%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ox0jeUXrM0 true
% Computer : n001.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 01:36:13 PM UTC 2026
% Result : Theorem 161.43s 23.88s
% Output : Refutation 161.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 215 ( 148 unt; 0 typ; 0 def)
% Number of atoms : 307 ( 97 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1267 ( 75 ~; 72 |; 2 &;1100 @)
% ( 10 <=>; 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 : 27 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 303 ( 0 ^; 303 !; 0 ?; 303 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(axiom_m6_type,type,
axiom_m6: $o ).
thf(necessarily_type,type,
necessarily: $i > $i ).
thf(axiom_m4_type,type,
axiom_m4: $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(op_possibly_type,type,
op_possibly: $o ).
thf(and_type,type,
and: $i > $i > $i ).
thf(adjunction_type,type,
adjunction: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(axiom_m5_type,type,
axiom_m5: $o ).
thf(possibly_type,type,
possibly: $i > $i ).
thf(axiom_m9_type,type,
axiom_m9: $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(axiom_m1_type,type,
axiom_m1: $o ).
thf(modus_ponens_strict_implies_type,type,
modus_ponens_strict_implies: $o ).
thf(op_strict_implies_type,type,
op_strict_implies: $o ).
thf(axiom_m2_type,type,
axiom_m2: $o ).
thf(strict_implies_type,type,
strict_implies: $i > $i > $i ).
thf(axiom_4_type,type,
axiom_4: $o ).
thf(strict_equiv_type,type,
strict_equiv: $i > $i > $i ).
thf(op_or_type,type,
op_or: $o ).
thf(substitution_strict_equiv_type,type,
substitution_strict_equiv: $o ).
thf(op_strict_equiv_type,type,
op_strict_equiv: $o ).
thf(not_type,type,
not: $i > $i ).
thf(sk__10_type,type,
sk__10: $i ).
thf(axiom_4,axiom,
( axiom_4
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ) ).
thf(zip_derived_cl24,plain,
( axiom_4
| ~ ( is_a_theorem @ ( implies @ ( necessarily @ sk__10 ) @ ( necessarily @ ( necessarily @ sk__10 ) ) ) ) ),
inference(cnf,[status(esa)],[axiom_4]) ).
thf(km4b_axiom_4,conjecture,
axiom_4 ).
thf(zf_stmt_0,negated_conjecture,
~ axiom_4,
inference('cnf.neg',[status(esa)],[km4b_axiom_4]) ).
thf(zip_derived_cl83,plain,
~ axiom_4,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl124,plain,
~ ( is_a_theorem @ ( implies @ ( necessarily @ sk__10 ) @ ( necessarily @ ( necessarily @ sk__10 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl24,zip_derived_cl83]) ).
thf(axiom_m4,axiom,
( axiom_m4
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( and @ X @ X ) ) ) ) ).
thf(zip_derived_cl43,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_implies @ X0 @ ( and @ X0 @ X0 ) ) )
| ~ axiom_m4 ),
inference(cnf,[status(esa)],[axiom_m4]) ).
thf(s1_0_axiom_m4,axiom,
axiom_m4 ).
thf(zip_derived_cl73,plain,
axiom_m4,
inference(cnf,[status(esa)],[s1_0_axiom_m4]) ).
thf(zip_derived_cl120,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ ( and @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl43,zip_derived_cl73]) ).
thf(zip_derived_cl120_001,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ ( and @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl43,zip_derived_cl73]) ).
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_cl60,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_cl66,plain,
op_strict_equiv,
inference(cnf,[status(esa)],[s1_0_op_strict_equiv]) ).
thf(zip_derived_cl178,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl66]) ).
thf(adjunction,axiom,
( adjunction
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ Y ) )
=> ( is_a_theorem @ ( and @ X @ Y ) ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( and @ X0 @ X1 ) )
| ~ ( is_a_theorem @ X1 )
| ~ ( is_a_theorem @ X0 )
| ~ adjunction ),
inference(cnf,[status(esa)],[adjunction]) ).
thf(s1_0_adjunction,axiom,
adjunction ).
