TSTP Solution File: LCL550+1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : LCL550+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4wifnykuqi true
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:00:10 EDT 2023
% Result : Theorem 19.06s 3.38s
% Output : Refutation 19.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 53
% Syntax : Number of formulae : 229 ( 135 unt; 25 typ; 0 def)
% Number of atoms : 303 ( 77 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1259 ( 80 ~; 77 |; 3 &;1080 @)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 284 ( 0 ^; 284 !; 0 ?; 284 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__type,type,
sk_: $i ).
thf(modus_ponens_strict_implies_type,type,
modus_ponens_strict_implies: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(axiom_m5_type,type,
axiom_m5: $o ).
thf(and_type,type,
and: $i > $i > $i ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(necessarily_type,type,
necessarily: $i > $i ).
thf(axiom_m4_type,type,
axiom_m4: $o ).
thf(axiom_m1_type,type,
axiom_m1: $o ).
thf(op_equiv_type,type,
op_equiv: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(axiom_m2_type,type,
axiom_m2: $o ).
thf(adjunction_type,type,
adjunction: $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(equiv_type,type,
equiv: $i > $i > $i ).
thf(modus_ponens_type,type,
modus_ponens: $o ).
thf(substitution_strict_equiv_type,type,
substitution_strict_equiv: $o ).
thf(op_strict_equiv_type,type,
op_strict_equiv: $o ).
thf(sk__1_type,type,
sk__1: $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(substitution_of_equivalents_type,type,
substitution_of_equivalents: $o ).
thf(not_type,type,
not: $i > $i ).
thf(strict_equiv_type,type,
strict_equiv: $i > $i > $i ).
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_cl3,plain,
( modus_ponens
| ~ ( is_a_theorem @ sk__1 ) ),
inference(cnf,[status(esa)],[modus_ponens]) ).
thf(hilbert_modus_ponens,conjecture,
modus_ponens ).
thf(zf_stmt_0,negated_conjecture,
~ modus_ponens,
inference('cnf.neg',[status(esa)],[hilbert_modus_ponens]) ).
thf(zip_derived_cl134,plain,
~ modus_ponens,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl136,plain,
~ ( is_a_theorem @ sk__1 ),
inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl134]) ).
thf(axiom_m4,axiom,
( axiom_m4
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( and @ X @ X ) ) ) ) ).
thf(zip_derived_cl98,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_cl128,plain,
axiom_m4,
inference(cnf,[status(esa)],[s1_0_axiom_m4]) ).
thf(zip_derived_cl159,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ X0 @ ( and @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl98,zip_derived_cl128]) ).
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_cl115,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_cl121,plain,
op_strict_equiv,
inference(cnf,[status(esa)],[s1_0_op_strict_equiv]) ).
thf(zip_derived_cl271,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl115,zip_derived_cl121]) ).
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_cl67,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_cl124,plain,
adjunction,
inference(cnf,[status(esa)],[s1_0_adjunction]) ).
thf(zip_derived_cl163,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_cl67,zip_derived_cl124]) ).
thf(zip_derived_cl274,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl271,zip_derived_cl163]) ).
thf(zip_derived_cl313,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X0 ) @ X0 ) )
| ( is_a_theorem @ ( strict_equiv @ X0 @ ( and @ X0 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl159,zip_derived_cl274]) ).
thf(axiom_m2,axiom,
( axiom_m2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ X ) ) ) ).
thf(zip_derived_cl94,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_cl126,plain,
axiom_m2,
inference(cnf,[status(esa)],[s1_0_axiom_m2]) ).
thf(zip_derived_cl161,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl126]) ).
thf(zip_derived_cl320,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ ( and @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl313,zip_derived_cl161]) ).
thf(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( strict_equiv @ X @ Y ) )
=> ( X = Y ) ) ) ).
thf(zip_derived_cl71,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_cl123,plain,
substitution_strict_equiv,
inference(cnf,[status(esa)],[s1_0_substitution_strict_equiv]) ).
thf(zip_derived_cl147,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl71,zip_derived_cl123]) ).
thf(zip_derived_cl324,plain,
! [X0: $i] :
( X0
= ( and @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl320,zip_derived_cl147]) ).
