TSTP Solution File: LCL570+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL570+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 06:54:41 EDT 2023
% Result : Theorem 180.77s 180.75s
% Output : CNFRefutation 180.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 111
% Syntax : Number of formulae : 272 ( 114 unt; 83 typ; 0 def)
% Number of atoms : 319 ( 74 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 227 ( 97 ~; 96 |; 17 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 37 ( 35 usr; 35 prp; 0-2 aty)
% Number of functors : 48 ( 48 usr; 39 con; 0-2 aty)
% Number of variables : 327 ( 31 sgn; 54 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
op_or: $o ).
tff(decl_23,type,
or: ( $i * $i ) > $i ).
tff(decl_24,type,
not: $i > $i ).
tff(decl_25,type,
and: ( $i * $i ) > $i ).
tff(decl_26,type,
op_and: $o ).
tff(decl_27,type,
op_implies_and: $o ).
tff(decl_28,type,
implies: ( $i * $i ) > $i ).
tff(decl_29,type,
op_implies_or: $o ).
tff(decl_30,type,
op_equiv: $o ).
tff(decl_31,type,
equiv: ( $i * $i ) > $i ).
tff(decl_32,type,
necessitation: $o ).
tff(decl_33,type,
is_a_theorem: $i > $o ).
tff(decl_34,type,
necessarily: $i > $i ).
tff(decl_35,type,
modus_ponens_strict_implies: $o ).
tff(decl_36,type,
strict_implies: ( $i * $i ) > $i ).
tff(decl_37,type,
adjunction: $o ).
tff(decl_38,type,
substitution_strict_equiv: $o ).
tff(decl_39,type,
strict_equiv: ( $i * $i ) > $i ).
tff(decl_40,type,
axiom_K: $o ).
tff(decl_41,type,
axiom_M: $o ).
tff(decl_42,type,
axiom_4: $o ).
tff(decl_43,type,
axiom_B: $o ).
tff(decl_44,type,
possibly: $i > $i ).
tff(decl_45,type,
axiom_5: $o ).
tff(decl_46,type,
axiom_s1: $o ).
tff(decl_47,type,
axiom_s2: $o ).
tff(decl_48,type,
axiom_s3: $o ).
tff(decl_49,type,
axiom_s4: $o ).
tff(decl_50,type,
axiom_m1: $o ).
tff(decl_51,type,
axiom_m2: $o ).
tff(decl_52,type,
axiom_m3: $o ).
tff(decl_53,type,
axiom_m4: $o ).
tff(decl_54,type,
axiom_m5: $o ).
tff(decl_55,type,
axiom_m6: $o ).
tff(decl_56,type,
axiom_m7: $o ).
tff(decl_57,type,
axiom_m8: $o ).
tff(decl_58,type,
axiom_m9: $o ).
tff(decl_59,type,
axiom_m10: $o ).
tff(decl_60,type,
op_possibly: $o ).
tff(decl_61,type,
op_necessarily: $o ).
tff(decl_62,type,
op_strict_implies: $o ).
tff(decl_63,type,
op_strict_equiv: $o ).
tff(decl_64,type,
op_implies: $o ).
tff(decl_65,type,
substitution_of_equivalents: $o ).
tff(decl_66,type,
esk1_0: $i ).
tff(decl_67,type,
esk2_0: $i ).
tff(decl_68,type,
esk3_0: $i ).
tff(decl_69,type,
esk4_0: $i ).
tff(decl_70,type,
esk5_0: $i ).
tff(decl_71,type,
esk6_0: $i ).
tff(decl_72,type,
esk7_0: $i ).
tff(decl_73,type,
esk8_0: $i ).
tff(decl_74,type,
esk9_0: $i ).
tff(decl_75,type,
esk10_0: $i ).
tff(decl_76,type,
esk11_0: $i ).
tff(decl_77,type,
esk12_0: $i ).
tff(decl_78,type,
esk13_0: $i ).
tff(decl_79,type,
esk14_0: $i ).