thf(zip_derived_cl69,plain,
adjunction,
inference(cnf,[status(esa)],[s1_0_adjunction]) ).
thf(zip_derived_cl140,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( and @ X0 @ X1 ) )
| ~ ( is_a_theorem @ X1 )
| ~ ( is_a_theorem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl12,zip_derived_cl69]) ).
thf(zip_derived_cl181,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl140]) ).
thf(zip_derived_cl212,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_equiv @ ( and @ X0 @ X0 ) @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X0 ) @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl120,zip_derived_cl181]) ).
thf(axiom_m2,axiom,
( axiom_m2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ X ) ) ) ).
thf(zip_derived_cl39,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ X0 ) )
| ~ axiom_m2 ),
inference(cnf,[status(esa)],[axiom_m2]) ).
thf(s1_0_axiom_m2,axiom,
axiom_m2 ).
thf(zip_derived_cl71,plain,
axiom_m2,
inference(cnf,[status(esa)],[s1_0_axiom_m2]) ).
thf(zip_derived_cl117,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl39,zip_derived_cl71]) ).
thf(zip_derived_cl217,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ ( and @ X0 @ X0 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl212,zip_derived_cl117]) ).
thf(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( strict_equiv @ X @ Y ) )
=> ( X = Y ) ) ) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 )
| ~ substitution_strict_equiv ),
inference(cnf,[status(esa)],[substitution_strict_equiv]) ).
thf(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv ).
thf(zip_derived_cl68,plain,
substitution_strict_equiv,
inference(cnf,[status(esa)],[s1_0_substitution_strict_equiv]) ).
thf(zip_derived_cl102,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl68]) ).
thf(zip_derived_cl220,plain,
! [X0: $i] :
( ( and @ X0 @ X0 )
= X0 ),
inference('s_sup-',[status(thm)],[zip_derived_cl217,zip_derived_cl102]) ).
thf(zip_derived_cl225,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl220]) ).
thf(axiom_m1,axiom,
( axiom_m1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ ( and @ Y @ X ) ) ) ) ).
thf(zip_derived_cl37,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) )
| ~ axiom_m1 ),
inference(cnf,[status(esa)],[axiom_m1]) ).
thf(s1_0_axiom_m1,axiom,
axiom_m1 ).
thf(zip_derived_cl70,plain,
axiom_m1,
inference(cnf,[status(esa)],[s1_0_axiom_m1]) ).
thf(zip_derived_cl159,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl70]) ).
thf(zip_derived_cl181_002,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl140]) ).
thf(zip_derived_cl215,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ ( and @ X1 @ X0 ) @ ( and @ X0 @ X1 ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ ( and @ X1 @ X0 ) @ ( and @ X0 @ X1 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl159,zip_derived_cl181]) ).
thf(zip_derived_cl159_003,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl70]) ).
thf(zip_derived_cl218,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_equiv @ ( and @ X1 @ X0 ) @ ( and @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl215,zip_derived_cl159]) ).
thf(zip_derived_cl102_004,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl68]) ).
thf(zip_derived_cl689,plain,
! [X0: $i,X1: $i] :
( ( and @ X0 @ X1 )
= ( and @ X1 @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl218,zip_derived_cl102]) ).
thf(op_implies_and,axiom,
( op_implies_and
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i] :
( ( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) )
| ~ op_implies_and ),
inference(cnf,[status(esa)],[op_implies_and]) ).
thf(hilbert_op_implies_and,axiom,
op_implies_and ).
thf(zip_derived_cl80,plain,
op_implies_and,
inference(cnf,[status(esa)],[hilbert_op_implies_and]) ).
thf(zip_derived_cl94,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl717,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ ( not @ X1 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl689,zip_derived_cl94]) ).
thf(zip_derived_cl94_005,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl830,plain,
! [X0: $i,X1: $i] :
( ( implies @ ( not @ X0 ) @ X1 )
= ( implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl717,zip_derived_cl94]) ).
thf(zip_derived_cl94_006,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(op_or,axiom,
( op_or
=> ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i] :
( ( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) )
| ~ op_or ),
inference(cnf,[status(esa)],[op_or]) ).