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(s1_0_op_or,axiom,
op_or ).
thf(zip_derived_cl117,plain,
op_or,
inference(cnf,[status(esa)],[s1_0_op_or]) ).
thf(zip_derived_cl211,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl117]) ).
thf(zip_derived_cl347,plain,
! [X0: $i] :
( ( or @ X0 @ X0 )
= ( not @ ( not @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl324,zip_derived_cl211]) ).
thf(zip_derived_cl211_001,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl117]) ).
thf(op_implies_and,axiom,
( op_implies_and
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) ) ).
thf(zip_derived_cl57,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_cl131,plain,
op_implies_and,
inference(cnf,[status(esa)],[hilbert_op_implies_and]) ).
thf(zip_derived_cl167,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(zip_derived_cl219,plain,
! [X0: $i,X1: $i] :
( ( implies @ ( not @ X1 ) @ X0 )
= ( or @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl211,zip_derived_cl167]) ).
thf(op_strict_implies,axiom,
( op_strict_implies
=> ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) ) ).
thf(zip_derived_cl114,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_cl119,plain,
op_strict_implies,
inference(cnf,[status(esa)],[s1_0_op_strict_implies]) ).
thf(zip_derived_cl164,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl119]) ).
thf(zip_derived_cl246,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X1 ) @ X0 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl219,zip_derived_cl164]) ).
thf(zip_derived_cl419,plain,
! [X0: $i] :
( ( strict_implies @ ( not @ X0 ) @ X0 )
= ( necessarily @ ( not @ ( not @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl347,zip_derived_cl246]) ).
thf(zip_derived_cl2,plain,
( modus_ponens
| ( is_a_theorem @ ( implies @ sk_ @ sk__1 ) ) ),
inference(cnf,[status(esa)],[modus_ponens]) ).
thf(zip_derived_cl134_002,plain,
~ modus_ponens,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl143,plain,
is_a_theorem @ ( implies @ sk_ @ sk__1 ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl134]) ).
thf(zip_derived_cl167_003,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(axiom_m1,axiom,
( axiom_m1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ ( and @ Y @ X ) ) ) ) ).
thf(zip_derived_cl92,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_cl125,plain,
axiom_m1,
inference(cnf,[status(esa)],[s1_0_axiom_m1]) ).
thf(zip_derived_cl209,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl125]) ).
thf(zip_derived_cl274_004,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl271,zip_derived_cl163]) ).
thf(zip_derived_cl318,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ ( and @ X1 @ X0 ) @ ( and @ X0 @ X1 ) ) )
| ( is_a_theorem @ ( strict_equiv @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl209,zip_derived_cl274]) ).
thf(zip_derived_cl209_005,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl125]) ).
thf(zip_derived_cl323,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_equiv @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl318,zip_derived_cl209]) ).
thf(zip_derived_cl147_006,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl71,zip_derived_cl123]) ).
thf(zip_derived_cl1004,plain,
! [X0: $i,X1: $i] :
( ( and @ X0 @ X1 )
= ( and @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl323,zip_derived_cl147]) ).
thf(zip_derived_cl167_007,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(zip_derived_cl1043,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ ( not @ X1 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1004,zip_derived_cl167]) ).
thf(zip_derived_cl211_008,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( not @ ( and @ ( not @ X0 ) @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl117]) ).
thf(zip_derived_cl1210,plain,
! [X0: $i,X1: $i] :
( ( or @ X0 @ X1 )
= ( implies @ ( not @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1043,zip_derived_cl211]) ).
thf(zip_derived_cl164_009,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl119]) ).
thf(zip_derived_cl1250,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl164]) ).
thf(zip_derived_cl324_010,plain,
! [X0: $i] :
( X0
= ( and @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl320,zip_derived_cl147]) ).
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(s1_0_op_equiv,axiom,
op_equiv ).
thf(zip_derived_cl120,plain,
op_equiv,
inference(cnf,[status(esa)],[s1_0_op_equiv]) ).
thf(zip_derived_cl256,plain,
! [X0: $i,X1: $i] :
( ( equiv @ X0 @ X1 )
= ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl120]) ).
thf(zip_derived_cl346,plain,
! [X0: $i] :
( ( equiv @ X0 @ X0 )
= ( implies @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl324,zip_derived_cl256]) ).
thf(zip_derived_cl219_011,plain,
! [X0: $i,X1: $i] :
( ( implies @ ( not @ X1 ) @ X0 )
= ( or @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl211,zip_derived_cl167]) ).
