85 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 726 ( 57 ~; 54 |; 1 &; 594 @)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 19 con; 0-2 aty)
% Number of variables : 163 ( 0 ^; 163 !; 0 ?; 163 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__92_type,type,
sk__92: $i ).
thf(axiom_M_type,type,
axiom_M: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(and_type,type,
and: $i > $i > $i ).
thf(axiom_4_type,type,
axiom_4: $o ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(necessarily_type,type,
necessarily: $i > $i ).
thf(implies_1_type,type,
implies_1: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(strict_implies_type,type,
strict_implies: $i > $i > $i ).
thf(op_strict_implies_type,type,
op_strict_implies: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(and_1_type,type,
and_1: $o ).
thf(necessitation_type,type,
necessitation: $o ).
thf(or_3_type,type,
or_3: $o ).
thf(equiv_type,type,
equiv: $i > $i > $i ).
thf(axiom_m9_type,type,
axiom_m9: $o ).
thf(and_3_type,type,
and_3: $o ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(op_strict_equiv_type,type,
op_strict_equiv: $o ).
thf(possibly_type,type,
possibly: $i > $i ).
thf(or_1_type,type,
or_1: $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(op_possibly_type,type,
op_possibly: $o ).
thf(substitution_of_equivalents_type,type,
substitution_of_equivalents: $o ).
thf(implies_2_type,type,
implies_2: $o ).
thf(not_type,type,
not: $i > $i ).
thf(strict_equiv_type,type,
strict_equiv: $i > $i > $i ).
thf(axiom_m9,axiom,
( axiom_m9
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X ) ) @ ( possibly @ X ) ) ) ) ).
thf(zip_derived_cl127,plain,
( axiom_m9
| ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sk__92 ) ) @ ( possibly @ sk__92 ) ) ) ),
inference(cnf,[status(esa)],[axiom_m9]) ).
thf(s1_0_m6s3m9b_axiom_m9,conjecture,
axiom_m9 ).
thf(zf_stmt_0,negated_conjecture,
~ axiom_m9,
inference('cnf.neg',[status(esa)],[s1_0_m6s3m9b_axiom_m9]) ).
thf(zip_derived_cl146,plain,
~ axiom_m9,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl227,plain,
~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sk__92 ) ) @ ( possibly @ sk__92 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl127,zip_derived_cl146]) ).
thf(and_3,axiom,
( and_3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ).
thf(zip_derived_cl19,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( implies @ X0 @ ( implies @ X1 @ ( and @ X0 @ X1 ) ) ) )
| ~ and_3 ),
inference(cnf,[status(esa)],[and_3]) ).
thf(hilbert_and_3,axiom,
and_3 ).
thf(zip_derived_cl70,plain,
and_3,
inference(cnf,[status(esa)],[hilbert_and_3]) ).
thf(zip_derived_cl304,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ X0 @ ( implies @ X1 @ ( and @ X0 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19,zip_derived_cl70]) ).
thf(implies_2,axiom,
( implies_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ X0 @ ( implies @ X0 @ X1 ) ) @ ( implies @ X0 @ X1 ) ) )
| ~ implies_2 ),
inference(cnf,[status(esa)],[implies_2]) ).
thf(hilbert_implies_2,axiom,
implies_2 ).
thf(zip_derived_cl66,plain,
implies_2,
inference(cnf,[status(esa)],[hilbert_implies_2]) ).
thf(zip_derived_cl207,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ ( implies @ X0 @ ( implies @ X0 @ X1 ) ) @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl11,zip_derived_cl66]) ).
thf(modus_ponens,axiom,
( modus_ponens
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ ( implies @ X @ Y ) ) )
=> ( is_a_theorem @ Y ) ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 )
| ~ modus_ponens ),
inference(cnf,[status(esa)],[modus_ponens]) ).
thf(hilbert_modus_ponens,axiom,
modus_ponens ).
thf(zip_derived_cl63,plain,
modus_ponens,
inference(cnf,[status(esa)],[hilbert_modus_ponens]) ).
thf(zip_derived_cl147,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl63]) ).
thf(zip_derived_cl208,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ ( implies @ X1 @ X0 ) ) )
| ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl207,zip_derived_cl147]) ).