thf(s1_0_op_or,axiom,
op_or ).
thf(zip_derived_cl62,plain,
op_or,
inference(cnf,[status(esa)],[s1_0_op_or]) ).
thf(zip_derived_cl84,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl62]) ).
thf(zip_derived_cl98,plain,
! [X0: $i,X1: $i] :
( ( or @ X1 @ X0 )
= ( implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl84]) ).
thf(zip_derived_cl98_007,plain,
! [X0: $i,X1: $i] :
( ( or @ X1 @ X0 )
= ( implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl84]) ).
thf(zip_derived_cl853,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( or @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl830,zip_derived_cl98,zip_derived_cl98]) ).
thf(zip_derived_cl98_008,plain,
! [X0: $i,X1: $i] :
( ( or @ X1 @ X0 )
= ( implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl84]) ).
thf(op_strict_implies,axiom,
( op_strict_implies
=> ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) ) ).
thf(zip_derived_cl59,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_cl64,plain,
op_strict_implies,
inference(cnf,[status(esa)],[s1_0_op_strict_implies]) ).
thf(zip_derived_cl116,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl135,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X1 ) @ X0 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl98,zip_derived_cl116]) ).
thf(zip_derived_cl854,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl853,zip_derived_cl135]) ).
thf(zip_derived_cl135_009,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X1 ) @ X0 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl98,zip_derived_cl116]) ).
thf(zip_derived_cl941,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl854,zip_derived_cl135]) ).
thf(zip_derived_cl181_010,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl140]) ).
thf(zip_derived_cl957,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ ( not @ X0 ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ ( not @ X1 ) @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ ( not @ X0 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl941,zip_derived_cl181]) ).
thf(zip_derived_cl57475,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_equiv @ X0 @ ( not @ ( not @ X0 ) ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ ( not @ ( not @ X0 ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl225,zip_derived_cl957]) ).
thf(zip_derived_cl220_011,plain,
! [X0: $i] :
( ( and @ X0 @ X0 )
= X0 ),
inference('s_sup-',[status(thm)],[zip_derived_cl217,zip_derived_cl102]) ).
thf(zip_derived_cl84_012,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl62]) ).
thf(zip_derived_cl235,plain,
! [X0: $i] :
( ( or @ X0 @ X0 )
= ( not @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl220,zip_derived_cl84]) ).
thf(zip_derived_cl854_013,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl853,zip_derived_cl135]) ).
thf(zip_derived_cl235_014,plain,
! [X0: $i] :
( ( or @ X0 @ X0 )
= ( not @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl220,zip_derived_cl84]) ).
thf(zip_derived_cl98_015,plain,
! [X0: $i,X1: $i] :
( ( or @ X1 @ X0 )
= ( implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl84]) ).
thf(zip_derived_cl247,plain,
! [X0: $i,X1: $i] :
( ( or @ ( not @ X0 ) @ X1 )
= ( implies @ ( or @ X0 @ X0 ) @ X1 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl235,zip_derived_cl98]) ).
thf(zip_derived_cl116_016,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl369,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X1 @ X1 ) @ X0 )
= ( necessarily @ ( or @ ( not @ X1 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl247,zip_derived_cl116]) ).
thf(zip_derived_cl942,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X0 @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl854,zip_derived_cl369]) ).
thf(zip_derived_cl225_017,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl220]) ).
thf(zip_derived_cl1058,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl942,zip_derived_cl225]) ).
thf(zip_derived_cl1058_018,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl942,zip_derived_cl225]) ).
thf(zip_derived_cl140_019,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( and @ X0 @ X1 ) )
| ~ ( is_a_theorem @ X1 )
| ~ ( is_a_theorem @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl12,zip_derived_cl69]) ).
thf(axiom_m5,axiom,
( axiom_m5
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ Z ) ) @ ( strict_implies @ X @ Z ) ) ) ) ).
thf(zip_derived_cl45,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X2 ) ) @ ( strict_implies @ X0 @ X2 ) ) )
| ~ axiom_m5 ),
inference(cnf,[status(esa)],[axiom_m5]) ).