thf(zip_derived_cl386,plain,
! [X0: $i] :
( ( equiv @ ( not @ X0 ) @ ( not @ X0 ) )
= ( or @ X0 @ ( not @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl346,zip_derived_cl219]) ).
thf(zip_derived_cl346_012,plain,
! [X0: $i] :
( ( equiv @ X0 @ X0 )
= ( implies @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl324,zip_derived_cl256]) ).
thf(zip_derived_cl164_013,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl119]) ).
thf(zip_derived_cl384,plain,
! [X0: $i] :
( ( strict_implies @ X0 @ X0 )
= ( necessarily @ ( equiv @ X0 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl346,zip_derived_cl164]) ).
thf(zip_derived_cl324_014,plain,
! [X0: $i] :
( X0
= ( and @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl320,zip_derived_cl147]) ).
thf(zip_derived_cl271_015,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl115,zip_derived_cl121]) ).
thf(zip_derived_cl348,plain,
! [X0: $i] :
( ( strict_equiv @ X0 @ X0 )
= ( strict_implies @ X0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl324,zip_derived_cl271]) ).
thf(zip_derived_cl473,plain,
! [X0: $i] :
( ( strict_equiv @ X0 @ X0 )
= ( necessarily @ ( equiv @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl384,zip_derived_cl348]) ).
thf(zip_derived_cl610,plain,
! [X0: $i] :
( ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) )
= ( necessarily @ ( or @ X0 @ ( not @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl386,zip_derived_cl473]) ).
thf(zip_derived_cl1291,plain,
! [X0: $i] :
( ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) )
= ( strict_implies @ ( not @ ( not @ X0 ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1250,zip_derived_cl610]) ).
thf(zip_derived_cl1291_016,plain,
! [X0: $i] :
( ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) )
= ( strict_implies @ ( not @ ( not @ X0 ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1250,zip_derived_cl610]) ).
thf(zip_derived_cl163_017,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_cl67,zip_derived_cl124]) ).
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_cl100,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_cl129,plain,
axiom_m5,
inference(cnf,[status(esa)],[s1_0_axiom_m5]) ).
thf(zip_derived_cl371,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_cl100,zip_derived_cl129]) ).
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_cl63,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_cl122,plain,
modus_ponens_strict_implies,
inference(cnf,[status(esa)],[s1_0_modus_ponens_strict_implies]) ).
thf(zip_derived_cl156,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_cl63,zip_derived_cl122]) ).
thf(zip_derived_cl372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_a_theorem @ ( and @ ( strict_implies @ X1 @ X2 ) @ ( strict_implies @ X2 @ X0 ) ) )
| ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl371,zip_derived_cl156]) ).
thf(zip_derived_cl510,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('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl372]) ).
thf(zip_derived_cl2100,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) ) )
| ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ X0 ) ) @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1291,zip_derived_cl510]) ).
thf(zip_derived_cl320_018,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ ( and @ X0 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl313,zip_derived_cl161]) ).
thf(zip_derived_cl324_019,plain,
! [X0: $i] :
( X0
= ( and @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl320,zip_derived_cl147]) ).
thf(zip_derived_cl335,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl320,zip_derived_cl324]) ).
thf(zip_derived_cl2148,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ X0 ) ) @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2100,zip_derived_cl335]) ).
thf(zip_derived_cl2830,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) ) )
| ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ ( not @ ( not @ X0 ) ) ) ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1291,zip_derived_cl2148]) ).
thf(zip_derived_cl335_020,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl320,zip_derived_cl324]) ).
thf(zip_derived_cl2833,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ ( not @ ( not @ X0 ) ) ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2830,zip_derived_cl335]) ).
thf(zip_derived_cl1250_021,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1210,zip_derived_cl164]) ).
thf(zip_derived_cl246_022,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X1 ) @ X0 )
= ( necessarily @ ( or @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl219,zip_derived_cl164]) ).
thf(zip_derived_cl1290,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1250,zip_derived_cl246]) ).
thf(zip_derived_cl4526,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X0 ) @ ( not @ ( not @ ( not @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2833,zip_derived_cl1290]) ).
thf(zip_derived_cl156_023,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_cl63,zip_derived_cl122]) ).
