TSTP Solution File: LCL485+1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : LCL485+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 18:25:02 EDT 2023
% Result : Theorem 6.69s 1.37s
% Output : CNFRefutation 6.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 153 ( 71 unt; 0 def)
% Number of atoms : 275 ( 37 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 217 ( 95 ~; 95 |; 12 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 256 ( 30 sgn; 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',op_implies_or) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',op_and) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_op_implies_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',op_implies_and) ).
fof(r5,axiom,
( r5
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6)))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',r5) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',op_or) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_op_and) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',hilbert_op_implies_and) ).
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/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',modus_ponens) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_r5) ).
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',r2) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',hilbert_op_or) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_modus_ponens) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_r2) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',r3) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_r3) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',r1) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_r1) ).
fof(r4,axiom,
( r4
<=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',r4) ).
fof(principia_r4,axiom,
r4,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_r4) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.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/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',op_equiv) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',substitution_of_equivalents) ).
fof(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',principia_op_equiv) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',implies_2) ).
fof(hilbert_implies_2,conjecture,
implies_2,
file('/export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p',hilbert_implies_2) ).
fof(c_0_26,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_27,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_28,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_30,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_31,plain,
! [X111,X112,X113] :
( ( ~ r5
| is_a_theorem(implies(implies(X112,X113),implies(or(X111,X112),or(X111,X113)))) )
& ( ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))
| r5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])]) ).
fof(c_0_32,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_33,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_35,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_36,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_38,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_39,plain,
( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
| ~ r5 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
fof(c_0_41,plain,
! [X97,X98] :
( ( ~ r2
| is_a_theorem(implies(X98,or(X97,X98))) )
& ( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
| r2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])]) ).
cnf(c_0_42,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_44,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_45,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_46,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_51,plain,
not(not(implies(not(X1),not(not(X2))))) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,plain,
not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_45,c_0_43]) ).
fof(c_0_53,plain,
! [X101,X102] :
( ( ~ r3
| is_a_theorem(implies(or(X101,X102),or(X102,X101))) )
& ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])]) ).
cnf(c_0_54,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_46,c_0_47])]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_34]),c_0_34]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_57,plain,
implies(not(X1),X2) = or(X1,X2),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_56,c_0_34]) ).
cnf(c_0_62,plain,
implies(not(not(X1)),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_57]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(implies(not(X1),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_57]) ).
fof(c_0_69,plain,
! [X95] :
( ( ~ r1
| is_a_theorem(implies(or(X95,X95),X95)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])]) ).
cnf(c_0_70,plain,
( is_a_theorem(implies(X1,not(not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_65]) ).
cnf(c_0_71,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_57]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_74,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_75,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
fof(c_0_76,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])])])]) ).
cnf(c_0_77,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_70]),c_0_62]) ).
cnf(c_0_78,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34]) ).
cnf(c_0_79,plain,
( is_a_theorem(implies(not(X1),not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_57]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_81,plain,
( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
| ~ r4 ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]) ).
cnf(c_0_83,plain,
( is_a_theorem(implies(X1,or(X2,X3)))
| ~ is_a_theorem(or(X3,X2)) ),
inference(spm,[status(thm)],[c_0_77,c_0_63]) ).
cnf(c_0_84,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_66,c_0_78]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(not(X1),not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(X1,or(implies(X2,X3),X2))),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_56]) ).
cnf(c_0_89,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_57]) ).
cnf(c_0_90,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_85]),c_0_62]) ).
cnf(c_0_91,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_54,c_0_86]) ).
cnf(c_0_92,plain,
is_a_theorem(or(X1,or(implies(X2,X3),X2))),
inference(spm,[status(thm)],[c_0_87,c_0_57]) ).
fof(c_0_93,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_94,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_95,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_88]) ).
cnf(c_0_96,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
cnf(c_0_97,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_80]) ).
cnf(c_0_98,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_90]),c_0_62]) ).
cnf(c_0_99,plain,
is_a_theorem(or(implies(X1,X2),or(X3,X1))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_100,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_101,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_102,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_103,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).
cnf(c_0_104,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_34]) ).
cnf(c_0_105,plain,
( is_a_theorem(not(or(X1,X1)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_80]) ).
cnf(c_0_106,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,not(X1))) ),
inference(spm,[status(thm)],[c_0_97,c_0_34]) ).
cnf(c_0_107,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_57]) ).
cnf(c_0_108,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_98]) ).
cnf(c_0_109,plain,
is_a_theorem(or(implies(X1,X2),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_99,c_0_34]) ).
cnf(c_0_110,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_111,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_112,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_113,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_80,c_0_34]) ).