thf(s1_0_axiom_m5,axiom,
axiom_m5 ).
thf(zip_derived_cl74,plain,
axiom_m5,
inference(cnf,[status(esa)],[s1_0_axiom_m5]) ).
thf(zip_derived_cl655,plain,
! [X0: $i,X1: $i,X2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X2 ) ) @ ( strict_implies @ X0 @ X2 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl45,zip_derived_cl74]) ).
thf(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ ( strict_implies @ X @ Y ) ) )
=> ( is_a_theorem @ Y ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 )
| ~ modus_ponens_strict_implies ),
inference(cnf,[status(esa)],[modus_ponens_strict_implies]) ).
thf(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies ).
thf(zip_derived_cl67,plain,
modus_ponens_strict_implies,
inference(cnf,[status(esa)],[s1_0_modus_ponens_strict_implies]) ).
thf(zip_derived_cl126,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl67]) ).
thf(zip_derived_cl656,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( and @ ( strict_implies @ X1 @ X2 ) @ ( strict_implies @ X2 @ X0 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl655,zip_derived_cl126]) ).
thf(zip_derived_cl9050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ X2 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ( is_a_theorem @ ( strict_implies @ X2 @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl140,zip_derived_cl656]) ).
thf(zip_derived_cl9129,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ X1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1058,zip_derived_cl9050]) ).
thf(zip_derived_cl9242,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( or @ ( or @ X0 @ X0 ) @ ( or @ X0 @ X0 ) ) @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1058,zip_derived_cl9129]) ).
thf(zip_derived_cl235_020,plain,
! [X0: $i] :
( ( or @ X0 @ X0 )
= ( not @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl220,zip_derived_cl84]) ).
thf(zip_derived_cl941_021,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl854,zip_derived_cl135]) ).
thf(zip_derived_cl9290,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X0 ) @ ( not @ ( or @ X0 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9242,zip_derived_cl235,zip_derived_cl941]) ).
thf(zip_derived_cl181_022,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl140]) ).
thf(zip_derived_cl11707,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_equiv @ ( not @ ( or @ X0 @ X0 ) ) @ ( not @ X0 ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ ( not @ ( or @ X0 @ X0 ) ) @ ( not @ X0 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9290,zip_derived_cl181]) ).
thf(zip_derived_cl178_023,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl66]) ).
thf(zip_derived_cl159_024,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl70]) ).
thf(zip_derived_cl182,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl159]) ).
thf(zip_derived_cl178_025,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl60,zip_derived_cl66]) ).
thf(zip_derived_cl187,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl182,zip_derived_cl178]) ).
thf(zip_derived_cl181_026,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl140]) ).
thf(zip_derived_cl685,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl187,zip_derived_cl181]) ).
thf(zip_derived_cl187_027,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl182,zip_derived_cl178]) ).
thf(zip_derived_cl688,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_equiv @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl685,zip_derived_cl187]) ).
thf(zip_derived_cl102_028,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl68]) ).
thf(zip_derived_cl5854,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( strict_equiv @ X1 @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl688,zip_derived_cl102]) ).
thf(zip_derived_cl941_029,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl854,zip_derived_cl135]) ).
thf(zip_derived_cl369_030,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X1 @ X1 ) @ X0 )
= ( necessarily @ ( or @ ( not @ X1 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl247,zip_derived_cl116]) ).
thf(zip_derived_cl225_031,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl220]) ).
thf(zip_derived_cl391,plain,
! [X0: $i] : ( is_a_theorem @ ( necessarily @ ( or @ ( not @ X0 ) @ ( or @ X0 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl369,zip_derived_cl225]) ).
thf(zip_derived_cl135_032,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X1 ) @ X0 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl98,zip_derived_cl116]) ).
thf(zip_derived_cl402,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ X0 ) ) @ ( or @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl391,zip_derived_cl135]) ).
thf(zip_derived_cl11794,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ ( not @ X0 ) @ ( not @ ( or @ X0 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl11707,zip_derived_cl5854,zip_derived_cl941,zip_derived_cl402]) ).