thf(zip_derived_cl4527,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( not @ X0 ) )
| ( is_a_theorem @ ( not @ ( not @ ( not @ X0 ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4526,zip_derived_cl156]) ).
thf(zip_derived_cl4647,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ( is_a_theorem @ ( not @ ( not @ ( not @ ( and @ X1 @ ( not @ X0 ) ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl167,zip_derived_cl4527]) ).
thf(zip_derived_cl167_024,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(zip_derived_cl4672,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ( is_a_theorem @ ( not @ ( not @ ( implies @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4647,zip_derived_cl167]) ).
thf(zip_derived_cl5197,plain,
is_a_theorem @ ( not @ ( not @ ( implies @ sk_ @ sk__1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl143,zip_derived_cl4672]) ).
thf(zip_derived_cl161_025,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl126]) ).
thf(zip_derived_cl2148_026,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ X0 ) ) @ X1 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2100,zip_derived_cl335]) ).
thf(zip_derived_cl2818,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ ( not @ ( and @ X0 @ X1 ) ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl161,zip_derived_cl2148]) ).
thf(zip_derived_cl1290_027,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ ( not @ X0 ) @ X1 )
= ( strict_implies @ ( not @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1250,zip_derived_cl246]) ).
thf(zip_derived_cl5796,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X0 ) @ ( not @ ( and @ X0 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2818,zip_derived_cl1290]) ).
thf(zip_derived_cl156_028,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_cl63,zip_derived_cl122]) ).
thf(zip_derived_cl5797,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( not @ X1 ) )
| ( is_a_theorem @ ( not @ ( and @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5796,zip_derived_cl156]) ).
thf(zip_derived_cl6168,plain,
! [X0: $i] : ( is_a_theorem @ ( not @ ( and @ ( not @ ( implies @ sk_ @ sk__1 ) ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5197,zip_derived_cl5797]) ).
thf(zip_derived_cl1043_029,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ ( not @ X1 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1004,zip_derived_cl167]) ).
thf(zip_derived_cl6208,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6168,zip_derived_cl1043]) ).
thf(zip_derived_cl4672_030,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ( is_a_theorem @ ( not @ ( not @ ( implies @ X1 @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4647,zip_derived_cl167]) ).
thf(zip_derived_cl6269,plain,
! [X0: $i] : ( is_a_theorem @ ( not @ ( not @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6208,zip_derived_cl4672]) ).
thf(zip_derived_cl5797_031,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( not @ X1 ) )
| ( is_a_theorem @ ( not @ ( and @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5796,zip_derived_cl156]) ).
thf(zip_derived_cl6637,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( not @ ( and @ ( not @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ) @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6269,zip_derived_cl5797]) ).
thf(zip_derived_cl1043_032,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ ( not @ X1 ) @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1004,zip_derived_cl167]) ).
thf(zip_derived_cl6650,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( implies @ X1 @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6637,zip_derived_cl1043]) ).
thf(zip_derived_cl6208_033,plain,
! [X0: $i] : ( is_a_theorem @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6168,zip_derived_cl1043]) ).
thf(zip_derived_cl256_034,plain,
! [X0: $i,X1: $i] :
( ( equiv @ X0 @ X1 )
= ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl120]) ).
thf(zip_derived_cl163_035,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_cl67,zip_derived_cl124]) ).
thf(zip_derived_cl259,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( implies @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl256,zip_derived_cl163]) ).
thf(zip_derived_cl6268,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( implies @ ( implies @ sk_ @ sk__1 ) @ X0 ) )
| ( is_a_theorem @ ( equiv @ X0 @ ( implies @ sk_ @ sk__1 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6208,zip_derived_cl259]) ).
thf(zip_derived_cl8610,plain,
! [X0: $i] : ( is_a_theorem @ ( equiv @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) @ ( implies @ sk_ @ sk__1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6650,zip_derived_cl6268]) ).
thf(zip_derived_cl256_036,plain,
! [X0: $i,X1: $i] :
( ( equiv @ X0 @ X1 )
= ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl120]) ).
thf(zip_derived_cl209_037,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl125]) ).
thf(zip_derived_cl260,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( equiv @ X1 @ X0 ) @ ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl256,zip_derived_cl209]) ).
thf(zip_derived_cl256_038,plain,
! [X0: $i,X1: $i] :
( ( equiv @ X0 @ X1 )
= ( and @ ( implies @ X0 @ X1 ) @ ( implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl120]) ).
