TSTP Solution File: LCL521+1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LCL521+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n003.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:13:01 EDT 2023
% Result : Theorem 742.24s 121.02s
% Output : CNFRefutation 742.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 22
% Syntax : Number of formulae : 301 ( 208 unt; 0 def)
% Number of atoms : 432 ( 125 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 239 ( 108 ~; 108 |; 10 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 623 ( 84 sgn; 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',op_implies_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',op_implies_and) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',op_and) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',principia_op_implies_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_op_implies_and) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',principia_op_and) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',kn2) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',op_or) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',modus_ponens) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_kn2) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_op_or) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',kn1) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_modus_ponens) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_kn1) ).
fof(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',kn3) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_kn3) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',op_equiv) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',substitution_of_equivalents) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',rosser_op_equiv) ).
fof(substitution_of_equivalents_0001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',substitution_of_equivalents_0001) ).
fof(r4,axiom,
( r4
<=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',r4) ).
fof(principia_r4,conjecture,
r4,
file('/export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p',principia_r4) ).
fof(c_0_22,plain,
! [X123,X124] :
( ~ op_implies_or
| implies(X123,X124) = or(not(X123),X124) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])]) ).
fof(c_0_23,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
fof(c_0_24,plain,
! [X119,X120] :
( ~ op_and
| and(X119,X120) = not(or(not(X119),not(X120))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])]) ).
cnf(c_0_25,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
cnf(c_0_27,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
cnf(c_0_29,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_31,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
fof(c_0_32,plain,
! [X73,X74] :
( ( ~ kn2
| is_a_theorem(implies(and(X73,X74),X73)) )
& ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])]) ).
fof(c_0_33,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_34,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_35,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_36,plain,
! [X7,X8] :
( ( ~ modus_ponens
| ~ is_a_theorem(X7)
| ~ is_a_theorem(implies(X7,X8))
| is_a_theorem(X8) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
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])])])])]) ).
cnf(c_0_37,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_39,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
fof(c_0_42,plain,
! [X71] :
( ( ~ kn1
| is_a_theorem(implies(X71,and(X71,X71))) )
& ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])]) ).
cnf(c_0_43,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_46,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35]),c_0_40]),c_0_41])]) ).
cnf(c_0_47,plain,
or(implies(X1,X2),X3) = implies(not(implies(X1,not(not(X2)))),X3),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_48,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_50,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_51,plain,
is_a_theorem(or(implies(X1,not(X2)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_35]),c_0_46]) ).
cnf(c_0_52,plain,
or(implies(X1,not(not(X2))),X3) = or(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
fof(c_0_54,plain,
! [X77,X78,X79] :
( ( ~ kn3
| is_a_theorem(implies(implies(X77,X78),implies(not(and(X78,X79)),not(and(X79,X77))))) )
& ( ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))
| kn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])]) ).
cnf(c_0_55,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_56,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( is_a_theorem(not(implies(X1,not(X1))))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_35]) ).
cnf(c_0_58,plain,
implies(not(not(X1)),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))
| ~ kn3 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_61,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( is_a_theorem(not(implies(X1,not(not(not(X1))))))
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(not(implies(X2,not(X3)))),not(not(implies(X3,not(X1))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_35]),c_0_35]),c_0_60])]) ).
cnf(c_0_64,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,plain,
not(not(or(X1,not(not(X2))))) = implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,not(X3)),not(not(implies(X3,not(X1))))))),
inference(rw,[status(thm)],[c_0_63,c_0_58]) ).
cnf(c_0_67,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
( is_a_theorem(implies(implies(X1,not(X2)),not(not(implies(X2,not(X3))))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(not(X1),not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_53]),c_0_35]),c_0_40]),c_0_46]),c_0_46]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(implies(not(or(X1,X1)),not(X2)),implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_40]) ).
cnf(c_0_71,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_40]),c_0_30]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(implies(not(or(X1,X1)),X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_46]),c_0_71]) ).
cnf(c_0_73,plain,
is_a_theorem(or(implies(X1,not(X2)),not(not(X1)))),
inference(spm,[status(thm)],[c_0_51,c_0_58]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(or(or(X1,X1),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_72,c_0_46]) ).
cnf(c_0_75,plain,
is_a_theorem(or(implies(X1,X2),not(not(X1)))),
inference(spm,[status(thm)],[c_0_73,c_0_52]) ).
cnf(c_0_76,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(or(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_74]) ).
cnf(c_0_77,plain,
is_a_theorem(or(or(X1,X2),not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_75,c_0_46]) ).
