TSTP Solution File: LCL528+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 07:44:54 EDT 2023
% Result : Theorem 72.73s 10.77s
% Output : CNFRefutation 72.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 39
% Syntax : Number of formulae : 283 ( 134 unt; 0 def)
% Number of atoms : 471 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 340 ( 152 ~; 145 |; 2 &)
% ( 15 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 20 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 424 ( 16 sgn; 142 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
fof(f54,axiom,
( axiom_K
<=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_K) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
fof(f63,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f79,axiom,
axiom_K,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_K) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f83,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f86,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f88,conjecture,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f89,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[],[f88]) ).
fof(f104,plain,
~ axiom_m1,
inference(flattening,[],[f89]) ).
fof(f105,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
fof(f107,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f108,plain,
( axiom_K
=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f109,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f113,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f115,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f116,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f117,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f118,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f119,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f120,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f121,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f122,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f123,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f124,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f129,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f124]) ).
fof(f130,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f123]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f122]) ).
fof(f133,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f121]) ).
fof(f134,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f120]) ).
fof(f135,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f119]) ).
fof(f136,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f118]) ).
fof(f137,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f117]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f116]) ).
fof(f139,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f115]) ).
fof(f141,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f113]) ).
fof(f145,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f146,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f147,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f148,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f109]) ).
fof(f149,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(ennf_transformation,[],[f108]) ).
fof(f150,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f107]) ).
fof(f152,plain,
( axiom_m1
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f154,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f156,plain,
( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f152,f156]) ).
fof(f158,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f130]) ).
fof(f159,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f131]) ).
fof(f160,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f132]) ).
fof(f161,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f162,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f134]) ).
fof(f163,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f135]) ).
fof(f164,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f136]) ).
fof(f165,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f138]) ).
fof(f167,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f169,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f141]) ).
fof(f173,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f145]) ).
fof(f174,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f146]) ).
fof(f175,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f147]) ).
fof(f177,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f179,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f180,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f181,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f182,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f183,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f184,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f185,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f186,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f187,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f189,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f193,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f194,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f148]) ).
fof(f195,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(cnf_transformation,[],[f149]) ).
fof(f196,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f150]) ).
fof(f198,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(cnf_transformation,[],[f157]) ).
fof(f200,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f154]) ).
fof(f203,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f204,plain,
axiom_K,
inference(cnf_transformation,[],[f79]) ).
fof(f205,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f208,plain,
op_or,
inference(cnf_transformation,[],[f83]) ).
fof(f209,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f210,plain,
op_equiv,
inference(cnf_transformation,[],[f86]) ).
fof(f212,plain,
~ axiom_m1,
inference(cnf_transformation,[],[f104]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_50,plain,
( ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents
| X0 = X1 ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_51,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_52,plain,
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_53,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_54,plain,
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_55,plain,
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_56,plain,
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_57,plain,
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_58,plain,
( ~ or_1
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_60,plain,
( ~ or_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_64,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_65,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_66,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_68,plain,
op_implies_and,
inference(cnf_transformation,[],[f177]) ).
cnf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f179]) ).
cnf(c_71,plain,
modus_tollens,
inference(cnf_transformation,[],[f180]) ).
cnf(c_72,plain,
implies_1,
inference(cnf_transformation,[],[f181]) ).
cnf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f182]) ).
cnf(c_74,plain,
implies_3,
inference(cnf_transformation,[],[f183]) ).
cnf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f184]) ).
cnf(c_76,plain,
and_2,
inference(cnf_transformation,[],[f185]) ).
cnf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f186]) ).
cnf(c_78,plain,
or_1,
inference(cnf_transformation,[],[f187]) ).
cnf(c_80,plain,
or_3,
inference(cnf_transformation,[],[f189]) ).
cnf(c_84,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f193]) ).
cnf(c_85,plain,
( ~ is_a_theorem(X0)
| ~ necessitation
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_86,plain,
( ~ axiom_K
| is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_87,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_89,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0)))
| axiom_m1 ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_91,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_94,plain,
necessitation,
inference(cnf_transformation,[],[f203]) ).
