TSTP Solution File: LCL505+1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : LCL505+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:19:04 EDT 2024
% Result : Theorem 165.94s 21.85s
% Output : CNFRefutation 165.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 18
% Syntax : Number of formulae : 132 ( 57 unt; 0 def)
% Number of atoms : 254 ( 28 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 224 ( 102 ~; 101 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 229 ( 24 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',op_implies_and) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_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.jBNB844cRs/E---3.1_31355.p',modus_ponens) ).
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/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_modus_ponens) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_kn3) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',kn2) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_kn1) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',op_equiv) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',rosser_op_equiv) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',substitution_of_equivalents) ).
fof(substitution_of_equivalents_0001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',substitution_of_equivalents_0001) ).
fof(hilbert_implies_3,conjecture,
implies_3,
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',hilbert_implies_3) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
file('/export/starexec/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p',implies_3) ).
fof(c_0_18,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
fof(c_0_19,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_20,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_22,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])]) ).
fof(c_0_23,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])]) ).
cnf(c_0_24,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_26,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_27,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_29,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_23]) ).
cnf(c_0_30,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_32,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_27,c_0_28])]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_34,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_35,plain,
( is_a_theorem(or(and(X1,X2),not(and(X2,X3))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_36,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(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])]) ).
cnf(c_0_37,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(and(X3,X1)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
fof(c_0_40,plain,
! [X71] :
( ( ~ kn1
| is_a_theorem(implies(X71,and(X71,X71))) )
& ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])]) ).
cnf(c_0_41,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_45,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X2,and(X1,X3))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_47,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_30]) ).
cnf(c_0_48,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(and(X3,X1)))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_47]) ).
cnf(c_0_50,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(X1,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_30]),c_0_25]),c_0_30]) ).
cnf(c_0_51,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_25]),c_0_30]) ).
cnf(c_0_52,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(or(X2,X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_25]),c_0_30]) ).
cnf(c_0_53,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( is_a_theorem(or(and(X1,X1),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_55,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
cnf(c_0_56,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_57,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(and(X2,X2)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_54]) ).
cnf(c_0_58,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_53]) ).
cnf(c_0_59,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
cnf(c_0_60,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_55,c_0_30]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
cnf(c_0_62,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_25]),c_0_30]) ).
cnf(c_0_65,plain,
is_a_theorem(not(and(not(X1),or(X1,X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_60]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(and(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_61,c_0_48]) ).
cnf(c_0_67,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_25]),c_0_30]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_69,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_65]) ).
cnf(c_0_70,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(not(X3),X3))) ),
inference(spm,[status(thm)],[c_0_52,c_0_66]) ).
cnf(c_0_71,plain,
( is_a_theorem(implies(and(X1,X2),and(X3,X1)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_72,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(and(X1,X1),X1)) ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_73,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_69,c_0_51]) ).
cnf(c_0_75,plain,
is_a_theorem(or(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_70,c_0_51]) ).
cnf(c_0_76,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_71]) ).
cnf(c_0_77,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_72,c_0_54]) ).
cnf(c_0_78,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_73]),c_0_30]) ).
cnf(c_0_79,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_74]) ).
cnf(c_0_80,plain,
is_a_theorem(or(X1,or(not(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_25]),c_0_30]) ).
fof(c_0_81,plain,
! [X125,X126] :
( ~ op_equiv
| equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
cnf(c_0_82,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_78]) ).
cnf(c_0_84,plain,
is_a_theorem(not(not(or(not(X1),X1)))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
fof(c_0_87,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(fof_nnf,[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_88,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(or(X2,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_89,plain,
is_a_theorem(or(or(not(X1),X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_84]),c_0_30]) ).
cnf(c_0_90,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]) ).
cnf(c_0_91,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_92,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents_0001]) ).
cnf(c_0_93,plain,
( is_a_theorem(and(X1,or(not(X2),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_90,c_0_30]) ).
cnf(c_0_95,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,not(X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_30]) ).
cnf(c_0_96,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_97,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_68])]) ).
cnf(c_0_98,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_53]) ).
