TSTP Solution File: LCL558+1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 18:13:07 EDT 2023
% Result : Theorem 6.90s 1.44s
% Output : CNFRefutation 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 32
% Syntax : Number of formulae : 202 ( 105 unt; 0 def)
% Number of atoms : 368 ( 87 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 291 ( 125 ~; 128 |; 18 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 22 con; 0-2 aty)
% Number of variables : 335 ( 45 sgn; 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',adjunction) ).
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/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',op_strict_equiv) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',substitution_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_substitution_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',axiom_m1) ).
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/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',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/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',axiom_m5) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',op_implies_and) ).
fof(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_axiom_m1) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_axiom_m5) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',op_strict_implies) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',hilbert_op_implies_and) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',axiom_m2) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_op_strict_implies) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_op_or) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_axiom_m2) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',axiom_m4) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_axiom_m4) ).
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/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',axiom_m3) ).
fof(s1_0_axiom_m3,axiom,
axiom_m3,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_axiom_m3) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',substitution_of_equivalents) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',op_equiv) ).
fof(substitution_of_equivalents_0001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',substitution_of_equivalents_0001) ).
fof(s1_0_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_op_equiv) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',op_possibly) ).
fof(s1_0_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',s1_0_op_possibly) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',or_1) ).
fof(hilbert_or_1,conjecture,
or_1,
file('/export/starexec/sandbox2/tmp/tmp.SWqDFXWkvp/E---3.1_5763.p',hilbert_or_1) ).
fof(c_0_32,plain,
! [X133,X134] :
( ( ~ adjunction
| ~ is_a_theorem(X133)
| ~ is_a_theorem(X134)
| is_a_theorem(and(X133,X134)) )
& ( is_a_theorem(esk59_0)
| adjunction )
& ( is_a_theorem(esk60_0)
| adjunction )
& ( ~ is_a_theorem(and(esk59_0,esk60_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])])])])]) ).
fof(c_0_33,plain,
! [X209,X210] :
( ~ op_strict_equiv
| strict_equiv(X209,X210) = and(strict_implies(X209,X210),strict_implies(X210,X209)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])]) ).
fof(c_0_34,plain,
! [X137,X138] :
( ( ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X137,X138))
| X137 = X138 )
& ( is_a_theorem(strict_equiv(esk61_0,esk62_0))
| substitution_strict_equiv )
& ( esk61_0 != esk62_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])])])])]) ).
cnf(c_0_35,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_37,plain,
( strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1))
| ~ op_strict_equiv ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(c_0_39,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_41,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_35,c_0_36])]) ).
cnf(c_0_42,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
fof(c_0_43,plain,
! [X169,X170] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X169,X170),and(X170,X169))) )
& ( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_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_44,plain,
! [X129,X130] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(X129)
| ~ is_a_theorem(strict_implies(X129,X130))
| is_a_theorem(X130) )
& ( is_a_theorem(esk57_0)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(esk57_0,esk58_0))
| modus_ponens_strict_implies )
& ( ~ is_a_theorem(esk58_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_45,plain,
! [X185,X186,X187] :
( ( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X185,X186),strict_implies(X186,X187)),strict_implies(X185,X187))) )
& ( ~ is_a_theorem(strict_implies(and(strict_implies(esk85_0,esk86_0),strict_implies(esk86_0,esk87_0)),strict_implies(esk85_0,esk87_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_46,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])])]) ).
cnf(c_0_47,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_48,plain,
( is_a_theorem(strict_equiv(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_49,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_51,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_44]) ).
cnf(c_0_52,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_53,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_45]) ).
cnf(c_0_54,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
fof(c_0_55,plain,
! [X207,X208] :
( ~ op_strict_implies
| strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
fof(c_0_56,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_57,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_59,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_61,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_51,c_0_52])]) ).
cnf(c_0_62,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_53,c_0_54])]) ).
fof(c_0_63,plain,
! [X173,X174] :
( ( ~ axiom_m2
| is_a_theorem(strict_implies(and(X173,X174),X173)) )
& ( ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_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_64,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_65,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_66,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_68,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_69,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_60])]) ).