cnf(c_0_78,plain,
is_a_theorem(implies(not(implies(X1,X2)),not(not(X1)))),
inference(spm,[status(thm)],[c_0_75,c_0_46]) ).
cnf(c_0_79,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,not(not(X3))))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_71]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_30]),c_0_58]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_78]),c_0_58]),c_0_40]) ).
fof(c_0_82,plain,
! [X125,X126] :
( ~ op_equiv
| equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
cnf(c_0_83,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_58]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_46]),c_0_71]) ).
fof(c_0_85,plain,
! [X11,X12] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X11,X12))
| X11 = X12 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])]) ).
cnf(c_0_86,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_87,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,not(X3)),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_46]),c_0_40]) ).
cnf(c_0_89,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents_0001]) ).
cnf(c_0_92,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_93,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_46]),c_0_71]) ).
cnf(c_0_94,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_46]),c_0_30]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),not(not(or(X3,not(X1))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_46]),c_0_71]) ).
cnf(c_0_96,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(X1,not(implies(X1,not(not(not(X1))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_58]),c_0_35]),c_0_58]) ).
cnf(c_0_98,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),or(X3,not(X1))))),
inference(spm,[status(thm)],[c_0_93,c_0_30]) ).
cnf(c_0_99,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_94]) ).
cnf(c_0_100,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(not(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_75]) ).
cnf(c_0_101,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(not(X3),not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_58]),c_0_65]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(or(X2,not(X3)),not(not(implies(X3,not(X1))))))),
inference(spm,[status(thm)],[c_0_66,c_0_46]) ).
cnf(c_0_103,plain,
implies(or(X1,not(not(X2))),X3) = implies(implies(not(X1),X2),X3),
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
cnf(c_0_104,plain,
( X1 = X2
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[c_0_96,c_0_35]) ).
cnf(c_0_105,plain,
( is_a_theorem(not(implies(X1,not(not(not(X1))))))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_97]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_83,c_0_98]) ).
cnf(c_0_107,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_99]) ).
cnf(c_0_108,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_57]) ).
cnf(c_0_109,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(X2),not(X1)))),
inference(spm,[status(thm)],[c_0_83,c_0_101]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_102]),c_0_40]) ).
cnf(c_0_111,plain,
implies(or(X1,not(not(X2))),X3) = implies(or(X1,X2),X3),
inference(spm,[status(thm)],[c_0_103,c_0_46]) ).
cnf(c_0_112,plain,
( X1 = not(not(X2))
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_58]),c_0_71]) ).
cnf(c_0_113,plain,
( is_a_theorem(not(implies(implies(X1,X2),not(implies(X1,X2)))))
| ~ is_a_theorem(implies(X1,not(not(X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_40]),c_0_71]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_80,c_0_58]) ).
cnf(c_0_115,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_106]) ).
cnf(c_0_116,plain,
( is_a_theorem(implies(implies(X1,X2),or(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_93]) ).
cnf(c_0_117,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_107,c_0_99]) ).
cnf(c_0_118,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_83,c_0_94]) ).
cnf(c_0_119,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_108,c_0_65]) ).
cnf(c_0_120,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_67,c_0_46]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_72]),c_0_30]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(not(X1),not(not(implies(X1,X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_94]),c_0_30]),c_0_46]) ).
cnf(c_0_123,plain,
( is_a_theorem(implies(X1,not(not(X2))))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_64,c_0_40]) ).
cnf(c_0_124,plain,
( is_a_theorem(implies(not(X1),not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_109]) ).
cnf(c_0_125,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_46]),c_0_111]) ).
cnf(c_0_126,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114])]) ).
cnf(c_0_127,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,or(X2,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_115]),c_0_30]) ).
cnf(c_0_128,plain,
( is_a_theorem(implies(implies(X1,X2),or(X2,X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_129,plain,
is_a_theorem(or(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_107,c_0_118]) ).
cnf(c_0_130,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_131,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(or(X2,X2),X2),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_121]),c_0_30]),c_0_71]),c_0_46]) ).
cnf(c_0_132,plain,
is_a_theorem(implies(X1,not(not(or(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_46]),c_0_58]) ).
cnf(c_0_133,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_123]) ).
cnf(c_0_134,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(or(X2,X3),or(X3,X1)))),
inference(spm,[status(thm)],[c_0_93,c_0_46]) ).
cnf(c_0_135,plain,
is_a_theorem(implies(not(or(X1,X2)),not(or(X2,X1)))),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_136,plain,
( is_a_theorem(implies(implies(X1,X2),or(X2,not(X3))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_95]),c_0_126]) ).
cnf(c_0_137,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_55,c_0_115]) ).
cnf(c_0_138,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_139,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_129,c_0_30]) ).