cnf(c_0_115,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,plain,
is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_34]),c_0_34]) ).
cnf(c_0_117,plain,
( X1 = X2
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111]),c_0_43]) ).
cnf(c_0_118,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_34]) ).
cnf(c_0_119,plain,
( is_a_theorem(implies(implies(X1,not(X1)),X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_34]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(not(X1),not(X1))),
inference(spm,[status(thm)],[c_0_67,c_0_114]) ).
cnf(c_0_121,plain,
is_a_theorem(or(X1,implies(or(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_122,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_117,c_0_62]),c_0_118]) ).
cnf(c_0_123,plain,
( is_a_theorem(not(implies(X1,not(X1))))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_119]) ).
cnf(c_0_124,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_120]),c_0_34]) ).
cnf(c_0_125,plain,
( is_a_theorem(implies(or(X1,X2),X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_121]) ).
cnf(c_0_126,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124])]) ).
cnf(c_0_127,plain,
( is_a_theorem(implies(or(X1,X2),or(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_128,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_67,c_0_60]) ).
cnf(c_0_129,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_34]) ).
cnf(c_0_130,plain,
( is_a_theorem(implies(or(X1,X2),X3))
| ~ is_a_theorem(implies(or(X1,X4),X3))
| ~ is_a_theorem(implies(X2,X4)) ),
inference(spm,[status(thm)],[c_0_64,c_0_127]) ).
cnf(c_0_131,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(implies(not(X3),X2)) ),
inference(spm,[status(thm)],[c_0_71,c_0_128]) ).
cnf(c_0_132,plain,
is_a_theorem(implies(X1,not(implies(X1,not(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_114]),c_0_62]) ).
cnf(c_0_133,plain,
( is_a_theorem(not(implies(X1,X2)))
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_129]) ).
cnf(c_0_134,plain,
( is_a_theorem(implies(or(X1,X2),X3))
| ~ is_a_theorem(implies(or(X2,X1),X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_135,plain,
( is_a_theorem(implies(or(X1,X2),X1))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_90]),c_0_126]) ).
cnf(c_0_136,plain,
is_a_theorem(or(implies(X1,not(or(X2,X2))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_126]),c_0_57]) ).
fof(c_0_137,plain,
! [X23,X24] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24))) )
& ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).
fof(c_0_138,negated_conjecture,
~ implies_2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_2])]) ).
cnf(c_0_139,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_117,c_0_133]),c_0_126]) ).
cnf(c_0_140,plain,
( is_a_theorem(implies(or(X1,X2),X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_141,plain,
is_a_theorem(or(or(X1,not(or(X2,X2))),X2)),
inference(spm,[status(thm)],[c_0_136,c_0_57]) ).
cnf(c_0_142,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_143,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_144,plain,
( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) ),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_145,negated_conjecture,
~ implies_2,
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_146,plain,
( or(X1,X2) = X2
| ~ is_a_theorem(implies(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_56])]) ).
cnf(c_0_147,plain,
is_a_theorem(implies(not(X1),or(X2,not(or(X1,X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_141]),c_0_57]) ).
cnf(c_0_148,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_139,c_0_90]),c_0_126]),c_0_126]),c_0_72])]) ).
cnf(c_0_149,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_142]),c_0_143])]) ).
cnf(c_0_150,plain,
~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))),
inference(sr,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_151,plain,
implies(X1,implies(X1,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(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]),c_0_149]),c_0_34]),c_0_148]),c_0_149]) ).
cnf(c_0_152,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_124])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL485+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 2400
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Oct 2 12:11:21 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 Running first-order model finding
% 0.21/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.moTau9jgBm/E---3.1_12833.p
% 6.69/1.37 # Version: 3.1pre001
% 6.69/1.37 # Preprocessing class: FSMSSLSSSSSNFFN.
% 6.69/1.37 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.69/1.37 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 6.69/1.37 # Starting new_bool_3 with 300s (1) cores
% 6.69/1.37 # Starting new_bool_1 with 300s (1) cores
% 6.69/1.37 # Starting sh5l with 300s (1) cores
% 6.69/1.37 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 12911 completed with status 0
% 6.69/1.37 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 6.69/1.37 # Preprocessing class: FSMSSLSSSSSNFFN.
% 6.69/1.37 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.69/1.37 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 6.69/1.37 # No SInE strategy applied
% 6.69/1.37 # Search class: FGUSF-FFMM21-MFFFFFNN
% 6.69/1.37 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.69/1.37 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 6.69/1.37 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 6.69/1.37 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 6.69/1.37 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 6.69/1.37 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 6.69/1.37 # G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with pid 12923 completed with status 0
% 6.69/1.37 # Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI
% 6.69/1.37 # Preprocessing class: FSMSSLSSSSSNFFN.