tff(decl_80,type,
esk15_0: $i ).
tff(decl_81,type,
esk16_0: $i ).
tff(decl_82,type,
esk17_0: $i ).
tff(decl_83,type,
esk18_0: $i ).
tff(decl_84,type,
esk19_0: $i ).
tff(decl_85,type,
esk20_0: $i ).
tff(decl_86,type,
esk21_0: $i ).
tff(decl_87,type,
esk22_0: $i ).
tff(decl_88,type,
esk23_0: $i ).
tff(decl_89,type,
esk24_0: $i ).
tff(decl_90,type,
esk25_0: $i ).
tff(decl_91,type,
esk26_0: $i ).
tff(decl_92,type,
esk27_0: $i ).
tff(decl_93,type,
esk28_0: $i ).
tff(decl_94,type,
esk29_0: $i ).
tff(decl_95,type,
esk30_0: $i ).
tff(decl_96,type,
esk31_0: $i ).
tff(decl_97,type,
esk32_0: $i ).
tff(decl_98,type,
esk33_0: $i ).
tff(decl_99,type,
esk34_0: $i ).
tff(decl_100,type,
esk35_0: $i ).
tff(decl_101,type,
esk36_0: $i ).
tff(decl_102,type,
esk37_0: $i ).
tff(decl_103,type,
esk38_0: $i ).
tff(decl_104,type,
esk39_0: $i ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X1,X2] : strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(strict_implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
fof(axiom_m3,axiom,
( axiom_m3
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m3) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m3) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(s1_0_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_possibly) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X1] : is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
fof(s1_0_m10_axiom_m10,axiom,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+6.ax',s1_0_m10_axiom_m10) ).
fof(axiom_K,axiom,
( axiom_K
<=> ! [X1,X2] : is_a_theorem(implies(necessarily(implies(X1,X2)),implies(necessarily(X1),necessarily(X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_K) ).
fof(km5_axiom_K,conjecture,
axiom_K,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_K) ).
fof(c_0_28,plain,
! [X26,X27] :
( ( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X26,X27))
| X26 = X27 )
& ( is_a_theorem(strict_equiv(esk6_0,esk7_0))
| substitution_strict_equiv )
& ( esk6_0 != esk7_0
| substitution_strict_equiv ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_strict_equiv])])])])]) ).
fof(c_0_29,plain,
! [X98,X99] :
( ~ op_strict_equiv
| strict_equiv(X98,X99) = and(strict_implies(X98,X99),strict_implies(X99,X98)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_32,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
fof(c_0_34,plain,
! [X22,X23] :
( ( ~ adjunction
| ~ is_a_theorem(X22)
| ~ is_a_theorem(X23)
| is_a_theorem(and(X22,X23)) )
& ( is_a_theorem(esk4_0)
| adjunction )
& ( is_a_theorem(esk5_0)
| adjunction )
& ( ~ is_a_theorem(and(esk4_0,esk5_0))
| adjunction ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[adjunction])])])])]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_36,plain,
strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_37,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
fof(c_0_39,plain,
! [X58,X59] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X58,X59),and(X59,X58))) )
& ( ~ is_a_theorem(strict_implies(and(esk22_0,esk23_0),and(esk23_0,esk22_0)))
| axiom_m1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])]) ).
fof(c_0_40,plain,
! [X10,X11] :
( ~ op_implies_and
| implies(X10,X11) = not(and(X10,not(X11))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_41,plain,
( X1 = X2
| ~ is_a_theorem(and(strict_implies(X1,X2),strict_implies(X2,X1))) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_43,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_45,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_47,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
fof(c_0_49,plain,
! [X18,X19] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(X18)
| ~ is_a_theorem(strict_implies(X18,X19))
| is_a_theorem(X19) )
& ( is_a_theorem(esk2_0)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(esk2_0,esk3_0))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(esk3_0)
| modus_ponens_strict_implies ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies])])])])]) ).