cnf(c_95,plain,
axiom_K,
inference(cnf_transformation,[],[f204]) ).
cnf(c_96,plain,
axiom_M,
inference(cnf_transformation,[],[f205]) ).
cnf(c_99,plain,
op_or,
inference(cnf_transformation,[],[f208]) ).
cnf(c_100,plain,
op_strict_implies,
inference(cnf_transformation,[],[f209]) ).
cnf(c_101,plain,
op_equiv,
inference(cnf_transformation,[],[f210]) ).
cnf(c_103,negated_conjecture,
~ axiom_m1,
inference(cnf_transformation,[],[f212]) ).
cnf(c_128,plain,
is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_87,c_96,c_87]) ).
cnf(c_131,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_94,c_85]) ).
cnf(c_137,plain,
is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_58,c_78,c_58]) ).
cnf(c_139,plain,
is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).
cnf(c_142,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
cnf(c_144,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_72,c_52]) ).
cnf(c_153,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
cnf(c_160,plain,
is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).
cnf(c_163,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).
cnf(c_166,plain,
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
cnf(c_169,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_65]) ).
cnf(c_172,plain,
is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_73,c_53]) ).
cnf(c_175,plain,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_71,c_51]) ).
cnf(c_178,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).
cnf(c_179,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_178]) ).
cnf(c_180,plain,
is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))),
inference(global_subsumption_just,[status(thm)],[c_86,c_95,c_86]) ).
cnf(c_183,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_64,c_99,c_64]) ).
cnf(c_189,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_101,c_66]) ).
cnf(c_195,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_54,c_74,c_54]) ).
cnf(c_198,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(global_subsumption_just,[status(thm)],[c_60,c_80,c_60]) ).
cnf(c_325,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_183,c_169]) ).
cnf(c_326,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_175,c_325]) ).
cnf(c_327,plain,
is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
inference(light_normalisation,[status(thm)],[c_180,c_163]) ).
cnf(c_656,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_163,c_131]) ).
cnf(c_657,plain,
is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_163,c_128]) ).
cnf(c_673,plain,
is_a_theorem(implies(X0,or(X1,and(X0,not(X1))))),
inference(superposition,[status(thm)],[c_325,c_160]) ).
cnf(c_674,plain,
is_a_theorem(or(X0,implies(X1,and(not(X0),X1)))),
inference(superposition,[status(thm)],[c_325,c_160]) ).
cnf(c_695,plain,
is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
inference(superposition,[status(thm)],[c_325,c_326]) ).
cnf(c_705,plain,
is_a_theorem(strict_implies(X0,implies(X1,and(X0,X1)))),
inference(superposition,[status(thm)],[c_160,c_656]) ).
cnf(c_706,plain,
is_a_theorem(strict_implies(X0,or(X0,X1))),
inference(superposition,[status(thm)],[c_137,c_656]) ).
cnf(c_735,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_169,c_325]) ).
cnf(c_737,plain,
implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
inference(superposition,[status(thm)],[c_169,c_169]) ).
cnf(c_755,plain,
is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(superposition,[status(thm)],[c_325,c_172]) ).
cnf(c_759,plain,
is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(light_normalisation,[status(thm)],[c_755,c_325]) ).
cnf(c_935,plain,
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_172,c_179]) ).
cnf(c_936,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X0,X2))) ),
inference(superposition,[status(thm)],[c_195,c_179]) ).
cnf(c_939,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_160,c_179]) ).
cnf(c_948,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_326,c_179]) ).
cnf(c_949,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(necessarily(X0),necessarily(X1))) ),
inference(superposition,[status(thm)],[c_327,c_179]) ).
cnf(c_950,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_657,c_179]) ).
cnf(c_953,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[c_673,c_179]) ).
cnf(c_1175,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_939,c_179]) ).
cnf(c_1784,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_189,c_1175]) ).
cnf(c_2091,plain,
implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[c_325,c_737]) ).
cnf(c_2361,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_160,c_935]) ).