cnf(c_0_70,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_61,c_0_62]) ).
cnf(c_0_71,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_73,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
cnf(c_0_74,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_75,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_67,c_0_69]) ).
cnf(c_0_76,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_70,c_0_41]) ).
cnf(c_0_77,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_78,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_75]),c_0_74]),c_0_74]) ).
fof(c_0_80,plain,
! [X183] :
( ( ~ axiom_m4
| is_a_theorem(strict_implies(X183,and(X183,X183))) )
& ( ~ is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))
| axiom_m4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])]) ).
cnf(c_0_81,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_78]) ).
cnf(c_0_83,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_84,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_85,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_81,c_0_82]) ).
cnf(c_0_86,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
cnf(c_0_87,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_85,c_0_67]) ).
cnf(c_0_88,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_86]),c_0_77])]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_86]),c_0_88]),c_0_82]) ).
cnf(c_0_90,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_88]),c_0_74]) ).
cnf(c_0_91,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_76,c_0_82]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(or(X1,X1),or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_74]) ).
cnf(c_0_93,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_86]),c_0_88]) ).
cnf(c_0_94,plain,
is_a_theorem(strict_implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_92,c_0_90]) ).
fof(c_0_95,plain,
! [X177,X178,X179] :
( ( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X177,X178),X179),and(X177,and(X178,X179)))) )
& ( ~ is_a_theorem(strict_implies(and(and(esk81_0,esk82_0),esk83_0),and(esk81_0,and(esk82_0,esk83_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_96,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_93,c_0_90]) ).
cnf(c_0_97,plain,
is_a_theorem(strict_implies(or(X1,X1),X1)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,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_95]) ).
cnf(c_0_99,plain,
axiom_m3,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m3]) ).
cnf(c_0_100,plain,
is_a_theorem(strict_implies(not(X1),not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_90]),c_0_82]) ).
cnf(c_0_101,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_89,c_0_74]) ).
cnf(c_0_102,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_98,c_0_99])]) ).
cnf(c_0_103,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_59,c_0_82]) ).
cnf(c_0_104,plain,
not(or(X1,X1)) = not(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_100]),c_0_82]),c_0_101])]) ).
cnf(c_0_105,plain,
( and(and(X1,X2),X3) = and(X1,and(X2,X3))
| ~ is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3))) ),
inference(spm,[status(thm)],[c_0_59,c_0_102]) ).
cnf(c_0_106,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_77,c_0_69]) ).
cnf(c_0_107,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_86]),c_0_88]),c_0_88]) ).
cnf(c_0_108,plain,
implies(X1,or(X2,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_104]),c_0_67]) ).
fof(c_0_109,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])])])])]) ).
fof(c_0_110,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_111,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_88]),c_0_82]) ).
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_105,c_0_88]),c_0_106])]) ).
cnf(c_0_113,plain,
( or(X1,X1) = X1
| ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_107,c_0_90]) ).
cnf(c_0_114,plain,
strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_108]),c_0_73]) ).
cnf(c_0_115,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_77,c_0_88]) ).
cnf(c_0_116,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_67,c_0_67]) ).
cnf(c_0_117,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_118,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents_0001]) ).
cnf(c_0_119,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_120,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_equiv]) ).
cnf(c_0_121,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_85,c_0_88]) ).
cnf(c_0_122,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_111,c_0_75]) ).
cnf(c_0_123,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_112,c_0_69]) ).
cnf(c_0_124,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_74,c_0_67]) ).
cnf(c_0_125,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114]),c_0_115])]) ).
cnf(c_0_126,plain,
implies(implies(X1,X2),and(X1,not(X2))) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_116,c_0_88]) ).
cnf(c_0_127,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
cnf(c_0_128,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_129,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_130,plain,
is_a_theorem(strict_implies(or(X1,X1),implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_90]),c_0_75]) ).
cnf(c_0_131,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_123]),c_0_67]) ).
cnf(c_0_132,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_76,c_0_89]) ).
cnf(c_0_133,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).
cnf(c_0_134,plain,
not(and(X1,or(X2,X2))) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_67,c_0_90]) ).