fof(c_0_50,plain,
! [X74,X75,X76] :
( ( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X74,X75),strict_implies(X75,X76)),strict_implies(X74,X76))) )
& ( ~ is_a_theorem(strict_implies(and(strict_implies(esk30_0,esk31_0),strict_implies(esk31_0,esk32_0)),strict_implies(esk30_0,esk32_0)))
| axiom_m5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m5])])])]) ).
fof(c_0_51,plain,
! [X96,X97] :
( ~ op_strict_implies
| strict_implies(X96,X97) = necessarily(implies(X96,X97)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
cnf(c_0_52,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_53,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48])]) ).
cnf(c_0_54,plain,
( is_a_theorem(X2)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_56,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
cnf(c_0_58,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_60,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_61,plain,
! [X72] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X72,and(X72,X72))) )
& ( ~ is_a_theorem(strict_implies(esk29_0,and(esk29_0,esk29_0)))
| axiom_m4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])]) ).
fof(c_0_62,plain,
! [X62,X63] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X62,X63),X62)) )
& ( ~ is_a_theorem(strict_implies(and(esk24_0,esk25_0),esk24_0))
| axiom_m2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])]) ).
cnf(c_0_63,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_64,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_65,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_66,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(spm,[status(thm)],[c_0_52,c_0_60]) ).
cnf(c_0_67,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_69,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_71,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_65]) ).
cnf(c_0_73,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_74,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_75,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X3,X2))
| ~ is_a_theorem(strict_implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_71,c_0_42]) ).
cnf(c_0_76,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(and(strict_implies(not(X3),X1),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_73]),c_0_74])]) ).
fof(c_0_78,plain,
! [X66,X67,X68] :
( ( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X66,X67),X68),and(X66,and(X67,X68)))) )
& ( ~ is_a_theorem(strict_implies(and(and(esk26_0,esk27_0),esk28_0),and(esk26_0,and(esk27_0,esk28_0))))
| axiom_m3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m3])])])]) ).
cnf(c_0_79,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_75,c_0_74]) ).
cnf(c_0_80,plain,
strict_implies(not(X1),and(not(X2),X3)) = strict_implies(implies(X3,X2),X1),
inference(spm,[status(thm)],[c_0_72,c_0_60]) ).
cnf(c_0_81,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X3),X1))
| ~ is_a_theorem(strict_implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_42]) ).
cnf(c_0_82,plain,
not(not(X1)) = implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_52,c_0_77]) ).
cnf(c_0_83,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(not(X2),X3))
| ~ is_a_theorem(strict_implies(X1,not(X3))) ),
inference(spm,[status(thm)],[c_0_75,c_0_72]) ).
cnf(c_0_84,plain,
( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_85,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_86,plain,
( is_a_theorem(strict_implies(not(X1),not(X2)))
| ~ is_a_theorem(strict_implies(implies(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,plain,
( is_a_theorem(strict_implies(implies(not(X1),X1),X2))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_73]),c_0_77]),c_0_82]) ).
cnf(c_0_88,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,implies(not(X2),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_73]),c_0_77]),c_0_82]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_90,plain,
( X1 = not(X2)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_47,c_0_72]) ).
cnf(c_0_91,plain,
( is_a_theorem(strict_implies(not(X1),not(X2)))
| ~ is_a_theorem(strict_implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(and(implies(not(X1),X1),X2),X1)),
inference(spm,[status(thm)],[c_0_88,c_0_74]) ).
cnf(c_0_93,plain,
not(and(implies(X1,X2),X3)) = implies(X3,and(not(X2),X1)),
inference(spm,[status(thm)],[c_0_60,c_0_60]) ).
cnf(c_0_94,plain,
is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X2,and(X3,X1)))),
inference(spm,[status(thm)],[c_0_89,c_0_53]) ).
cnf(c_0_95,plain,
( implies(not(X1),X1) = X1
| ~ is_a_theorem(strict_implies(X1,implies(not(X1),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_73]),c_0_77]),c_0_82]),c_0_77]),c_0_82]) ).
cnf(c_0_96,plain,
is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_77]) ).