cnf(c_0_140,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_130,c_0_89]) ).
cnf(c_0_141,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(or(X1,X1))))),
inference(spm,[status(thm)],[c_0_131,c_0_98]) ).
cnf(c_0_142,plain,
is_a_theorem(implies(or(X1,X2),implies(not(X2),X1))),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_143,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,or(X2,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_79,c_0_132]) ).
cnf(c_0_144,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
cnf(c_0_145,plain,
( is_a_theorem(not(not(not(implies(X1,not(X1))))))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_53]),c_0_35]) ).
cnf(c_0_146,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X3)))
| ~ is_a_theorem(or(X3,not(X1))) ),
inference(spm,[status(thm)],[c_0_50,c_0_134]) ).
cnf(c_0_147,plain,
is_a_theorem(or(or(X1,X2),not(or(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_135]),c_0_126]) ).
cnf(c_0_148,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(or(X2,X1))))),
inference(spm,[status(thm)],[c_0_136,c_0_125]) ).
cnf(c_0_149,plain,
( is_a_theorem(not(implies(X1,X2)))
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_150,plain,
is_a_theorem(or(X1,not(not(implies(X2,X2))))),
inference(spm,[status(thm)],[c_0_67,c_0_139]) ).
cnf(c_0_151,plain,
is_a_theorem(implies(implies(implies(X1,X2),not(X3)),implies(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_140]),c_0_40]) ).
cnf(c_0_152,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,not(X3)),implies(X3,not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_58]),c_0_40]) ).
cnf(c_0_153,plain,
( is_a_theorem(or(X1,not(or(X2,X2))))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_141]) ).
cnf(c_0_154,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_142]) ).
cnf(c_0_155,plain,
is_a_theorem(or(or(X1,X2),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_143,c_0_84]) ).
cnf(c_0_156,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(implies(X2,not(X2))),X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_157,plain,
is_a_theorem(implies(or(or(X1,X2),X3),or(X3,or(X2,X1)))),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_158,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_125]) ).
cnf(c_0_159,plain,
is_a_theorem(or(or(or(X1,X2),X3),not(or(X2,X1)))),
inference(spm,[status(thm)],[c_0_143,c_0_148]) ).
cnf(c_0_160,plain,
or(or(X1,not(not(X2))),X3) = or(implies(not(X1),X2),X3),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_161,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_149]),c_0_126]) ).
cnf(c_0_162,plain,
is_a_theorem(implies(X1,not(not(implies(X2,X2))))),
inference(spm,[status(thm)],[c_0_150,c_0_30]) ).
cnf(c_0_163,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_46]),c_0_126]) ).
cnf(c_0_164,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_83,c_0_152]) ).
cnf(c_0_165,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(implies(X1,or(X2,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_153]),c_0_30]) ).
cnf(c_0_166,plain,
is_a_theorem(implies(not(implies(X1,X2)),or(X1,X3))),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_167,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X2))) ),
inference(spm,[status(thm)],[c_0_107,c_0_30]) ).
cnf(c_0_168,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(implies(X2,not(X2)),X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_156,c_0_46]) ).
cnf(c_0_169,plain,
is_a_theorem(implies(or(or(X1,X2),or(X2,X1)),or(X2,X1))),
inference(spm,[status(thm)],[c_0_127,c_0_157]) ).
cnf(c_0_170,plain,
is_a_theorem(implies(or(X1,X2),or(or(X2,X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_30]) ).
cnf(c_0_171,plain,
or(or(X1,not(not(X2))),X3) = or(or(X1,X2),X3),
inference(spm,[status(thm)],[c_0_160,c_0_46]) ).
cnf(c_0_172,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(implies(implies(X1,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_126]),c_0_126]) ).
cnf(c_0_173,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(X3,not(X1)))),
inference(spm,[status(thm)],[c_0_163,c_0_46]) ).
cnf(c_0_174,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_110]),c_0_106])]) ).
cnf(c_0_175,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_50,c_0_164]) ).
cnf(c_0_176,plain,
is_a_theorem(implies(implies(implies(X1,X2),not(implies(X1,X2))),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_30]) ).
cnf(c_0_177,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_121,c_0_30]) ).
cnf(c_0_178,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X2))) ),
inference(spm,[status(thm)],[c_0_167,c_0_30]) ).
cnf(c_0_179,plain,
( is_a_theorem(implies(implies(X1,not(X1)),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_168,c_0_89]) ).
cnf(c_0_180,plain,
is_a_theorem(implies(or(or(X1,X2),implies(not(X2),X1)),implies(not(X2),X1))),
inference(spm,[status(thm)],[c_0_169,c_0_46]) ).