cnf(c_2362,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(superposition,[status(thm)],[c_198,c_935]) ).
cnf(c_2401,plain,
is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_2361,c_656]) ).
cnf(c_2653,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_2362,c_179]) ).
cnf(c_2748,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[status(thm)],[c_949,c_179]) ).
cnf(c_3328,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_2653,c_179]) ).
cnf(c_4368,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,and(X0,X1)))) ),
inference(superposition,[status(thm)],[c_705,c_2748]) ).
cnf(c_6210,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(strict_implies(X1,and(X0,X1))) ),
inference(demodulation,[status(thm)],[c_4368,c_163]) ).
cnf(c_6224,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_6210,c_950]) ).
cnf(c_6254,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(or(X1,and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[c_325,c_6224]) ).
cnf(c_8049,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_144,c_3328]) ).
cnf(c_8054,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_160,c_3328]) ).
cnf(c_9126,plain,
is_a_theorem(or(X0,not(and(not(X1),or(X0,X1))))),
inference(superposition,[status(thm)],[c_2091,c_674]) ).
cnf(c_9298,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_163,c_131]) ).
cnf(c_9452,plain,
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_172,c_179]) ).
cnf(c_9456,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_160,c_179]) ).
cnf(c_9466,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(necessarily(X0),necessarily(X1))) ),
inference(superposition,[status(thm)],[c_327,c_179]) ).
cnf(c_9591,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_9456,c_179]) ).
cnf(c_9967,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_189,c_9591]) ).
cnf(c_10052,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_144,c_9452]) ).
cnf(c_10054,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_160,c_9452]) ).
cnf(c_10069,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[status(thm)],[c_9466,c_179]) ).
cnf(c_10117,plain,
is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[status(thm)],[c_10052,c_9298]) ).
cnf(c_10130,plain,
is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_10054,c_9298]) ).
cnf(c_10139,plain,
is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_189,c_10130]) ).
cnf(c_11016,plain,
is_a_theorem(implies(and(not(X0),or(X1,X0)),X1)),
inference(superposition,[status(thm)],[c_9126,c_948]) ).
cnf(c_11115,plain,
( ~ is_a_theorem(and(not(X0),or(X1,X0)))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_11016,c_179]) ).
cnf(c_11116,plain,
is_a_theorem(strict_implies(and(not(X0),or(X1,X0)),X1)),
inference(superposition,[status(thm)],[c_11016,c_656]) ).
cnf(c_11140,plain,
( ~ is_a_theorem(necessarily(and(not(X0),or(X1,X0))))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[status(thm)],[c_11116,c_2748]) ).
cnf(c_11463,plain,
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_1175,c_11115]) ).
cnf(c_13007,plain,
( ~ is_a_theorem(not(and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_6254,c_11463]) ).
cnf(c_13039,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X1) ),
inference(light_normalisation,[status(thm)],[c_13007,c_169]) ).
cnf(c_13796,plain,
( ~ is_a_theorem(necessarily(implies(X0,X0)))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_10139,c_10069]) ).
cnf(c_14398,plain,
( ~ is_a_theorem(necessarily(or(X0,or(X0,X1))))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_759,c_13039]) ).
cnf(c_14408,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[status(thm)],[c_949,c_13039]) ).
cnf(c_20452,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_936,c_935]) ).
cnf(c_23406,plain,
( ~ is_a_theorem(and(not(X0),or(X1,X0)))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[status(thm)],[c_131,c_11140]) ).
cnf(c_23545,plain,
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(necessarily(X0)) ),
inference(superposition,[status(thm)],[c_1175,c_23406]) ).
cnf(c_26068,plain,
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(demodulation,[status(thm)],[c_13796,c_163]) ).
cnf(c_26069,plain,
is_a_theorem(necessarily(equiv(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_26068,c_10117]) ).
cnf(c_26978,plain,
( ~ is_a_theorem(not(and(X0,not(X1))))
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[status(thm)],[c_953,c_23545]) ).
cnf(c_27014,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X1)) ),
inference(light_normalisation,[status(thm)],[c_26978,c_169]) ).