cnf(c_0_97,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_74,c_0_53]) ).
cnf(c_0_98,plain,
is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(X2,and(X1,X3)))),
inference(spm,[status(thm)],[c_0_94,c_0_53]) ).
cnf(c_0_99,plain,
implies(implies(not(X1),X1),not(X1)) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_82]) ).
cnf(c_0_100,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X3,X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_97]) ).
cnf(c_0_101,plain,
and(X1,and(X2,X3)) = and(X2,and(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_98]),c_0_98])]) ).
cnf(c_0_102,plain,
implies(X1,implies(not(X2),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_99]),c_0_60]),c_0_82]),c_0_77]) ).
cnf(c_0_103,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_100,c_0_80]) ).
cnf(c_0_104,plain,
not(implies(X1,X2)) = implies(implies(X1,X2),and(X1,not(X2))),
inference(spm,[status(thm)],[c_0_82,c_0_52]) ).
cnf(c_0_105,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X1,and(X1,X2)))),
inference(spm,[status(thm)],[c_0_89,c_0_77]) ).
cnf(c_0_106,plain,
and(X1,and(X2,X3)) = and(and(X1,X3),X2),
inference(spm,[status(thm)],[c_0_53,c_0_101]) ).
cnf(c_0_107,plain,
strict_implies(X1,implies(not(X2),X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_102]),c_0_65]) ).
cnf(c_0_108,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_74,c_0_77]) ).
cnf(c_0_109,plain,
is_a_theorem(strict_implies(implies(implies(X1,X2),and(X1,not(X2))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_73]),c_0_77]),c_0_104]) ).
cnf(c_0_110,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_79,c_0_72]) ).
cnf(c_0_111,plain,
strict_implies(not(X1),and(X2,not(X3))) = strict_implies(implies(X2,X3),X1),
inference(spm,[status(thm)],[c_0_72,c_0_52]) ).
cnf(c_0_112,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_105]),c_0_97])]) ).
cnf(c_0_113,plain,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
inference(spm,[status(thm)],[c_0_106,c_0_53]) ).
cnf(c_0_114,plain,
implies(not(X1),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_107]),c_0_108])]) ).
cnf(c_0_115,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_109]),c_0_52]) ).
cnf(c_0_116,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_73]),c_0_77]),c_0_82]),c_0_111]),c_0_77]) ).
cnf(c_0_117,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_112,c_0_53]) ).
cnf(c_0_118,plain,
implies(not(X1),not(X2)) = implies(implies(not(X2),X2),X1),
inference(spm,[status(thm)],[c_0_66,c_0_82]) ).
cnf(c_0_119,plain,
not(and(X1,and(X2,not(X3)))) = implies(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_52,c_0_113]) ).
cnf(c_0_120,plain,
not(and(X1,X2)) = implies(X2,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_114]),c_0_77]) ).
cnf(c_0_121,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_115]) ).
cnf(c_0_122,plain,
is_a_theorem(strict_implies(not(X1),not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_123,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_118,c_0_114]) ).
cnf(c_0_124,plain,
implies(and(X1,not(X2)),not(X3)) = implies(and(X3,X1),X2),
inference(rw,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,plain,
is_a_theorem(strict_implies(not(X1),implies(and(X2,X1),X3))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,plain,
implies(and(X1,X2),X3) = implies(X1,implies(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_82]),c_0_114]),c_0_52]) ).
cnf(c_0_127,plain,
not(and(X1,and(not(X2),X3))) = implies(and(X1,X3),X2),
inference(spm,[status(thm)],[c_0_60,c_0_101]) ).
cnf(c_0_128,plain,
( is_a_theorem(strict_implies(X1,implies(and(X2,X3),X4)))
| ~ is_a_theorem(strict_implies(X1,not(X3))) ),
inference(spm,[status(thm)],[c_0_75,c_0_125]) ).
cnf(c_0_129,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_126,c_0_77]) ).