cnf(c_0_135,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_136,plain,
is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_129]),c_0_82]) ).
cnf(c_0_137,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,or(X3,X3))) ),
inference(spm,[status(thm)],[c_0_76,c_0_130]) ).
cnf(c_0_138,plain,
strict_implies(and(X1,not(X2)),X2) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_131]),c_0_73]) ).
cnf(c_0_139,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_132,c_0_129]) ).
cnf(c_0_140,plain,
necessarily(not(not(X1))) = strict_implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_78,c_0_90]) ).
cnf(c_0_141,plain,
implies(or(X1,X1),X2) = or(not(X1),X2),
inference(spm,[status(thm)],[c_0_74,c_0_90]) ).
cnf(c_0_142,plain,
or(X1,implies(X2,X1)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_133]),c_0_74]),c_0_79]) ).
cnf(c_0_143,plain,
or(X1,not(X2)) = implies(or(X2,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_134]),c_0_74]) ).
cnf(c_0_144,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_135,c_0_41]) ).
cnf(c_0_145,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_61,c_0_136]) ).
cnf(c_0_146,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,X3)) ),
inference(rw,[status(thm)],[c_0_137,c_0_114]) ).
cnf(c_0_147,plain,
strict_implies(not(X1),implies(X2,X1)) = strict_implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_133]),c_0_82]) ).
cnf(c_0_148,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(spm,[status(thm)],[c_0_78,c_0_125]) ).
cnf(c_0_149,plain,
is_a_theorem(necessarily(not(not(implies(X1,X1))))),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
fof(c_0_150,plain,
! [X205] :
( ~ op_possibly
| possibly(X205) = not(necessarily(not(X205))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])]) ).
cnf(c_0_151,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_141,c_0_125]) ).
cnf(c_0_152,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(spm,[status(thm)],[c_0_142,c_0_74]) ).
cnf(c_0_153,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_143,c_0_125]) ).
cnf(c_0_154,plain,
( not(X1) = X2
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_74]) ).
cnf(c_0_155,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_145,c_0_74]) ).
cnf(c_0_156,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(necessarily(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_157,plain,
is_a_theorem(necessarily(not(not(or(X1,not(X1)))))),
inference(spm,[status(thm)],[c_0_149,c_0_74]) ).
cnf(c_0_158,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_90,c_0_125]) ).
cnf(c_0_159,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_160,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[s1_0_op_possibly]) ).
cnf(c_0_161,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]),c_0_153]) ).
cnf(c_0_162,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X2,X1))),
inference(spm,[status(thm)],[c_0_101,c_0_79]) ).
cnf(c_0_163,plain,
( not(X1) = not(X2)
| ~ is_a_theorem(not(X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_164,plain,
is_a_theorem(strict_implies(X1,implies(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]),c_0_153]) ).
cnf(c_0_165,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
cnf(c_0_166,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_61,c_0_82]) ).
cnf(c_0_167,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_161]),c_0_73]) ).
cnf(c_0_168,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(spm,[status(thm)],[c_0_61,c_0_162]) ).
cnf(c_0_169,plain,
( X1 = not(X2)
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_158]) ).
cnf(c_0_170,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_164]) ).
cnf(c_0_171,plain,
is_a_theorem(strict_implies(possibly(X1),implies(necessarily(not(X1)),X2))),
inference(spm,[status(thm)],[c_0_89,c_0_165]) ).
cnf(c_0_172,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(strict_implies(or(X1,X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_166,c_0_90]) ).
cnf(c_0_173,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_148]),c_0_158]),c_0_167]) ).
cnf(c_0_174,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_168,c_0_90]) ).
cnf(c_0_175,plain,
( X1 = X2
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_169,c_0_158]) ).
cnf(c_0_176,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_177,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_172,c_0_125]) ).
cnf(c_0_178,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_173,c_0_158]) ).
cnf(c_0_179,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[c_0_174,c_0_125]) ).
cnf(c_0_180,plain,
( X1 = strict_implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_94]),c_0_125]),c_0_158]) ).