cnf(c_27874,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(necessarily(X1))) ),
inference(superposition,[status(thm)],[c_949,c_27014]) ).
cnf(c_39802,plain,
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(superposition,[status(thm)],[c_706,c_14408]) ).
cnf(c_41919,plain,
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_39802,c_14398]) ).
cnf(c_47367,plain,
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_10054,c_9967]) ).
cnf(c_47384,plain,
is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_47367,c_142]) ).
cnf(c_50990,plain,
and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_47384,c_166]) ).
cnf(c_51068,plain,
implies(X0,X0) = equiv(X0,X0),
inference(superposition,[status(thm)],[c_50990,c_189]) ).
cnf(c_51092,plain,
is_a_theorem(necessarily(implies(X0,X0))),
inference(demodulation,[status(thm)],[c_26069,c_51068]) ).
cnf(c_95737,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(necessarily(and(X0,X0)))) ),
inference(superposition,[status(thm)],[c_2401,c_27874]) ).
cnf(c_108869,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(or(and(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_95737,c_41919]) ).
cnf(c_143658,plain,
( ~ is_a_theorem(necessarily(implies(X0,X0)))
| is_a_theorem(or(equiv(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_189,c_108869]) ).
cnf(c_149820,plain,
is_a_theorem(or(equiv(X0,X0),X1)),
inference(global_subsumption_just,[status(thm)],[c_143658,c_51092,c_143658]) ).
cnf(c_149843,plain,
is_a_theorem(implies(X0,and(equiv(X1,X1),X0))),
inference(superposition,[status(thm)],[c_149820,c_8054]) ).
cnf(c_149848,plain,
is_a_theorem(implies(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_149820,c_8049]) ).
cnf(c_149964,plain,
is_a_theorem(implies(implies(equiv(X0,X0),X1),X1)),
inference(superposition,[status(thm)],[c_149848,c_20452]) ).
cnf(c_160449,plain,
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_2361,c_1784]) ).
cnf(c_160522,plain,
( ~ is_a_theorem(implies(and(equiv(X0,X0),X1),X1))
| is_a_theorem(equiv(and(equiv(X0,X0),X1),X1)) ),
inference(superposition,[status(thm)],[c_149843,c_1784]) ).
cnf(c_160523,plain,
( ~ is_a_theorem(implies(X0,implies(equiv(X1,X1),X0)))
| is_a_theorem(equiv(X0,implies(equiv(X1,X1),X0))) ),
inference(superposition,[status(thm)],[c_149964,c_1784]) ).
cnf(c_160543,plain,
is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_160449,c_142]) ).
cnf(c_160579,plain,
is_a_theorem(equiv(X0,implies(equiv(X1,X1),X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_160523,c_144]) ).
cnf(c_160580,plain,
is_a_theorem(equiv(and(equiv(X0,X0),X1),X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_160522,c_139]) ).
cnf(c_161182,plain,
and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_160543,c_166]) ).
cnf(c_161309,plain,
implies(X0,X0) = equiv(X0,X0),
inference(superposition,[status(thm)],[c_161182,c_189]) ).
cnf(c_163241,plain,
is_a_theorem(equiv(X0,implies(implies(X1,X1),X0))),
inference(demodulation,[status(thm)],[c_160579,c_161309]) ).
cnf(c_163264,plain,
implies(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_163241,c_166]) ).
cnf(c_163726,plain,
is_a_theorem(equiv(and(implies(X0,X0),X1),X1)),
inference(light_normalisation,[status(thm)],[c_160580,c_161309]) ).
cnf(c_163746,plain,
and(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_163726,c_166]) ).
cnf(c_165041,plain,
implies(implies(implies(X0,X0),X1),X2) = or(not(X1),X2),
inference(superposition,[status(thm)],[c_163746,c_735]) ).
cnf(c_165045,plain,
implies(implies(X0,X0),X1) = not(not(X1)),
inference(superposition,[status(thm)],[c_163746,c_169]) ).
cnf(c_165132,plain,
not(not(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_165045,c_163264]) ).