thf(zip_derived_cl268,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( equiv @ X1 @ X0 ) @ ( equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl260,zip_derived_cl256]) ).
thf(zip_derived_cl274_039,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl271,zip_derived_cl163]) ).
thf(zip_derived_cl316,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ ( equiv @ X1 @ X0 ) @ ( equiv @ X0 @ X1 ) ) )
| ( is_a_theorem @ ( strict_equiv @ ( equiv @ X0 @ X1 ) @ ( equiv @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl268,zip_derived_cl274]) ).
thf(zip_derived_cl268_040,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( equiv @ X1 @ X0 ) @ ( equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl260,zip_derived_cl256]) ).
thf(zip_derived_cl322,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_equiv @ ( equiv @ X0 @ X1 ) @ ( equiv @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl316,zip_derived_cl268]) ).
thf(zip_derived_cl147_041,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl71,zip_derived_cl123]) ).
thf(zip_derived_cl889,plain,
! [X0: $i,X1: $i] :
( ( equiv @ X0 @ X1 )
= ( equiv @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl322,zip_derived_cl147]) ).
thf(zip_derived_cl8626,plain,
! [X0: $i] : ( is_a_theorem @ ( equiv @ ( implies @ sk_ @ sk__1 ) @ ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8610,zip_derived_cl889]) ).
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(substitution_of_equivalents_042,axiom,
substitution_of_equivalents ).
thf(zip_derived_cl133,plain,
substitution_of_equivalents,
inference(cnf,[status(esa)],[substitution_of_equivalents]) ).
thf(zip_derived_cl144,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl4,zip_derived_cl133]) ).
thf(zip_derived_cl16751,plain,
! [X0: $i] :
( ( implies @ sk_ @ sk__1 )
= ( implies @ X0 @ ( implies @ sk_ @ sk__1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl8626,zip_derived_cl144]) ).
thf(zip_derived_cl167_043,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(zip_derived_cl5796_044,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X0 ) @ ( not @ ( and @ X0 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2818,zip_derived_cl1290]) ).
thf(zip_derived_cl5807,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X1 ) @ ( implies @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl167,zip_derived_cl5796]) ).
thf(zip_derived_cl16787,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X0 ) @ ( implies @ sk_ @ sk__1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl16751,zip_derived_cl5807]) ).
thf(zip_derived_cl16941,plain,
is_a_theorem @ ( necessarily @ ( not @ ( not @ ( implies @ sk_ @ sk__1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl419,zip_derived_cl16787]) ).
thf(zip_derived_cl167_045,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(zip_derived_cl4526_046,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_implies @ ( not @ X0 ) @ ( not @ ( not @ ( not @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2833,zip_derived_cl1290]) ).
thf(zip_derived_cl1291_047,plain,
! [X0: $i] :
( ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) )
= ( strict_implies @ ( not @ ( not @ X0 ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl1250,zip_derived_cl610]) ).
thf(zip_derived_cl274_048,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl271,zip_derived_cl163]) ).
thf(zip_derived_cl2089,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ ( not @ X0 ) @ ( not @ X0 ) ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ ( not @ ( not @ X0 ) ) ) )
| ( is_a_theorem @ ( strict_equiv @ ( not @ ( not @ X0 ) ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1291,zip_derived_cl274]) ).
thf(zip_derived_cl335_049,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ X0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl320,zip_derived_cl324]) ).
thf(zip_derived_cl271_050,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl115,zip_derived_cl121]) ).
thf(zip_derived_cl209_051,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X0 @ X1 ) @ ( and @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl125]) ).
thf(zip_derived_cl275,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl271,zip_derived_cl209]) ).
thf(zip_derived_cl271_052,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( and @ ( strict_implies @ X0 @ X1 ) @ ( strict_implies @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl115,zip_derived_cl121]) ).
thf(zip_derived_cl280,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl275,zip_derived_cl271]) ).
thf(zip_derived_cl274_053,plain,
! [X0: $i,X1: $i] :
( ( is_a_theorem @ ( strict_equiv @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X1 @ X0 ) )
| ~ ( is_a_theorem @ ( strict_implies @ X0 @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl271,zip_derived_cl163]) ).