thf(zip_derived_cl102_033,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl68]) ).
thf(zip_derived_cl22448,plain,
! [X0: $i] :
( ( not @ X0 )
= ( not @ ( or @ X0 @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11794,zip_derived_cl102]) ).
thf(zip_derived_cl22810,plain,
! [X0: $i] :
( ( not @ X0 )
= ( not @ ( not @ ( not @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl235,zip_derived_cl22448]) ).
thf(zip_derived_cl94_034,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl23274,plain,
! [X0: $i,X1: $i] :
( ( implies @ X1 @ ( not @ ( not @ X0 ) ) )
= ( not @ ( and @ X1 @ ( not @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl22810,zip_derived_cl94]) ).
thf(zip_derived_cl94_035,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl23434,plain,
! [X0: $i,X1: $i] :
( ( implies @ X1 @ ( not @ ( not @ X0 ) ) )
= ( implies @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl23274,zip_derived_cl94]) ).
thf(zip_derived_cl116_036,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl33155,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X1 @ ( not @ ( not @ X0 ) ) )
= ( necessarily @ ( implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl23434,zip_derived_cl116]) ).
thf(zip_derived_cl116_037,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl33243,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X1 @ ( not @ ( not @ X0 ) ) )
= ( strict_implies @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl33155,zip_derived_cl116]) ).
thf(zip_derived_cl225_038,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl220]) ).
thf(zip_derived_cl57533,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ ( not @ ( not @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57475,zip_derived_cl33243,zip_derived_cl225]) ).
thf(zip_derived_cl102_039,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl68]) ).
thf(zip_derived_cl57544,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl57533,zip_derived_cl102]) ).
thf(op_possibly,axiom,
( op_possibly
=> ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) ) ).
thf(zip_derived_cl57,plain,
! [X0: $i] :
( ( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) )
| ~ op_possibly ),
inference(cnf,[status(esa)],[op_possibly]) ).
thf(s1_0_op_possibly,axiom,
op_possibly ).
thf(zip_derived_cl61,plain,
op_possibly,
inference(cnf,[status(esa)],[s1_0_op_possibly]) ).
thf(zip_derived_cl104,plain,
! [X0: $i] :
( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl61]) ).
thf(zip_derived_cl57709,plain,
! [X0: $i] :
( ( possibly @ ( not @ X0 ) )
= ( not @ ( necessarily @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl57544,zip_derived_cl104]) ).
thf(axiom_m9,axiom,
( axiom_m9
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X ) ) @ ( possibly @ X ) ) ) ) ).
thf(zip_derived_cl53,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X0 ) ) @ ( possibly @ X0 ) ) )
| ~ axiom_m9 ),
inference(cnf,[status(esa)],[axiom_m9]) ).
thf(s1_0_m6s3m9b_axiom_m9,axiom,
axiom_m9 ).
thf(zip_derived_cl77,plain,
axiom_m9,
inference(cnf,[status(esa)],[s1_0_m6s3m9b_axiom_m9]) ).
thf(zip_derived_cl143,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X0 ) ) @ ( possibly @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl77]) ).
thf(zip_derived_cl181_040,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl178,zip_derived_cl140]) ).
thf(zip_derived_cl216,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_equiv @ ( possibly @ X0 ) @ ( possibly @ ( possibly @ X0 ) ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ X0 ) @ ( possibly @ ( possibly @ X0 ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl181]) ).
thf(axiom_m6,axiom,
( axiom_m6
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( possibly @ X ) ) ) ) ).
thf(zip_derived_cl47,plain,
! [X0: $i] :
( ( is_a_theorem @ ( strict_implies @ X0 @ ( possibly @ X0 ) ) )
| ~ axiom_m6 ),
inference(cnf,[status(esa)],[axiom_m6]) ).
thf(s1_0_m6s3m9b_axiom_m6,axiom,
axiom_m6 ).
thf(zip_derived_cl75,plain,
axiom_m6,
inference(cnf,[status(esa)],[s1_0_m6s3m9b_axiom_m6]) ).