cnf(c_165159,plain,
or(not(X0),X1) = implies(X0,X1),
inference(light_normalisation,[status(thm)],[c_165041,c_163264]) ).
cnf(c_165241,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[c_695,c_165132]) ).
cnf(c_165749,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_165132,c_735]) ).
cnf(c_165759,plain,
implies(X0,not(X1)) = not(and(X0,X1)),
inference(superposition,[status(thm)],[c_165132,c_169]) ).
cnf(c_171594,plain,
( ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| is_a_theorem(equiv(or(X0,X1),or(X1,X0))) ),
inference(superposition,[status(thm)],[c_165241,c_1784]) ).
cnf(c_171601,plain,
is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_171594,c_165241]) ).
cnf(c_177841,plain,
or(X0,X1) = or(X1,X0),
inference(superposition,[status(thm)],[c_171601,c_166]) ).
cnf(c_234445,plain,
or(X0,not(X1)) = implies(X1,X0),
inference(superposition,[status(thm)],[c_165159,c_177841]) ).
cnf(c_234517,plain,
is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_165159,c_326]) ).
cnf(c_247393,plain,
is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[c_234517,c_165749]) ).
cnf(c_313990,plain,
or(X0,implies(X1,not(X2))) = implies(and(X1,X2),X0),
inference(superposition,[status(thm)],[c_165759,c_234445]) ).
cnf(c_314285,plain,
is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(demodulation,[status(thm)],[c_247393,c_313990]) ).
cnf(c_314833,plain,
is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(superposition,[status(thm)],[c_314285,c_656]) ).
cnf(c_314862,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_153,c_314833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:12:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 72.73/10.77 % SZS status Started for theBenchmark.p
% 72.73/10.77 % SZS status Theorem for theBenchmark.p
% 72.73/10.77
% 72.73/10.77 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 72.73/10.77
% 72.73/10.77 ------ iProver source info
% 72.73/10.77
% 72.73/10.77 git: date: 2023-05-31 18:12:56 +0000
% 72.73/10.77 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 72.73/10.77 git: non_committed_changes: false
% 72.73/10.77 git: last_make_outside_of_git: false
% 72.73/10.77
% 72.73/10.77 ------ Parsing...
% 72.73/10.77 ------ Clausification by vclausify_rel & Parsing by iProver...
% 72.73/10.77
% 72.73/10.77 ------ Preprocessing... sup_sim: 3 sf_s rm: 27 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 72.73/10.77
% 72.73/10.77 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 72.73/10.77
% 72.73/10.77 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 72.73/10.77 ------ Proving...
% 72.73/10.77 ------ Problem Properties
% 72.73/10.77
% 72.73/10.77
% 72.73/10.77 clauses 26
% 72.73/10.77 conjectures 0
% 72.73/10.77 EPR 0
% 72.73/10.77 Horn 26
% 72.73/10.77 unary 23
% 72.73/10.77 binary 2
% 72.73/10.77 lits 30
% 72.73/10.77 lits eq 7
% 72.73/10.77 fd_pure 0
% 72.73/10.77 fd_pseudo 0
% 72.73/10.77 fd_cond 0
% 72.73/10.77 fd_pseudo_cond 1
% 72.73/10.77 AC symbols 0
% 72.73/10.77
% 72.73/10.77 ------ Schedule dynamic 5 is on
% 72.73/10.77
% 72.73/10.77 ------ no conjectures: strip conj schedule
% 72.73/10.77
% 72.73/10.77 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 72.73/10.77
% 72.73/10.77
% 72.73/10.77 ------
% 72.73/10.77 Current options:
% 72.73/10.77 ------
% 72.73/10.77
% 72.73/10.77
% 72.73/10.77
% 72.73/10.77
% 72.73/10.77 ------ Proving...
% 72.73/10.77
% 72.73/10.77
% 72.73/10.77 % SZS status Theorem for theBenchmark.p
% 72.73/10.77
% 72.73/10.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 72.73/10.77
% 72.73/10.78
%------------------------------------------------------------------------------