cnf(c_0_130,plain,
strict_implies(not(X1),not(X2)) = strict_implies(implies(not(X2),X2),X1),
inference(spm,[status(thm)],[c_0_72,c_0_82]) ).
cnf(c_0_131,plain,
is_a_theorem(strict_implies(implies(X1,X2),implies(and(X3,X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_127]),c_0_60]) ).
cnf(c_0_132,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_117]),c_0_52]) ).
cnf(c_0_133,plain,
is_a_theorem(strict_implies(and(not(X1),X2),implies(and(X3,X1),X4))),
inference(spm,[status(thm)],[c_0_128,c_0_74]) ).
cnf(c_0_134,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_129]),c_0_65]) ).
cnf(c_0_135,plain,
strict_implies(not(X1),not(X2)) = strict_implies(X2,X1),
inference(rw,[status(thm)],[c_0_130,c_0_114]) ).
cnf(c_0_136,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_82,c_0_114]) ).
cnf(c_0_137,plain,
is_a_theorem(strict_implies(X1,implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_114]),c_0_132]) ).
cnf(c_0_138,plain,
is_a_theorem(strict_implies(and(X1,not(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_53]) ).
cnf(c_0_139,plain,
strict_implies(X1,not(X2)) = strict_implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_140,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(strict_implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_137]) ).
cnf(c_0_141,plain,
is_a_theorem(strict_implies(X1,implies(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_120]),c_0_123]) ).
cnf(c_0_142,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_53]),c_0_126]) ).
cnf(c_0_143,plain,
implies(X1,implies(X2,X2)) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_144,plain,
implies(X1,implies(X2,X1)) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
fof(c_0_145,plain,
! [X94] :
( ~ op_possibly
| possibly(X94) = not(necessarily(not(X94))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])]) ).
cnf(c_0_146,plain,
strict_implies(X1,implies(X2,X2)) = strict_implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_143]),c_0_65]) ).
cnf(c_0_147,plain,
implies(X1,implies(implies(X1,X2),X2)) = implies(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_144]),c_0_143]),c_0_142]) ).
cnf(c_0_148,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_72]) ).
cnf(c_0_149,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_150,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[s1_0_op_possibly]) ).
fof(c_0_151,plain,
! [X92] :
( ( ~ axiom_m10
| is_a_theorem(strict_implies(possibly(X92),necessarily(possibly(X92)))) )
& ( ~ is_a_theorem(strict_implies(possibly(esk39_0),necessarily(possibly(esk39_0))))
| axiom_m10 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m10])])])]) ).
cnf(c_0_152,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(strict_implies(implies(X1,X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_146]),c_0_108])]) ).
cnf(c_0_153,plain,
strict_implies(X1,implies(implies(X1,X2),X2)) = strict_implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_147]),c_0_65]) ).
cnf(c_0_154,plain,
( is_a_theorem(and(not(X1),X2))
| ~ is_a_theorem(strict_implies(implies(X2,X1),X3))
| ~ is_a_theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_148,c_0_60]) ).
cnf(c_0_155,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_110,c_0_77]) ).
cnf(c_0_156,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150])]) ).
cnf(c_0_157,plain,
( is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_m10 ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_158,plain,
axiom_m10,
inference(split_conjunct,[status(thm)],[s1_0_m10_axiom_m10]) ).
cnf(c_0_159,plain,
implies(implies(implies(X1,X1),X2),X2) = implies(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_108])]) ).
cnf(c_0_160,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_87]),c_0_77]) ).
cnf(c_0_161,plain,
( is_a_theorem(strict_implies(not(X1),necessarily(not(X2))))
| ~ is_a_theorem(strict_implies(possibly(X2),X1)) ),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_162,plain,
is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_158])]) ).
cnf(c_0_163,plain,
not(necessarily(possibly(X1))) = possibly(necessarily(not(X1))),
inference(spm,[status(thm)],[c_0_156,c_0_156]) ).
cnf(c_0_164,plain,
strict_implies(implies(implies(X1,X1),X2),X2) = strict_implies(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_159]),c_0_65]) ).