thf(zip_derived_cl704,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) )
| ( is_a_theorem @ ( strict_equiv @ ( strict_equiv @ X0 @ X1 ) @ ( strict_equiv @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl280,zip_derived_cl274]) ).
thf(zip_derived_cl280_054,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_equiv @ X1 @ X0 ) @ ( strict_equiv @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl275,zip_derived_cl271]) ).
thf(zip_derived_cl708,plain,
! [X0: $i,X1: $i] : ( is_a_theorem @ ( strict_equiv @ ( strict_equiv @ X0 @ X1 ) @ ( strict_equiv @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl704,zip_derived_cl280]) ).
thf(zip_derived_cl147_055,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl71,zip_derived_cl123]) ).
thf(zip_derived_cl1492,plain,
! [X0: $i,X1: $i] :
( ( strict_equiv @ X0 @ X1 )
= ( strict_equiv @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl708,zip_derived_cl147]) ).
thf(zip_derived_cl2143,plain,
! [X0: $i] :
( ~ ( is_a_theorem @ ( strict_implies @ X0 @ ( not @ ( not @ X0 ) ) ) )
| ( is_a_theorem @ ( strict_equiv @ X0 @ ( not @ ( not @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2089,zip_derived_cl335,zip_derived_cl1492]) ).
thf(zip_derived_cl4533,plain,
! [X0: $i] : ( is_a_theorem @ ( strict_equiv @ ( not @ X0 ) @ ( not @ ( not @ ( not @ X0 ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4526,zip_derived_cl2143]) ).
thf(zip_derived_cl147_056,plain,
! [X0: $i,X1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl71,zip_derived_cl123]) ).
thf(zip_derived_cl7478,plain,
! [X0: $i] :
( ( not @ X0 )
= ( not @ ( not @ ( not @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4533,zip_derived_cl147]) ).
thf(zip_derived_cl7732,plain,
! [X0: $i,X1: $i] :
( ( not @ ( and @ X1 @ ( not @ X0 ) ) )
= ( not @ ( not @ ( implies @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl167,zip_derived_cl7478]) ).
thf(zip_derived_cl167_057,plain,
! [X0: $i,X1: $i] :
( ( implies @ X0 @ X1 )
= ( not @ ( and @ X0 @ ( not @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl131]) ).
thf(zip_derived_cl7761,plain,
! [X0: $i,X1: $i] :
( ( implies @ X1 @ X0 )
= ( not @ ( not @ ( implies @ X1 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl7732,zip_derived_cl167]) ).
thf(zip_derived_cl164_058,plain,
! [X0: $i,X1: $i] :
( ( strict_implies @ X0 @ X1 )
= ( necessarily @ ( implies @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl119]) ).
thf(zip_derived_cl16985,plain,
is_a_theorem @ ( strict_implies @ sk_ @ sk__1 ),
inference(demod,[status(thm)],[zip_derived_cl16941,zip_derived_cl7761,zip_derived_cl164]) ).
thf(zip_derived_cl156_059,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_cl63,zip_derived_cl122]) ).
thf(zip_derived_cl16988,plain,
( ~ ( is_a_theorem @ sk_ )
| ( is_a_theorem @ sk__1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl16985,zip_derived_cl156]) ).
thf(zip_derived_cl1,plain,
( modus_ponens
| ( is_a_theorem @ sk_ ) ),
inference(cnf,[status(esa)],[modus_ponens]) ).
thf(zip_derived_cl134_060,plain,
~ modus_ponens,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl140,plain,
is_a_theorem @ sk_,
inference(demod,[status(thm)],[zip_derived_cl1,zip_derived_cl134]) ).
thf(zip_derived_cl16994,plain,
is_a_theorem @ sk__1,
inference(demod,[status(thm)],[zip_derived_cl16988,zip_derived_cl140]) ).
thf(zip_derived_cl16996,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl136,zip_derived_cl16994]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL550+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.4wifnykuqi true
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 18:21:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 50s
% 1.08/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 50s
% 19.06/3.38 % Solved by fo/fo5.sh.
% 19.06/3.38 % done 1712 iterations in 2.582s
% 19.06/3.38 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 19.06/3.38 % SZS output start Refutation
% See solution above
% 19.06/3.38
% 19.06/3.38
% 19.06/3.38 % Terminating...
% 19.06/3.47 % Runner terminated.
% 19.06/3.47 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------