cnf(c_0_181,plain,
is_a_theorem(implies(implies(not(X1),X2),or(or(X2,X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_30]) ).
cnf(c_0_182,plain,
implies(or(X1,X2),or(X1,X2)) = implies(X1,or(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]) ).
cnf(c_0_183,plain,
or(X1,X2) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_125]),c_0_125])]) ).
cnf(c_0_184,plain,
is_a_theorem(implies(X1,not(implies(implies(not(X1),X2),not(implies(not(X1),X2)))))),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_185,plain,
implies(X1,not(X1)) = not(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_177]),c_0_140])]) ).
cnf(c_0_186,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_111]),c_0_30]),c_0_46]) ).
cnf(c_0_187,plain,
( is_a_theorem(implies(X1,not(implies(X2,not(X2)))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_188,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),
inference(spm,[status(thm)],[c_0_127,c_0_163]) ).
cnf(c_0_189,plain,
or(or(X1,X2),implies(not(X2),X1)) = implies(not(X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_180]),c_0_181])]) ).
cnf(c_0_190,plain,
implies(X1,or(X1,X2)) = implies(X2,or(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_182]) ).
cnf(c_0_191,plain,
or(X1,implies(X1,X2)) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_172,c_0_84]) ).
cnf(c_0_192,plain,
or(implies(X1,X1),X2) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_172,c_0_94]) ).
cnf(c_0_193,plain,
implies(not(implies(X1,X1)),X2) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_184]),c_0_185]),c_0_126]) ).
cnf(c_0_194,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),or(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_150]),c_0_126]) ).
cnf(c_0_195,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X3),or(X3,X1)))),
inference(spm,[status(thm)],[c_0_93,c_0_46]) ).
cnf(c_0_196,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_186]),c_0_126]),c_0_126]),c_0_94])]) ).
cnf(c_0_197,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,or(X1,X3)))),
inference(spm,[status(thm)],[c_0_84,c_0_46]) ).
cnf(c_0_198,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_187]),c_0_185]),c_0_126]) ).
cnf(c_0_199,plain,
is_a_theorem(implies(or(implies(implies(or(X1,X1),X2),or(X1,X1)),implies(implies(or(X1,X1),X2),or(X1,X1))),X1)),
inference(spm,[status(thm)],[c_0_165,c_0_188]) ).
cnf(c_0_200,plain,
implies(X1,X1) = implies(X2,implies(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_30]),c_0_183]),c_0_191]),c_0_30]),c_0_192]),c_0_30]) ).
cnf(c_0_201,plain,
implies(implies(X1,X2),implies(X1,X2)) = implies(X2,implies(X1,X2)),
inference(spm,[status(thm)],[c_0_182,c_0_174]) ).
cnf(c_0_202,plain,
implies(X1,implies(implies(X2,X2),X1)) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_190]),c_0_174]) ).
cnf(c_0_203,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_127,c_0_194]) ).
cnf(c_0_204,plain,
is_a_theorem(or(or(X1,X2),not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_143,c_0_141]) ).
cnf(c_0_205,plain,
is_a_theorem(or(or(implies(X1,X2),X3),X1)),
inference(spm,[status(thm)],[c_0_143,c_0_163]) ).
cnf(c_0_206,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_83,c_0_195]) ).
cnf(c_0_207,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_93,c_0_196]) ).
cnf(c_0_208,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,not(X3)),implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_66,c_0_40]) ).
cnf(c_0_209,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X3),implies(not(X3),X1)))),
inference(spm,[status(thm)],[c_0_95,c_0_65]) ).
cnf(c_0_210,plain,
is_a_theorem(implies(or(X1,X2),or(X2,or(X1,X3)))),
inference(spm,[status(thm)],[c_0_197,c_0_46]) ).
cnf(c_0_211,plain,
implies(X1,X1) = implies(implies(implies(X2,X3),X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_196]),c_0_196]),c_0_196]),c_0_196]),c_0_196]) ).
cnf(c_0_212,plain,
implies(X1,implies(X2,X1)) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_201]),c_0_200]) ).
cnf(c_0_213,plain,
implies(implies(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_202]),c_0_80]),c_0_203])]) ).
cnf(c_0_214,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_30]) ).
cnf(c_0_215,plain,
is_a_theorem(implies(or(X1,X1),or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_204]),c_0_30]) ).
cnf(c_0_216,plain,
is_a_theorem(or(X1,or(implies(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_158,c_0_205]) ).
cnf(c_0_217,plain,
implies(not(X1),X2) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_142]),c_0_206])]) ).