thf(zip_derived_cl307,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ ( and @ X0 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl304,zip_derived_cl208]) ).
thf(op_equiv,axiom,
( op_equiv
=> ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ).
thf(zip_derived_cl59,plain,
! [X0: $i,X1: $i] :
( ( ( equiv @ X0 @ X1 )
= ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) )
| ~ op_equiv ),
inference(cnf,[status(esa)],[op_equiv]) ).
thf(hilbert_op_equiv,axiom,
op_equiv ).
thf(zip_derived_cl62,plain,
op_equiv,
inference(cnf,[status(esa)],[hilbert_op_equiv]) ).
thf(zip_derived_cl427,plain,
! [X0: $i,X1: $i] :
( ( equiv @ X0 @ X1 )
= ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl62]) ).
thf(zip_derived_cl304_001,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ X0 @ ( implies @ X1 @ ( and @ X0 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19,zip_derived_cl70]) ).
thf(zip_derived_cl147_002,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl63]) ).
thf(zip_derived_cl305,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ X1 )
| ( is_a_theorem @ ( implies @ X0 @ ( and @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl304,zip_derived_cl147]) ).
thf(zip_derived_cl147_003,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl63]) ).
thf(zip_derived_cl1714,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ X1 )
| ~ ( is_a_theorem @ X0 )
| ( is_a_theorem @ ( and @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl305,zip_derived_cl147]) ).
thf(zip_derived_cl1773,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl427,zip_derived_cl1714]) ).
thf(zip_derived_cl2572,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( implies @ ( and @ X0 @ X0 ) @ X0 ) )
| ( is_a_theorem @ ( equiv @ ( and @ X0 @ X0 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl307,zip_derived_cl1773]) ).
thf(and_1,axiom,
( and_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ).
thf(zip_derived_cl15,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( implies @ ( and @ X0 @ X1 ) @ X0 ) )
| ~ and_1 ),
inference(cnf,[status(esa)],[and_1]) ).
thf(hilbert_and_1,axiom,
and_1 ).
thf(zip_derived_cl68,plain,
and_1,
inference(cnf,[status(esa)],[hilbert_and_1]) ).
thf(zip_derived_cl170,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ ( and @ X0 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl15,zip_derived_cl68]) ).
thf(zip_derived_cl2616,plain,
! [X0: $i] : ( is_a_theorem @ ( equiv @ ( and @ X0 @ X0 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2572,zip_derived_cl170]) ).
thf(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( equiv @ X @ Y ) )
=> ( X = Y ) ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( equiv @ X0 @ X1 ) )
| ( X0 = X1 )
| ~ substitution_of_equivalents ),
inference(cnf,[status(esa)],[substitution_of_equivalents]) ).
thf(use_substitution_of_equivalents,axiom,
substitution_of_equivalents ).
thf(zip_derived_cl77,plain,
substitution_of_equivalents,
inference(cnf,[status(esa)],[use_substitution_of_equivalents]) ).
thf(zip_derived_cl155,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl4,zip_derived_cl77]) ).
thf(zip_derived_cl2629,plain,
! [X0: $i] :
( ( and @ X0 @ X0 )
= X0 ),
inference('sup-',[status(thm)],[zip_derived_cl2616,zip_derived_cl155]) ).
thf(op_or,axiom,
( op_or
=> ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ).
thf(zip_derived_cl55,plain,
! [X0: $i,X1: $i] :
( ( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) )
| ~ op_or ),
inference(cnf,[status(esa)],[op_or]) ).
thf(hilbert_op_or,axiom,
op_or ).
thf(zip_derived_cl60,plain,
op_or,
inference(cnf,[status(esa)],[hilbert_op_or]) ).
thf(zip_derived_cl336,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl60]) ).
thf(zip_derived_cl2671,plain,
! [X0: $i] :
( ( or @ X0 @ X0 )
= ( not @ ( not @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2629,zip_derived_cl336]) ).
thf(implies_1,axiom,
( implies_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( implies @ X0 @ ( implies @ X1 @ X0 ) ) )
| ~ implies_1 ),
inference(cnf,[status(esa)],[implies_1]) ).
thf(hilbert_implies_1,axiom,
implies_1 ).