cnf(c_0_165,plain,
strict_implies(X1,implies(X2,X1)) = strict_implies(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_144]),c_0_65]) ).
cnf(c_0_166,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(not(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_138]),c_0_120]),c_0_123]) ).
cnf(c_0_167,plain,
is_a_theorem(strict_implies(possibly(necessarily(not(X1))),necessarily(not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]) ).
fof(c_0_168,plain,
! [X30,X31] :
( ( ~ axiom_K
| is_a_theorem(implies(necessarily(implies(X30,X31)),implies(necessarily(X30),necessarily(X31)))) )
& ( ~ is_a_theorem(implies(necessarily(implies(esk8_0,esk9_0)),implies(necessarily(esk8_0),necessarily(esk9_0))))
| axiom_K ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_K])])])]) ).
fof(c_0_169,negated_conjecture,
~ axiom_K,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[km5_axiom_K])]) ).
cnf(c_0_170,plain,
implies(implies(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_164]),c_0_108]),c_0_165]),c_0_108])]) ).
cnf(c_0_171,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_166,c_0_136]) ).
cnf(c_0_172,plain,
is_a_theorem(strict_implies(possibly(strict_implies(X1,X2)),strict_implies(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_60]),c_0_65]),c_0_65]) ).
cnf(c_0_173,plain,
( axiom_K
| ~ is_a_theorem(implies(necessarily(implies(esk8_0,esk9_0)),implies(necessarily(esk8_0),necessarily(esk9_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_168]) ).
cnf(c_0_174,negated_conjecture,
~ axiom_K,
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_175,plain,
necessarily(X1) = strict_implies(implies(X2,X2),X1),
inference(spm,[status(thm)],[c_0_65,c_0_170]) ).
cnf(c_0_176,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_177,plain,
~ is_a_theorem(implies(strict_implies(esk8_0,esk9_0),implies(necessarily(esk8_0),necessarily(esk9_0)))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_65]),c_0_174]) ).
cnf(c_0_178,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_175]),c_0_176])]) ).
cnf(c_0_179,plain,
~ is_a_theorem(implies(necessarily(esk8_0),implies(strict_implies(esk8_0,esk9_0),necessarily(esk9_0)))),
inference(rw,[status(thm)],[c_0_177,c_0_142]) ).
cnf(c_0_180,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_178,c_0_65]) ).
cnf(c_0_181,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X3,X1)),strict_implies(X3,X2))),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_182,plain,
~ is_a_theorem(strict_implies(necessarily(esk8_0),implies(strict_implies(esk8_0,esk9_0),necessarily(esk9_0)))),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_183,plain,
strict_implies(X1,implies(X2,X3)) = strict_implies(and(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_126]),c_0_65]) ).
cnf(c_0_184,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(not(X1),X3)),strict_implies(not(X3),X2))),
inference(spm,[status(thm)],[c_0_181,c_0_72]) ).
cnf(c_0_185,plain,
strict_implies(not(X1),and(X2,not(X2))) = necessarily(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_175]),c_0_104]),c_0_170]) ).
cnf(c_0_186,plain,
~ is_a_theorem(strict_implies(and(necessarily(esk8_0),strict_implies(esk8_0,esk9_0)),necessarily(esk9_0))),
inference(rw,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_187,plain,
is_a_theorem(strict_implies(and(necessarily(X1),strict_implies(X1,X2)),necessarily(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_82]),c_0_114]),c_0_185]) ).
cnf(c_0_188,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL570+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 19:15:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 180.77/180.75 % Version : CSE_E---1.5
% 180.77/180.75 % Problem : theBenchmark.p
% 180.77/180.75 % Proof found
% 180.77/180.75 % SZS status Theorem for theBenchmark.p
% 180.77/180.75 % SZS output start Proof
% See solution above
% 180.77/180.77 % Total time : 180.174000 s
% 180.77/180.77 % SZS output end Proof
% 180.77/180.77 % Total time : 180.186000 s
%------------------------------------------------------------------------------