cnf(c_0_218,plain,
or(X1,X2) = implies(implies(X2,X1),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_207]),c_0_163])]) ).
cnf(c_0_219,plain,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_83,c_0_208]) ).
cnf(c_0_220,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))),
inference(spm,[status(thm)],[c_0_83,c_0_209]) ).
cnf(c_0_221,plain,
is_a_theorem(implies(or(X1,or(X1,X2)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_127,c_0_210]) ).
cnf(c_0_222,plain,
implies(X1,or(X1,X2)) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_182]),c_0_182]),c_0_200]) ).
cnf(c_0_223,plain,
implies(implies(X1,X2),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_211]),c_0_212]),c_0_213]),c_0_126]),c_0_80])]) ).
cnf(c_0_224,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_164]),c_0_164])]) ).
cnf(c_0_225,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_161,c_0_214]) ).
cnf(c_0_226,plain,
is_a_theorem(implies(or(X1,X1),implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_215,c_0_46]) ).
cnf(c_0_227,plain,
is_a_theorem(implies(X1,or(or(X1,X2),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_46]),c_0_30]) ).
cnf(c_0_228,plain,
implies(not(X1),X2) = implies(implies(X1,X2),X2),
inference(rw,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_229,plain,
implies(X1,X2) = implies(not(X2),not(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_219]),c_0_109])]) ).
cnf(c_0_230,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_220]),c_0_220])]) ).
cnf(c_0_231,plain,
is_a_theorem(implies(or(X1,or(X2,X1)),or(X2,X1))),
inference(spm,[status(thm)],[c_0_221,c_0_183]) ).
cnf(c_0_232,plain,
implies(X1,or(X2,X1)) = implies(X2,X2),
inference(rw,[status(thm)],[c_0_190,c_0_222]) ).
cnf(c_0_233,plain,
implies(implies(X1,not(X2)),X2) = X2,
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_234,plain,
( implies(not(X1),X2) = X1
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_196]),c_0_196]) ).
cnf(c_0_235,plain,
implies(implies(not(X1),X2),X2) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_174,c_0_218]) ).
cnf(c_0_236,plain,
implies(X1,X1) = implies(X2,implies(implies(X3,implies(implies(X4,X2),X2)),implies(implies(X4,X2),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_227]),c_0_218]),c_0_218]) ).
cnf(c_0_237,plain,
implies(implies(X1,not(X2)),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_30,c_0_218]) ).
cnf(c_0_238,plain,
implies(implies(X1,X2),not(X1)) = implies(X2,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_58]) ).
cnf(c_0_239,plain,
implies(implies(not(X1),X2),X1) = implies(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_230]),c_0_126]) ).
cnf(c_0_240,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_231]),c_0_232]),c_0_80])]) ).
cnf(c_0_241,plain,
implies(implies(X1,implies(not(X2),X3)),X4) = implies(implies(X1,or(X2,not(not(X3)))),X4),
inference(spm,[status(thm)],[c_0_71,c_0_65]) ).
cnf(c_0_242,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_243,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_213]),c_0_174]),c_0_213]),c_0_126]) ).
cnf(c_0_244,plain,
implies(X1,implies(implies(X2,implies(X1,X3)),implies(X1,X3))) = implies(implies(X2,implies(X1,X3)),implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_237]),c_0_237]),c_0_213]),c_0_237]),c_0_237]) ).
cnf(c_0_245,plain,
implies(implies(X1,X2),not(implies(not(X2),X1))) = not(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_224]),c_0_223]) ).
cnf(c_0_246,plain,
implies(not(X1),or(X2,X1)) = or(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_240]) ).
cnf(c_0_247,plain,
( X1 = implies(not(X2),X3)
| ~ is_a_theorem(not(implies(implies(X1,or(X2,X3)),not(implies(implies(not(X2),X3),X1))))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_241]),c_0_126]) ).
cnf(c_0_248,plain,
implies(implies(X1,implies(implies(X1,X2),X2)),X3) = X3,
inference(spm,[status(thm)],[c_0_242,c_0_243]) ).
cnf(c_0_249,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_240]),c_0_174]),c_0_174]) ).
cnf(c_0_250,plain,
implies(implies(X1,X2),implies(X2,X3)) = implies(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_237]),c_0_237]) ).
cnf(c_0_251,plain,
implies(implies(X1,X2),X2) = implies(not(X2),X1),
inference(rw,[status(thm)],[c_0_46,c_0_218]) ).
cnf(c_0_252,plain,
implies(or(X1,X2),not(X2)) = not(X2),
inference(spm,[status(thm)],[c_0_223,c_0_246]) ).