thf(zip_derived_cl65,plain,
implies_1,
inference(cnf,[status(esa)],[hilbert_implies_1]) ).
thf(zip_derived_cl168,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ X0 @ ( implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9,zip_derived_cl65]) ).
thf(zip_derived_cl208_004,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ ( implies @ X1 @ X0 ) ) )
| ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl207,zip_derived_cl147]) ).
thf(zip_derived_cl297,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl168,zip_derived_cl208]) ).
thf(or_3,axiom,
( or_3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ X0 @ X1 ) @ ( implies @ ( implies @ X2 @ X1 ) @ ( implies @ ( or @ X0 @ X2 ) @ X1 ) ) ) )
| ~ or_3 ),
inference(cnf,[status(esa)],[or_3]) ).
thf(hilbert_or_3,axiom,
or_3 ).
thf(zip_derived_cl73,plain,
or_3,
inference(cnf,[status(esa)],[hilbert_or_3]) ).
thf(zip_derived_cl313,plain,
! [X0: $i,X1: $i,X2: $i] : ( is_a_theorem @ ( implies @ ( implies @ X0 @ X1 ) @ ( implies @ ( implies @ X2 @ X1 ) @ ( implies @ ( or @ X0 @ X2 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl25,zip_derived_cl73]) ).
thf(zip_derived_cl208_005,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ ( implies @ X1 @ X0 ) ) )
| ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl207,zip_derived_cl147]) ).
thf(zip_derived_cl316,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ ( implies @ X1 @ X0 ) @ ( implies @ ( or @ X1 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl313,zip_derived_cl208]) ).
thf(zip_derived_cl147_006,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl63]) ).
thf(zip_derived_cl1962,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ( is_a_theorem @ ( implies @ ( or @ X1 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl316,zip_derived_cl147]) ).
thf(zip_derived_cl1989,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ ( or @ X0 @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl297,zip_derived_cl1962]) ).
thf(zip_derived_cl1773_007,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl427,zip_derived_cl1714]) ).
thf(zip_derived_cl2596,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( implies @ X0 @ ( or @ X0 @ X0 ) ) )
| ( is_a_theorem @ ( equiv @ X0 @ ( or @ X0 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1989,zip_derived_cl1773]) ).
thf(or_1,axiom,
( or_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ).
thf(zip_derived_cl21,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( implies @ X0 @ ( or @ X0 @ X1 ) ) )
| ~ or_1 ),
inference(cnf,[status(esa)],[or_1]) ).
thf(hilbert_or_1,axiom,
or_1 ).
thf(zip_derived_cl71,plain,
or_1,
inference(cnf,[status(esa)],[hilbert_or_1]) ).
thf(zip_derived_cl191,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ X0 @ ( or @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl21,zip_derived_cl71]) ).
thf(zip_derived_cl2619,plain,
! [X0: $i] : ( is_a_theorem @ ( equiv @ X0 @ ( or @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2596,zip_derived_cl191]) ).
thf(zip_derived_cl155_008,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl4,zip_derived_cl77]) ).
thf(zip_derived_cl2908,plain,
! [X0: $i] :
( X0
= ( or @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2619,zip_derived_cl155]) ).
thf(zip_derived_cl3346,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2671,zip_derived_cl2908]) ).
thf(zip_derived_cl3346_009,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2671,zip_derived_cl2908]) ).
thf(op_possibly,axiom,
( op_possibly
=> ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) ) ).
thf(zip_derived_cl130,plain,
! [X0: $i] :
( ( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) )
| ~ op_possibly ),
inference(cnf,[status(esa)],[op_possibly]) ).
thf(km4b_op_possibly,axiom,
op_possibly ).
thf(zip_derived_cl134,plain,
op_possibly,
inference(cnf,[status(esa)],[km4b_op_possibly]) ).
thf(zip_derived_cl165,plain,
! [X0: $i] :
( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl130,zip_derived_cl134]) ).
thf(zip_derived_cl3348,plain,
! [X0: $i] :
( ( possibly @ ( not @ X0 ) )
= ( not @ ( necessarily @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3346,zip_derived_cl165]) ).
thf(zip_derived_cl3346_010,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2671,zip_derived_cl2908]) ).