thf(zip_derived_cl113,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ ( possibly @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl75]) ).
thf(zip_derived_cl219,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ ( possibly @ X0 ) @ ( possibly @ ( possibly @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl216,zip_derived_cl113]) ).
thf(zip_derived_cl102_041,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl16,zip_derived_cl68]) ).
thf(zip_derived_cl349,plain,
! [X0: $i] :
( ( possibly @ X0 )
= ( possibly @ ( possibly @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl219,zip_derived_cl102]) ).
thf(zip_derived_cl59032,plain,
! [X0: $i] :
( ( not @ ( necessarily @ X0 ) )
= ( possibly @ ( not @ ( necessarily @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl57709,zip_derived_cl349]) ).
thf(zip_derived_cl104_042,plain,
! [X0: $i] :
( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl61]) ).
thf(zip_derived_cl57544_043,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl57533,zip_derived_cl102]) ).
thf(zip_derived_cl58019,plain,
! [X0: $i] :
( ( necessarily @ ( not @ X0 ) )
= ( not @ ( possibly @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl57544]) ).
thf(zip_derived_cl61099,plain,
! [X0: $i] :
( ( necessarily @ ( not @ ( not @ ( necessarily @ X0 ) ) ) )
= ( not @ ( not @ ( necessarily @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl59032,zip_derived_cl58019]) ).
thf(zip_derived_cl57544_044,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl57533,zip_derived_cl102]) ).
thf(zip_derived_cl57544_045,plain,
! [X0: $i] :
( X0
= ( not @ ( not @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl57533,zip_derived_cl102]) ).
thf(zip_derived_cl61139,plain,
! [X0: $i] :
( ( necessarily @ ( necessarily @ X0 ) )
= ( necessarily @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl61099,zip_derived_cl57544,zip_derived_cl57544]) ).
thf(zip_derived_cl225_046,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl220]) ).
thf(zip_derived_cl225_047,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl220]) ).
thf(zip_derived_cl22448_048,plain,
! [X0: $i] :
( ( not @ X0 )
= ( not @ ( or @ X0 @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11794,zip_derived_cl102]) ).
thf(zip_derived_cl94_049,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl22748,plain,
! [X0: $i,X1: $i] :
( ( implies @ X1 @ ( or @ X0 @ X0 ) )
= ( not @ ( and @ X1 @ ( not @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl22448,zip_derived_cl94]) ).
thf(zip_derived_cl94_050,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl22903,plain,
! [X0: $i,X1: $i] :
( ( implies @ X1 @ ( or @ X0 @ X0 ) )
= ( implies @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl22748,zip_derived_cl94]) ).
thf(zip_derived_cl116_051,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl29610,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X1 @ ( or @ X0 @ X0 ) )
= ( necessarily @ ( implies @ X1 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl22903,zip_derived_cl116]) ).
thf(zip_derived_cl116_052,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl29692,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X1 @ ( or @ X0 @ X0 ) )
= ( strict_implies @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl29610,zip_derived_cl116]) ).
thf(zip_derived_cl126_053,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl67]) ).
thf(zip_derived_cl34288,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( or @ X0 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl29692,zip_derived_cl126]) ).
thf(zip_derived_cl37758,plain,
! [X0: $i] :
( ( is_a_theorem @ ( or @ X0 @ X0 ) )
| ~ ( is_a_theorem @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl225,zip_derived_cl34288]) ).
thf(zip_derived_cl853_054,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( or @ X1 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl830,zip_derived_cl98,zip_derived_cl98]) ).
thf(zip_derived_cl369_055,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X1 @ X1 ) @ X0 )
= ( necessarily @ ( or @ ( not @ X1 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl247,zip_derived_cl116]) ).
thf(zip_derived_cl862,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X0 @ X0 ) @ X1 )
= ( necessarily @ ( or @ X1 @ ( not @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl853,zip_derived_cl369]) ).
thf(zip_derived_cl369_056,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X1 @ X1 ) @ X0 )
= ( necessarily @ ( or @ ( not @ X1 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl247,zip_derived_cl116]) ).