cnf(c_0_253,plain,
( implies(not(X1),X2) = X2
| ~ is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_228]),c_0_218]),c_0_58]),c_0_248]),c_0_126]) ).
cnf(c_0_254,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_212]),c_0_174]),c_0_126]),c_0_213]) ).
cnf(c_0_255,plain,
implies(not(X1),implies(X2,X1)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_249,c_0_229]) ).
cnf(c_0_256,plain,
implies(implies(implies(X1,X2),X2),implies(X1,X3)) = implies(X1,X3),
inference(spm,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_257,plain,
implies(implies(implies(X1,X2),X2),not(X1)) = not(X1),
inference(rw,[status(thm)],[c_0_252,c_0_218]) ).
cnf(c_0_258,plain,
implies(not(X1),implies(X1,X2)) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_46,c_0_191]) ).
cnf(c_0_259,plain,
implies(not(implies(X1,X2)),implies(X1,implies(X3,X2))) = implies(X1,implies(X3,X2)),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_260,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X3),X2),implies(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_255]),c_0_126]) ).
cnf(c_0_261,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_218]),c_0_218]) ).
cnf(c_0_262,plain,
implies(implies(implies(implies(implies(X1,X2),X2),X3),X3),not(X1)) = not(X1),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_263,plain,
implies(implies(X1,X2),implies(X1,implies(X3,X2))) = implies(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_126]),c_0_229]),c_0_201]),c_0_212]) ).
cnf(c_0_264,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_212]),c_0_126]),c_0_174]),c_0_213]) ).
cnf(c_0_265,plain,
implies(implies(implies(X1,X2),implies(implies(implies(X1,X2),X3),X2)),implies(implies(implies(X1,X2),X3),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_260]),c_0_228]),c_0_261]) ).
cnf(c_0_266,plain,
implies(implies(implies(X1,X2),implies(X3,X2)),not(X1)) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_263]),c_0_213]) ).
cnf(c_0_267,plain,
implies(implies(implies(X1,X2),implies(implies(X3,X1),X2)),implies(implies(X3,X1),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_264]),c_0_228]),c_0_261]) ).
cnf(c_0_268,plain,
implies(not(implies(X1,X2)),implies(implies(implies(X1,X2),X3),X2)) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_228,c_0_265]) ).
cnf(c_0_269,plain,
implies(not(X1),implies(implies(X1,X2),implies(X3,X2))) = implies(implies(X1,X2),implies(X3,X2)),
inference(spm,[status(thm)],[c_0_223,c_0_266]) ).
cnf(c_0_270,plain,
implies(implies(implies(X1,X2),implies(X3,not(X1))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_229]),c_0_126]),c_0_126]) ).
cnf(c_0_271,plain,
implies(implies(implies(X1,X2),X3),implies(X2,X3)) = implies(X3,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_267]),c_0_201]),c_0_212]) ).
cnf(c_0_272,plain,
implies(implies(implies(X1,implies(X2,X3)),X3),implies(X2,X3)) = implies(X1,implies(X2,X3)),
inference(spm,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_273,plain,
implies(implies(implies(X1,X2),implies(X1,X3)),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_270]),c_0_126]),c_0_174]) ).
cnf(c_0_274,plain,
implies(implies(X1,X2),implies(X3,not(X1))) = implies(X2,implies(X3,not(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_270]),c_0_271]),c_0_213]) ).
cnf(c_0_275,plain,
implies(implies(implies(implies(implies(X1,X2),X3),X3),X2),implies(X1,X2)) = implies(implies(implies(X1,X2),X3),X3),
inference(spm,[status(thm)],[c_0_272,c_0_251]) ).
cnf(c_0_276,plain,
implies(X1,X1) = implies(implies(implies(X2,X3),X4),implies(implies(X2,X4),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_163]),c_0_218]) ).
cnf(c_0_277,plain,
implies(implies(X1,X2),implies(X1,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_273]),c_0_271]),c_0_213]) ).
cnf(c_0_278,plain,
implies(X1,implies(X2,implies(X1,X3))) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_230]),c_0_239]),c_0_239]) ).
cnf(c_0_279,plain,
implies(implies(X1,not(X2)),not(implies(X2,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_238]),c_0_229]),c_0_223]) ).
fof(c_0_280,plain,
! [X105,X106,X107] :
( ( ~ r4
| is_a_theorem(implies(or(X105,or(X106,X107)),or(X106,or(X105,X107)))) )
& ( ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))
| r4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])]) ).
fof(c_0_281,negated_conjecture,
~ r4,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r4])]) ).
cnf(c_0_282,plain,
implies(implies(X1,X2),implies(X3,X2)) = implies(not(X1),implies(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_229]),c_0_126]),c_0_126]) ).