cnf(c_0_99,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,plain,
is_a_theorem(or(implies(and(X1,X2),X3),X1)),
inference(spm,[status(thm)],[c_0_98,c_0_56]) ).
cnf(c_0_101,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_25,c_0_99]) ).
cnf(c_0_102,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(implies(and(X1,X2),X3))) ),
inference(spm,[status(thm)],[c_0_34,c_0_100]) ).
cnf(c_0_103,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_99,c_0_101]) ).
cnf(c_0_104,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_105,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(and(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_106,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_104]) ).
cnf(c_0_107,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,and(X1,X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_108,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_107,c_0_71]) ).
cnf(c_0_109,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_108,c_0_77]) ).
cnf(c_0_110,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_99]) ).
cnf(c_0_111,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,not(X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_30]),c_0_110]) ).
cnf(c_0_112,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_111,c_0_66]) ).
cnf(c_0_113,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_114,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_78]) ).
cnf(c_0_115,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_99]),c_0_113]) ).
cnf(c_0_116,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_30]) ).
cnf(c_0_117,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_114,c_0_90]) ).
cnf(c_0_118,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X2,not(X2)),X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_30]) ).
cnf(c_0_119,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_116,c_0_30]),c_0_113]) ).
fof(c_0_120,negated_conjecture,
~ implies_3,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_3])]) ).
cnf(c_0_121,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_117]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_30]) ).
fof(c_0_123,plain,
! [X27,X28,X29] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X27,X28),implies(implies(X28,X29),implies(X27,X29)))) )
& ( ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))
| implies_3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])]) ).
fof(c_0_124,negated_conjecture,
~ implies_3,
inference(fof_nnf,[status(thm)],[c_0_120]) ).
cnf(c_0_125,plain,
or(X1,X2) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_122])]) ).
cnf(c_0_126,plain,
( implies_3
| ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_127,negated_conjecture,
~ implies_3,
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_128,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_110,c_0_125]) ).
cnf(c_0_129,plain,
~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0)))),
inference(sr,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_130,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_110]),c_0_128]) ).
cnf(c_0_131,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LCL505+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri May 3 08:58:24 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.jBNB844cRs/E---3.1_31355.p
% 165.94/21.85 # Version: 3.1.0
% 165.94/21.85 # Preprocessing class: FSMSSLSSSSSNFFN.
% 165.94/21.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 165.94/21.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 165.94/21.85 # Starting new_bool_3 with 300s (1) cores
% 165.94/21.85 # Starting new_bool_1 with 300s (1) cores
% 165.94/21.85 # Starting sh5l with 300s (1) cores
% 165.94/21.85 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 31509 completed with status 0
% 165.94/21.85 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 165.94/21.85 # Preprocessing class: FSMSSLSSSSSNFFN.
% 165.94/21.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 165.94/21.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 165.94/21.85 # No SInE strategy applied
% 165.94/21.85 # Search class: FGUSF-FFMM21-MFFFFFNN
% 165.94/21.85 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 165.94/21.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 165.94/21.85 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 165.94/21.85 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 165.94/21.85 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 165.94/21.85 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 165.94/21.85 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 31526 completed with status 0
% 165.94/21.85 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 165.94/21.85 # Preprocessing class: FSMSSLSSSSSNFFN.
% 165.94/21.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 165.94/21.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 165.94/21.85 # No SInE strategy applied
% 165.94/21.85 # Search class: FGUSF-FFMM21-MFFFFFNN
% 165.94/21.85 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 165.94/21.85 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 165.94/21.85 # Preprocessing time : 0.002 s
% 165.94/21.85 # Presaturation interreduction done
% 165.94/21.85
% 165.94/21.85 # Proof found!