% 6.69/1.37 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.69/1.37 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 6.69/1.37 # No SInE strategy applied
% 6.69/1.37 # Search class: FGUSF-FFMM21-MFFFFFNN
% 6.69/1.37 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.69/1.37 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 6.69/1.37 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 6.69/1.37 # Preprocessing time : 0.004 s
% 6.69/1.37 # Presaturation interreduction done
% 6.69/1.37
% 6.69/1.37 # Proof found!
% 6.69/1.37 # SZS status Theorem
% 6.69/1.37 # SZS output start CNFRefutation
% See solution above
% 6.69/1.38 # Parsed axioms : 45
% 6.69/1.38 # Removed by relevancy pruning/SinE : 0
% 6.69/1.38 # Initial clauses : 74
% 6.69/1.38 # Removed in clause preprocessing : 0
% 6.69/1.38 # Initial clauses in saturation : 74
% 6.69/1.38 # Processed clauses : 7903
% 6.69/1.38 # ...of these trivial : 757
% 6.69/1.38 # ...subsumed : 6062
% 6.69/1.38 # ...remaining for further processing : 1084
% 6.69/1.38 # Other redundant clauses eliminated : 0
% 6.69/1.38 # Clauses deleted for lack of memory : 0
% 6.69/1.38 # Backward-subsumed : 15
% 6.69/1.38 # Backward-rewritten : 171
% 6.69/1.38 # Generated clauses : 95421
% 6.69/1.38 # ...of the previous two non-redundant : 81293
% 6.69/1.38 # ...aggressively subsumed : 0
% 6.69/1.38 # Contextual simplify-reflections : 0
% 6.69/1.38 # Paramodulations : 95421
% 6.69/1.38 # Factorizations : 0
% 6.69/1.38 # NegExts : 0
% 6.69/1.38 # Equation resolutions : 0
% 6.69/1.38 # Total rewrite steps : 28809
% 6.69/1.38 # Propositional unsat checks : 0
% 6.69/1.38 # Propositional check models : 0
% 6.69/1.38 # Propositional check unsatisfiable : 0
% 6.69/1.38 # Propositional clauses : 0
% 6.69/1.38 # Propositional clauses after purity: 0
% 6.69/1.38 # Propositional unsat core size : 0
% 6.69/1.38 # Propositional preprocessing time : 0.000
% 6.69/1.38 # Propositional encoding time : 0.000
% 6.69/1.38 # Propositional solver time : 0.000
% 6.69/1.38 # Success case prop preproc time : 0.000
% 6.69/1.38 # Success case prop encoding time : 0.000
% 6.69/1.38 # Success case prop solver time : 0.000
% 6.69/1.38 # Current number of processed clauses : 837
% 6.69/1.38 # Positive orientable unit clauses : 307
% 6.69/1.38 # Positive unorientable unit clauses: 6
% 6.69/1.38 # Negative unit clauses : 7
% 6.69/1.38 # Non-unit-clauses : 517
% 6.69/1.38 # Current number of unprocessed clauses: 69420
% 6.69/1.38 # ...number of literals in the above : 104298
% 6.69/1.38 # Current number of archived formulas : 0
% 6.69/1.38 # Current number of archived clauses : 247
% 6.69/1.38 # Clause-clause subsumption calls (NU) : 105904
% 6.69/1.38 # Rec. Clause-clause subsumption calls : 105820
% 6.69/1.38 # Non-unit clause-clause subsumptions : 6007
% 6.69/1.38 # Unit Clause-clause subsumption calls : 4568
% 6.69/1.38 # Rewrite failures with RHS unbound : 40
% 6.69/1.38 # BW rewrite match attempts : 12540
% 6.69/1.38 # BW rewrite match successes : 643
% 6.69/1.38 # Condensation attempts : 0
% 6.69/1.38 # Condensation successes : 0
% 6.69/1.38 # Termbank termtop insertions : 944459
% 6.69/1.38
% 6.69/1.38 # -------------------------------------------------
% 6.69/1.38 # User time : 0.790 s
% 6.69/1.38 # System time : 0.037 s
% 6.69/1.38 # Total time : 0.827 s
% 6.69/1.38 # Maximum resident set size: 2000 pages
% 6.69/1.38
% 6.69/1.38 # -------------------------------------------------
% 6.69/1.38 # User time : 3.837 s
% 6.69/1.38 # System time : 0.163 s
% 6.69/1.38 # Total time : 4.000 s
% 6.69/1.38 # Maximum resident set size: 1724 pages
% 6.69/1.38 % E---3.1 exiting
%------------------------------------------------------------------------------