cnf(c_0_283,plain,
implies(implies(X1,X2),implies(implies(X1,X3),X2)) = implies(implies(X1,X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_213]),c_0_261]),c_0_212]),c_0_213]),c_0_213]) ).
cnf(c_0_284,plain,
implies(implies(not(X1),X2),implies(X3,X1)) = implies(X2,implies(X3,X1)),
inference(spm,[status(thm)],[c_0_277,c_0_229]) ).
cnf(c_0_285,plain,
implies(X1,implies(implies(implies(X1,X2),X3),X3)) = implies(implies(implies(X1,X2),X3),X3),
inference(spm,[status(thm)],[c_0_278,c_0_251]) ).
cnf(c_0_286,plain,
implies(implies(implies(X1,not(X2)),X3),X2) = implies(X3,X2),
inference(spm,[status(thm)],[c_0_277,c_0_279]) ).
cnf(c_0_287,plain,
implies(X1,not(implies(X2,X2))) = not(X1),
inference(spm,[status(thm)],[c_0_213,c_0_224]) ).
cnf(c_0_288,plain,
( r4
| ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_289,negated_conjecture,
~ r4,
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_290,plain,
implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X2)) = implies(X1,implies(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_282]),c_0_237]) ).
cnf(c_0_291,plain,
implies(X1,implies(implies(implies(X1,X2),X3),X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_251]),c_0_284]),c_0_239]) ).
cnf(c_0_292,plain,
implies(implies(X1,implies(implies(X1,X2),X3)),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_285]),c_0_237]) ).
cnf(c_0_293,plain,
implies(X1,implies(implies(X2,X1),X3)) = implies(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_286]),c_0_237]),c_0_71]) ).
cnf(c_0_294,plain,
not(implies(X1,not(implies(X2,X2)))) = X1,
inference(spm,[status(thm)],[c_0_126,c_0_287]) ).
cnf(c_0_295,plain,
~ is_a_theorem(implies(implies(not(esk50_0),implies(not(esk51_0),esk52_0)),implies(not(esk51_0),implies(not(esk50_0),esk52_0)))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_288,c_0_46]),c_0_46]),c_0_46]),c_0_46]),c_0_289]) ).
cnf(c_0_296,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_290]),c_0_290]) ).
cnf(c_0_297,plain,
implies(X1,implies(implies(X1,X2),X3)) = implies(X1,implies(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_292]),c_0_293]) ).
cnf(c_0_298,plain,
implies(implies(implies(X1,not(implies(X2,X2))),X3),X3) = implies(X1,X3),
inference(spm,[status(thm)],[c_0_228,c_0_294]) ).
cnf(c_0_299,plain,
implies(X1,implies(X2,X2)) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_174,c_0_192]) ).
cnf(c_0_300,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_295,c_0_296]),c_0_287]),c_0_287]),c_0_287]),c_0_287]),c_0_296]),c_0_297]),c_0_298]),c_0_296]),c_0_296]),c_0_297]),c_0_193]),c_0_299]),c_0_299]),c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL521+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n003.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 2400
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Oct 2 12:36:33 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.SCBecRAk1Z/E---3.1_7325.p
% 742.24/121.02 # Version: 3.1pre001
% 742.24/121.02 # Preprocessing class: FSMSSLSSSSSNFFN.
% 742.24/121.02 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 742.24/121.02 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 742.24/121.02 # Starting new_bool_3 with 300s (1) cores
% 742.24/121.02 # Starting new_bool_1 with 300s (1) cores
% 742.24/121.02 # Starting sh5l with 300s (1) cores
% 742.24/121.02 # new_bool_3 with pid 7404 completed with status 8
% 742.24/121.02 # sh5l with pid 7406 completed with status 8
% 742.24/121.02 # new_bool_1 with pid 7405 completed with status 8
% 742.24/121.02 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 7403 completed with status 0
% 742.24/121.02 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 742.24/121.02 # Preprocessing class: FSMSSLSSSSSNFFN.
% 742.24/121.02 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 742.24/121.02 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 742.24/121.02 # No SInE strategy applied
% 742.24/121.02 # Search class: FGUSF-FFMM21-MFFFFFNN
% 742.24/121.02 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 742.24/121.02 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 742.24/121.02 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 742.24/121.02 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 742.24/121.02 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 742.24/121.02 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 742.24/121.02 # U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 7417 completed with status 0
% 742.24/121.02 # Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 742.24/121.02 # Preprocessing class: FSMSSLSSSSSNFFN.