cnf(c_0_181,plain,
( X1 = implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_182,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_158]) ).
cnf(c_0_183,plain,
( X1 = or(X2,X3)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_175,c_0_179]) ).
cnf(c_0_184,plain,
( X1 = strict_implies(X2,implies(X3,X3))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_175,c_0_164]) ).
cnf(c_0_185,plain,
implies(X1,X1) = strict_implies(X2,X2),
inference(spm,[status(thm)],[c_0_180,c_0_176]) ).
cnf(c_0_186,plain,
implies(X1,X1) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_181,c_0_176]) ).
cnf(c_0_187,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_182,c_0_158]) ).
cnf(c_0_188,plain,
( strict_implies(X1,or(X1,X2)) = or(X3,X4)
| ~ is_a_theorem(X4) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_92]),c_0_125]) ).
cnf(c_0_189,plain,
is_a_theorem(strict_implies(strict_equiv(X1,X2),strict_implies(X1,X1))),
inference(spm,[status(thm)],[c_0_62,c_0_42]) ).
cnf(c_0_190,plain,
strict_implies(X1,implies(X2,X2)) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_94]),c_0_125]),c_0_158]),c_0_185]) ).
cnf(c_0_191,plain,
or(X1,implies(X2,X2)) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_142,c_0_186]) ).
fof(c_0_192,plain,
! [X45,X46] :
( ( ~ or_1
| is_a_theorem(implies(X45,or(X45,X46))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).
fof(c_0_193,negated_conjecture,
~ or_1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_or_1])]) ).
cnf(c_0_194,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_187,c_0_73]) ).
cnf(c_0_195,plain,
strict_implies(X1,or(X1,X2)) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_185]),c_0_190]),c_0_191]) ).
cnf(c_0_196,plain,
( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) ),
inference(split_conjunct,[status(thm)],[c_0_192]) ).
cnf(c_0_197,negated_conjecture,
~ or_1,
inference(split_conjunct,[status(thm)],[c_0_193]) ).
cnf(c_0_198,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ is_a_theorem(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_176])]) ).
cnf(c_0_199,plain,
~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))),
inference(sr,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_200,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_198,c_0_171]) ).
cnf(c_0_201,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_200])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : LCL558+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 2400
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Oct 2 12:25:53 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.44 Running first-order theorem proving
% 0.18/0.44 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.SWqDFXWkvp/E---3.1_5763.p
% 6.90/1.44 # Version: 3.1pre001
% 6.90/1.44 # Preprocessing class: FSLSSLSSSSSNFFN.
% 6.90/1.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.90/1.44 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 6.90/1.44 # Starting new_bool_3 with 300s (1) cores
% 6.90/1.44 # Starting new_bool_1 with 300s (1) cores
% 6.90/1.44 # Starting sh5l with 300s (1) cores
% 6.90/1.44 # H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 5845 completed with status 0
% 6.90/1.44 # Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 6.90/1.44 # Preprocessing class: FSLSSLSSSSSNFFN.
% 6.90/1.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.90/1.44 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 6.90/1.44 # No SInE strategy applied
% 6.90/1.44 # Search class: FGUSF-FFMM21-MFFFFFNN
% 6.90/1.44 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.90/1.44 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 675s (1) cores
% 6.90/1.44 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 6.90/1.44 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 6.90/1.44 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 6.90/1.44 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 6.90/1.44 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 5854 completed with status 0
% 6.90/1.44 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 6.90/1.44 # Preprocessing class: FSLSSLSSSSSNFFN.
% 6.90/1.44 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.90/1.44 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 6.90/1.44 # No SInE strategy applied
% 6.90/1.44 # Search class: FGUSF-FFMM21-MFFFFFNN
% 6.90/1.44 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.90/1.44 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 675s (1) cores
% 6.90/1.44 # Preprocessing time : 0.002 s
% 6.90/1.44 # Presaturation interreduction done
% 6.90/1.44
% 6.90/1.44 # Proof found!