thf(zip_derived_cl3519,plain,
! [X0: $i] :
( ( necessarily @ X0 )
= ( not @ ( possibly @ ( not @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3348,zip_derived_cl3346]) ).
thf(zip_derived_cl165_011,plain,
! [X0: $i] :
( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl130,zip_derived_cl134]) ).
thf(zip_derived_cl3346_012,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2671,zip_derived_cl2908]) ).
thf(zip_derived_cl3441,plain,
! [X0: $i] :
( ( necessarily @ ( not @ X0 ) )
= ( not @ ( possibly @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl165,zip_derived_cl3346]) ).
thf(zip_derived_cl3716,plain,
! [X0: $i] :
( ( necessarily @ ( necessarily @ X0 ) )
= ( not @ ( possibly @ ( possibly @ ( not @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3519,zip_derived_cl3441]) ).
thf(zip_derived_cl3346_013,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2671,zip_derived_cl2908]) ).
thf(zip_derived_cl5766,plain,
! [X0: $i] :
( ( possibly @ ( possibly @ ( not @ X0 ) ) )
= ( not @ ( necessarily @ ( necessarily @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3716,zip_derived_cl3346]) ).
thf(axiom_4,axiom,
( axiom_4
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ) ).
thf(zip_derived_cl96,plain,
! [X0: $i] :
( ( is_a_theorem @ ( implies @ ( necessarily @ X0 ) @ ( necessarily @ ( necessarily @ X0 ) ) ) )
| ~ axiom_4 ),
inference(cnf,[status(esa)],[axiom_4]) ).
thf(km4b_axiom_4,axiom,
axiom_4 ).
thf(zip_derived_cl138,plain,
axiom_4,
inference(cnf,[status(esa)],[km4b_axiom_4]) ).
thf(zip_derived_cl257,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X0 ) @ ( necessarily @ ( necessarily @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl96,zip_derived_cl138]) ).
thf(zip_derived_cl1773_014,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl427,zip_derived_cl1714]) ).
thf(zip_derived_cl2601,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( necessarily @ X0 ) ) @ ( necessarily @ X0 ) ) )
| ( is_a_theorem @ ( equiv @ ( necessarily @ ( necessarily @ X0 ) ) @ ( necessarily @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl257,zip_derived_cl1773]) ).
thf(axiom_M,axiom,
( axiom_M
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ X ) ) ) ).
thf(zip_derived_cl94,plain,
! [X0: $i] :
( ( is_a_theorem @ ( implies @ ( necessarily @ X0 ) @ X0 ) )
| ~ axiom_M ),
inference(cnf,[status(esa)],[axiom_M]) ).
thf(km4b_axiom_M,axiom,
axiom_M ).
thf(zip_derived_cl137,plain,
axiom_M,
inference(cnf,[status(esa)],[km4b_axiom_M]) ).
thf(zip_derived_cl158,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X0 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl137]) ).
thf(zip_derived_cl2620,plain,
! [X0: $i] : ( is_a_theorem @ ( equiv @ ( necessarily @ ( necessarily @ X0 ) ) @ ( necessarily @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2601,zip_derived_cl158]) ).
thf(zip_derived_cl155_015,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl4,zip_derived_cl77]) ).
thf(zip_derived_cl6343,plain,
! [X0: $i] :
( ( necessarily @ ( necessarily @ X0 ) )
= ( necessarily @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl2620,zip_derived_cl155]) ).
thf(zip_derived_cl3348_016,plain,
! [X0: $i] :
( ( possibly @ ( not @ X0 ) )
= ( not @ ( necessarily @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3346,zip_derived_cl165]) ).
thf(zip_derived_cl6373,plain,
! [X0: $i] :
( ( possibly @ ( possibly @ ( not @ X0 ) ) )
= ( possibly @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5766,zip_derived_cl6343,zip_derived_cl3348]) ).
thf(zip_derived_cl6490,plain,
! [X0: $i] :
( ( possibly @ ( possibly @ X0 ) )
= ( possibly @ ( not @ ( not @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3346,zip_derived_cl6373]) ).
thf(zip_derived_cl3346_017,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2671,zip_derived_cl2908]) ).
thf(zip_derived_cl6497,plain,
! [X0: $i] :
( ( possibly @ ( possibly @ X0 ) )
= ( possibly @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl6490,zip_derived_cl3346]) ).