% 165.94/21.85 # SZS status Theorem
% 165.94/21.85 # SZS output start CNFRefutation
% See solution above
% 165.94/21.85 # Parsed axioms : 43
% 165.94/21.85 # Removed by relevancy pruning/SinE : 0
% 165.94/21.85 # Initial clauses : 72
% 165.94/21.85 # Removed in clause preprocessing : 0
% 165.94/21.85 # Initial clauses in saturation : 72
% 165.94/21.85 # Processed clauses : 58009
% 165.94/21.85 # ...of these trivial : 2160
% 165.94/21.85 # ...subsumed : 50396
% 165.94/21.85 # ...remaining for further processing : 5453
% 165.94/21.85 # Other redundant clauses eliminated : 0
% 165.94/21.85 # Clauses deleted for lack of memory : 0
% 165.94/21.85 # Backward-subsumed : 684
% 165.94/21.85 # Backward-rewritten : 1443
% 165.94/21.85 # Generated clauses : 1061308
% 165.94/21.85 # ...of the previous two non-redundant : 984628
% 165.94/21.85 # ...aggressively subsumed : 0
% 165.94/21.85 # Contextual simplify-reflections : 4
% 165.94/21.85 # Paramodulations : 1061308
% 165.94/21.85 # Factorizations : 0
% 165.94/21.85 # NegExts : 0
% 165.94/21.85 # Equation resolutions : 0
% 165.94/21.85 # Disequality decompositions : 0
% 165.94/21.85 # Total rewrite steps : 906559
% 165.94/21.85 # ...of those cached : 853821
% 165.94/21.85 # Propositional unsat checks : 1
% 165.94/21.85 # Propositional check models : 0
% 165.94/21.85 # Propositional check unsatisfiable : 0
% 165.94/21.85 # Propositional clauses : 0
% 165.94/21.85 # Propositional clauses after purity: 0
% 165.94/21.85 # Propositional unsat core size : 0
% 165.94/21.85 # Propositional preprocessing time : 0.000
% 165.94/21.85 # Propositional encoding time : 2.090
% 165.94/21.85 # Propositional solver time : 0.901
% 165.94/21.85 # Success case prop preproc time : 0.000
% 165.94/21.85 # Success case prop encoding time : 0.000
% 165.94/21.85 # Success case prop solver time : 0.000
% 165.94/21.85 # Current number of processed clauses : 3267
% 165.94/21.85 # Positive orientable unit clauses : 517
% 165.94/21.85 # Positive unorientable unit clauses: 6
% 165.94/21.85 # Negative unit clauses : 7
% 165.94/21.85 # Non-unit-clauses : 2737
% 165.94/21.85 # Current number of unprocessed clauses: 905670
% 165.94/21.85 # ...number of literals in the above : 2026623
% 165.94/21.85 # Current number of archived formulas : 0
% 165.94/21.85 # Current number of archived clauses : 2186
% 165.94/21.85 # Clause-clause subsumption calls (NU) : 1609904
% 165.94/21.85 # Rec. Clause-clause subsumption calls : 1504598
% 165.94/21.85 # Non-unit clause-clause subsumptions : 48328
% 165.94/21.85 # Unit Clause-clause subsumption calls : 41775
% 165.94/21.85 # Rewrite failures with RHS unbound : 0
% 165.94/21.85 # BW rewrite match attempts : 33382
% 165.94/21.85 # BW rewrite match successes : 3310
% 165.94/21.85 # Condensation attempts : 0
% 165.94/21.85 # Condensation successes : 0
% 165.94/21.85 # Termbank termtop insertions : 33283640
% 165.94/21.85 # Search garbage collected termcells : 1095
% 165.94/21.85
% 165.94/21.85 # -------------------------------------------------
% 165.94/21.85 # User time : 18.434 s
% 165.94/21.85 # System time : 0.684 s
% 165.94/21.85 # Total time : 19.118 s
% 165.94/21.85 # Maximum resident set size: 2000 pages
% 165.94/21.85
% 165.94/21.85 # -------------------------------------------------
% 165.94/21.85 # User time : 99.835 s
% 165.94/21.85 # System time : 3.677 s
% 165.94/21.85 # Total time : 103.512 s
% 165.94/21.85 # Maximum resident set size: 1736 pages
% 165.94/21.85 % E---3.1 exiting
% 165.94/21.85 % E exiting
%------------------------------------------------------------------------------