% 6.90/1.44 # SZS status Theorem
% 6.90/1.44 # SZS output start CNFRefutation
% See solution above
% 6.90/1.44 # Parsed axioms : 77
% 6.90/1.44 # Removed by relevancy pruning/SinE : 0
% 6.90/1.44 # Initial clauses : 135
% 6.90/1.44 # Removed in clause preprocessing : 0
% 6.90/1.44 # Initial clauses in saturation : 135
% 6.90/1.44 # Processed clauses : 7190
% 6.90/1.44 # ...of these trivial : 374
% 6.90/1.44 # ...subsumed : 5251
% 6.90/1.44 # ...remaining for further processing : 1565
% 6.90/1.44 # Other redundant clauses eliminated : 0
% 6.90/1.44 # Clauses deleted for lack of memory : 0
% 6.90/1.44 # Backward-subsumed : 112
% 6.90/1.44 # Backward-rewritten : 335
% 6.90/1.44 # Generated clauses : 77292
% 6.90/1.44 # ...of the previous two non-redundant : 70953
% 6.90/1.44 # ...aggressively subsumed : 0
% 6.90/1.44 # Contextual simplify-reflections : 0
% 6.90/1.44 # Paramodulations : 77292
% 6.90/1.44 # Factorizations : 0
% 6.90/1.44 # NegExts : 0
% 6.90/1.44 # Equation resolutions : 0
% 6.90/1.44 # Total rewrite steps : 55218
% 6.90/1.44 # Propositional unsat checks : 0
% 6.90/1.44 # Propositional check models : 0
% 6.90/1.44 # Propositional check unsatisfiable : 0
% 6.90/1.44 # Propositional clauses : 0
% 6.90/1.44 # Propositional clauses after purity: 0
% 6.90/1.44 # Propositional unsat core size : 0
% 6.90/1.44 # Propositional preprocessing time : 0.000
% 6.90/1.44 # Propositional encoding time : 0.000
% 6.90/1.44 # Propositional solver time : 0.000
% 6.90/1.44 # Success case prop preproc time : 0.000
% 6.90/1.44 # Success case prop encoding time : 0.000
% 6.90/1.44 # Success case prop solver time : 0.000
% 6.90/1.44 # Current number of processed clauses : 1001
% 6.90/1.44 # Positive orientable unit clauses : 247
% 6.90/1.44 # Positive unorientable unit clauses: 18
% 6.90/1.44 # Negative unit clauses : 4
% 6.90/1.44 # Non-unit-clauses : 732
% 6.90/1.44 # Current number of unprocessed clauses: 61724
% 6.90/1.44 # ...number of literals in the above : 117539
% 6.90/1.44 # Current number of archived formulas : 0
% 6.90/1.44 # Current number of archived clauses : 564
% 6.90/1.44 # Clause-clause subsumption calls (NU) : 87570
% 6.90/1.44 # Rec. Clause-clause subsumption calls : 55145
% 6.90/1.44 # Non-unit clause-clause subsumptions : 4751
% 6.90/1.44 # Unit Clause-clause subsumption calls : 6529
% 6.90/1.44 # Rewrite failures with RHS unbound : 0
% 6.90/1.44 # BW rewrite match attempts : 3677
% 6.90/1.44 # BW rewrite match successes : 316
% 6.90/1.44 # Condensation attempts : 0
% 6.90/1.44 # Condensation successes : 0
% 6.90/1.44 # Termbank termtop insertions : 1027104
% 6.90/1.44
% 6.90/1.44 # -------------------------------------------------
% 6.90/1.44 # User time : 0.933 s
% 6.90/1.44 # System time : 0.035 s
% 6.90/1.44 # Total time : 0.968 s
% 6.90/1.44 # Maximum resident set size: 2240 pages
% 6.90/1.44
% 6.90/1.44 # -------------------------------------------------
% 6.90/1.44 # User time : 4.522 s
% 6.90/1.44 # System time : 0.174 s
% 6.90/1.44 # Total time : 4.696 s
% 6.90/1.44 # Maximum resident set size: 1764 pages
% 6.90/1.44 % E---3.1 exiting
% 6.90/1.44 % E---3.1 exiting
%------------------------------------------------------------------------------