thf(zip_derived_cl1002,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X0 @ X0 ) @ ( not @ X1 ) )
= ( strict_implies @ ( or @ X1 @ X1 ) @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl862,zip_derived_cl369]) ).
thf(zip_derived_cl1058_057,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl942,zip_derived_cl225]) ).
thf(zip_derived_cl1920,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ ( not @ ( not @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1002,zip_derived_cl1058]) ).
thf(zip_derived_cl126_058,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl67]) ).
thf(zip_derived_cl7891,plain,
! [X0: $i] :
( ( is_a_theorem @ ( not @ ( not @ X0 ) ) )
| ~ ( is_a_theorem @ ( or @ X0 @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1920,zip_derived_cl126]) ).
thf(zip_derived_cl38138,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ X0 )
| ( is_a_theorem @ ( not @ ( not @ X0 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl37758,zip_derived_cl7891]) ).
thf(zip_derived_cl94_059,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl104_060,plain,
! [X0: $i] :
( ( possibly @ X0 )
= ( not @ ( necessarily @ ( not @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl61]) ).
thf(zip_derived_cl109,plain,
! [X0: $i,X1: $i] :
( ( possibly @ ( and @ X1 @ ( not @ X0 ) ) )
= ( not @ ( necessarily @ ( implies @ X1 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl104]) ).
thf(zip_derived_cl116_061,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl64]) ).
thf(zip_derived_cl576,plain,
! [X0: $i,X1: $i] :
( ( possibly @ ( and @ X1 @ ( not @ X0 ) ) )
= ( not @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl116]) ).
thf(zip_derived_cl942_062,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( or @ X0 @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl854,zip_derived_cl369]) ).
thf(zip_derived_cl113_063,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ ( possibly @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl75]) ).
thf(zip_derived_cl9129_064,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) )
| ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ X1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1058,zip_derived_cl9050]) ).
thf(zip_derived_cl9241,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( or @ X0 @ X0 ) @ ( possibly @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl113,zip_derived_cl9129]) ).
thf(zip_derived_cl9456,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ ( possibly @ X0 ) ) @ ( not @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl942,zip_derived_cl9241]) ).
thf(zip_derived_cl126_065,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ X0 )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl67]) ).
thf(zip_derived_cl9873,plain,
! [X0: $i] :
( ( is_a_theorem @ ( not @ X0 ) )
| ~ ( is_a_theorem @ ( not @ ( possibly @ X0 ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl9456,zip_derived_cl126]) ).
thf(zip_derived_cl9937,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( not @ ( and @ X1 @ ( not @ X0 ) ) ) )
| ~ ( is_a_theorem @ ( not @ ( not @ ( strict_implies @ X1 @ X0 ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl576,zip_derived_cl9873]) ).
thf(zip_derived_cl94_066,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl80]) ).
thf(zip_derived_cl9945,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( not @ ( not @ ( strict_implies @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9937,zip_derived_cl94]) ).
thf(zip_derived_cl38230,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ( is_a_theorem @ ( implies @ X1 @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl38138,zip_derived_cl9945]) ).
thf(zip_derived_cl39397,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl225,zip_derived_cl38230]) ).
thf(zip_derived_cl61147,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl61139,zip_derived_cl39397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ox0jeUXrM0 true
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 04:31:16 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Running portfolio for 300 s
% 0.09/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.12.3
% 0.13/0.36 % 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
% 0.41/0.65 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.41/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.41/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.41/0.71 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.41/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.41/0.72 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.41/0.72 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.41/0.76 % /export/starexec/sandbox/solver/bin/fo/fo17_bce.sh running for 50s
% 0.41/0.76 % /export/starexec/sandbox/solver/bin/fo/fo8.sh running for 50s
% 0.41/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 161.43/23.88 % Solved by fo/fo8.sh.
% 161.43/23.88 % done 4174 iterations in 23.074s
% 161.43/23.88 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 161.43/23.88 % SZS output start Refutation
% See solution above
% 161.43/23.89
% 161.43/23.89
% 161.43/23.89 % Terminating...
% 0.46/23.95 % Runner terminated.
% 0.46/23.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------