thf(zip_derived_cl2629_018,plain,
! [X0: $i] :
( ( and @ X0 @ X0 )
= X0 ),
inference('sup-',[status(thm)],[zip_derived_cl2616,zip_derived_cl155]) ).
thf(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) ) ).
thf(zip_derived_cl133,plain,
! [X0: $i,X1: $i] :
( ( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) )
| ~ op_strict_equiv ),
inference(cnf,[status(esa)],[op_strict_equiv]) ).
thf(s1_0_op_strict_equiv,axiom,
op_strict_equiv ).
thf(zip_derived_cl145,plain,
op_strict_equiv,
inference(cnf,[status(esa)],[s1_0_op_strict_equiv]) ).
thf(zip_derived_cl435,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl133,zip_derived_cl145]) ).
thf(zip_derived_cl2675,plain,
! [X0: $i] :
( ( strict_equiv @ X0 @ X0 )
= ( strict_implies @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl2629,zip_derived_cl435]) ).
thf(zip_derived_cl435_019,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl133,zip_derived_cl145]) ).
thf(zip_derived_cl307_020,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ ( and @ X0 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl304,zip_derived_cl208]) ).
thf(zip_derived_cl147_021,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl63]) ).
thf(zip_derived_cl481,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ X0 )
| ( is_a_theorem @ ( and @ X0 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl307,zip_derived_cl147]) ).
thf(zip_derived_cl495,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_equiv @ X0 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl435,zip_derived_cl481]) ).
thf(zip_derived_cl297_022,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl168,zip_derived_cl208]) ).
thf(op_strict_implies,axiom,
( op_strict_implies
=> ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) ) ).
thf(zip_derived_cl132,plain,
! [X0: $i,X1: $i] :
( ( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) )
| ~ op_strict_implies ),
inference(cnf,[status(esa)],[op_strict_implies]) ).
thf(s1_0_op_strict_implies,axiom,
op_strict_implies ).
thf(zip_derived_cl143,plain,
op_strict_implies,
inference(cnf,[status(esa)],[s1_0_op_strict_implies]) ).
thf(zip_derived_cl203,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl143]) ).
thf(necessitation,axiom,
( necessitation
<=> ! [X: $i] :
( ( is_a_theorem @ X )
=> ( is_a_theorem @ ( necessarily @ X ) ) ) ) ).
thf(zip_derived_cl78,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ X0 )
| ( is_a_theorem @ ( necessarily @ X0 ) )
| ~ necessitation ),
inference(cnf,[status(esa)],[necessitation]) ).
thf(km4b_necessitation,axiom,
necessitation ).
thf(zip_derived_cl135,plain,
necessitation,
inference(cnf,[status(esa)],[km4b_necessitation]) ).
thf(zip_derived_cl156,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ X0 )
| ( is_a_theorem @ ( necessarily @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl78,zip_derived_cl135]) ).
thf(zip_derived_cl204,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl203,zip_derived_cl156]) ).
thf(zip_derived_cl309,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl297,zip_derived_cl204]) ).
thf(zip_derived_cl497,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl495,zip_derived_cl309]) ).
thf(zip_derived_cl6522,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl227,zip_derived_cl6497,zip_derived_cl2675,zip_derived_cl497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fMmRZiZjcY true
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 15:50:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Running portfolio for 300 s
% 0.10/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Number of cores: 8
% 0.10/0.37 % Python version: Python 3.12.3
% 0.10/0.37 % Running in FO mode
% 0.37/0.58 % Total configuration time : 435
% 0.37/0.58 % Estimated wc time : 1092
% 0.37/0.58 % Estimated cpu time (7 cpus) : 156.0
% 0.41/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.41/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.41/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.41/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.41/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.41/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.41/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.41/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.41/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 50s
% 0.41/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 50s
% 11.43/2.29 % Solved by fo/fo5.sh.
% 11.43/2.29 % done 1465 iterations in 1.531s
% 11.43/2.29 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 11.43/2.29 % SZS output start Refutation
% See solution above
% 11.43/2.29
% 11.43/2.29
% 11.43/2.29 % Terminating...
% 3.06/2.32 % Runner terminated.
% 3.06/2.34 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------