% 742.24/121.02 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 742.24/121.02 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 742.24/121.02 # No SInE strategy applied
% 742.24/121.02 # Search class: FGUSF-FFMM21-MFFFFFNN
% 742.24/121.02 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 742.24/121.02 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 742.24/121.02 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 742.24/121.02 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 742.24/121.02 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 742.24/121.02 # Preprocessing time : 0.003 s
% 742.24/121.02 # Presaturation interreduction done
% 742.24/121.02
% 742.24/121.02 # Proof found!
% 742.24/121.02 # SZS status Theorem
% 742.24/121.02 # SZS output start CNFRefutation
% See solution above
% 742.24/121.02 # Parsed axioms : 43
% 742.24/121.02 # Removed by relevancy pruning/SinE : 0
% 742.24/121.02 # Initial clauses : 72
% 742.24/121.02 # Removed in clause preprocessing : 0
% 742.24/121.02 # Initial clauses in saturation : 72
% 742.24/121.02 # Processed clauses : 134249
% 742.24/121.02 # ...of these trivial : 18975
% 742.24/121.02 # ...subsumed : 109498
% 742.24/121.02 # ...remaining for further processing : 5776
% 742.24/121.02 # Other redundant clauses eliminated : 0
% 742.24/121.02 # Clauses deleted for lack of memory : 796752
% 742.24/121.02 # Backward-subsumed : 117
% 742.24/121.02 # Backward-rewritten : 2539
% 742.24/121.02 # Generated clauses : 4360729
% 742.24/121.02 # ...of the previous two non-redundant : 3110185
% 742.24/121.02 # ...aggressively subsumed : 0
% 742.24/121.02 # Contextual simplify-reflections : 0
% 742.24/121.02 # Paramodulations : 4360729
% 742.24/121.02 # Factorizations : 0
% 742.24/121.02 # NegExts : 0
% 742.24/121.02 # Equation resolutions : 0
% 742.24/121.02 # Total rewrite steps : 20975612
% 742.24/121.02 # Propositional unsat checks : 0
% 742.24/121.02 # Propositional check models : 0
% 742.24/121.02 # Propositional check unsatisfiable : 0
% 742.24/121.02 # Propositional clauses : 0
% 742.24/121.02 # Propositional clauses after purity: 0
% 742.24/121.02 # Propositional unsat core size : 0
% 742.24/121.02 # Propositional preprocessing time : 0.000
% 742.24/121.02 # Propositional encoding time : 0.000
% 742.24/121.02 # Propositional solver time : 0.000
% 742.24/121.02 # Success case prop preproc time : 0.000
% 742.24/121.02 # Success case prop encoding time : 0.000
% 742.24/121.02 # Success case prop solver time : 0.000
% 742.24/121.02 # Current number of processed clauses : 3059
% 742.24/121.02 # Positive orientable unit clauses : 2313
% 742.24/121.02 # Positive unorientable unit clauses: 29
% 742.24/121.02 # Negative unit clauses : 21
% 742.24/121.02 # Non-unit-clauses : 696
% 742.24/121.02 # Current number of unprocessed clauses: 1278121
% 742.24/121.02 # ...number of literals in the above : 1610885
% 742.24/121.02 # Current number of archived formulas : 0
% 742.24/121.02 # Current number of archived clauses : 2717
% 742.24/121.02 # Clause-clause subsumption calls (NU) : 679068
% 742.24/121.02 # Rec. Clause-clause subsumption calls : 654273
% 742.24/121.02 # Non-unit clause-clause subsumptions : 40365
% 742.24/121.02 # Unit Clause-clause subsumption calls : 122236
% 742.24/121.02 # Rewrite failures with RHS unbound : 0
% 742.24/121.02 # BW rewrite match attempts : 1448216
% 742.24/121.02 # BW rewrite match successes : 17499
% 742.24/121.02 # Condensation attempts : 0
% 742.24/121.02 # Condensation successes : 0
% 742.24/121.02 # Termbank termtop insertions : 140333669
% 742.24/121.02
% 742.24/121.02 # -------------------------------------------------
% 742.24/121.02 # User time : 116.559 s
% 742.24/121.02 # System time : 2.134 s
% 742.24/121.02 # Total time : 118.694 s
% 742.24/121.02 # Maximum resident set size: 2004 pages
% 742.24/121.02
% 742.24/121.02 # -------------------------------------------------
% 742.24/121.02 # User time : 731.333 s
% 742.24/121.02 # System time : 10.647 s
% 742.24/121.02 # Total time : 741.979 s
% 742.24/121.02 # Maximum resident set size: 1724 pages
% 742.24/121.02 % E---3.1 exiting
% 742.24/121.02 % E---3.1 exiting
%------------------------------------------------------------------------------