TSTP Solution File: LCL513+1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : LCL513+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n007.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 08:27:46 EDT 2024
% Result : Theorem 8.61s 1.62s
% Output : CNFRefutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of formulae : 133 ( 55 unt; 0 def)
% Number of atoms : 253 ( 22 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 220 ( 100 ~; 99 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 230 ( 37 sgn 36 !; 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.9vLVU8T1ht/E---3.1_18641.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.9vLVU8T1ht/E---3.1_18641.p',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.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.9vLVU8T1ht/E---3.1_18641.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.9vLVU8T1ht/E---3.1_18641.p',kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',rosser_modus_ponens) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',rosser_kn3) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',kn2) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',rosser_kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.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.9vLVU8T1ht/E---3.1_18641.p',op_equiv) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.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.9vLVU8T1ht/E---3.1_18641.p',substitution_of_equivalents) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',substitution_of_equivalents) ).
fof(hilbert_equivalence_2,conjecture,
equivalence_2,
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',hilbert_equivalence_2) ).
fof(equivalence_2,axiom,
( equivalence_2
<=> ! [X1,X2] : is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))) ),
file('/export/starexec/sandbox/tmp/tmp.9vLVU8T1ht/E---3.1_18641.p',equivalence_2) ).
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(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_48,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_49,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_51,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_52,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_54,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_55,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(and(X2,X2))) ),
inference(spm,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_56,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_25]),c_0_30]) ).
cnf(c_0_57,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(spm,[status(thm)],[c_0_57,c_0_25]) ).
cnf(c_0_60,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_58]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_62,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_50,c_0_25]) ).
cnf(c_0_63,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(and(X1,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_61]) ).
cnf(c_0_64,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_65,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_62]) ).
cnf(c_0_66,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,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_68,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,not(X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(and(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_65,c_0_52]) ).
cnf(c_0_70,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,not(X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_66]) ).
cnf(c_0_71,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_67]) ).
cnf(c_0_72,plain,
is_a_theorem(not(and(X1,and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X3)))
| ~ is_a_theorem(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_30]),c_0_25]) ).
cnf(c_0_74,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_71,c_0_25]),c_0_30]) ).
cnf(c_0_75,plain,
( is_a_theorem(not(and(and(not(X1),X1),X2)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_72]) ).
cnf(c_0_76,plain,
( is_a_theorem(implies(X1,not(not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_49]) ).
cnf(c_0_77,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_78,plain,
( is_a_theorem(or(and(X1,X1),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_46]) ).
cnf(c_0_79,plain,
( is_a_theorem(not(and(and(not(X1),X1),X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
is_a_theorem(or(and(X1,implies(X2,X3)),and(implies(X1,and(X2,not(X3))),implies(X1,and(X2,not(X3)))))),
inference(spm,[status(thm)],[c_0_48,c_0_77]) ).
cnf(c_0_81,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_78]) ).
cnf(c_0_82,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_77,c_0_30]) ).
cnf(c_0_83,plain,
is_a_theorem(not(and(and(not(X1),X1),X2))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_51]) ).
cnf(c_0_85,plain,
is_a_theorem(not(and(not(X1),or(X1,X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_82]) ).
cnf(c_0_86,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,and(not(X3),X3))) ),
inference(spm,[status(thm)],[c_0_71,c_0_83]) ).
cnf(c_0_87,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_84,c_0_48]),c_0_25]),c_0_30]) ).
cnf(c_0_88,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_71,c_0_85]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_86,c_0_49]) ).
cnf(c_0_90,plain,
( is_a_theorem(implies(and(X1,X2),and(X3,X1)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_91,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(and(X1,X1),X1)) ),
inference(spm,[status(thm)],[c_0_87,c_0_78]) ).
cnf(c_0_92,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_88,c_0_49]) ).
cnf(c_0_93,plain,
is_a_theorem(implies(X1,or(not(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_25]),c_0_30]) ).
cnf(c_0_94,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_90]) ).
cnf(c_0_95,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_91,c_0_78]) ).
cnf(c_0_96,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_92]) ).
cnf(c_0_97,plain,
is_a_theorem(or(X1,or(not(X2),X2))),
inference(spm,[status(thm)],[c_0_93,c_0_30]) ).
fof(c_0_98,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_99,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_94,c_0_95]) ).
cnf(c_0_100,plain,
is_a_theorem(not(not(or(not(X1),X1)))),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_102,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_103,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(not(X3),X3))) ),
inference(spm,[status(thm)],[c_0_74,c_0_69]) ).
fof(c_0_104,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_105,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(or(X2,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_61]) ).
cnf(c_0_106,plain,
is_a_theorem(or(or(not(X1),X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_100]),c_0_30]) ).
cnf(c_0_107,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102])]) ).
cnf(c_0_108,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_74,c_0_30]) ).
cnf(c_0_109,plain,
is_a_theorem(or(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_103,c_0_49]) ).
cnf(c_0_110,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_111,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_112,plain,
( is_a_theorem(and(X1,or(not(X2),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_107,c_0_30]) ).
cnf(c_0_114,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(not(X3),X3),X1)) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
fof(c_0_115,negated_conjecture,
~ equivalence_2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_equivalence_2])]) ).
cnf(c_0_116,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
cnf(c_0_117,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_58])]) ).
cnf(c_0_118,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_114,c_0_67]) ).
fof(c_0_119,plain,
! [X63,X64] :
( ( ~ equivalence_2
| is_a_theorem(implies(equiv(X63,X64),implies(X64,X63))) )
& ( ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))
| equivalence_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])])]) ).
fof(c_0_120,negated_conjecture,
~ equivalence_2,
inference(fof_nnf,[status(thm)],[c_0_115]) ).
cnf(c_0_121,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,plain,
is_a_theorem(or(implies(X1,not(not(X1))),X2)),
inference(spm,[status(thm)],[c_0_118,c_0_49]) ).
cnf(c_0_123,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0))) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_124,negated_conjecture,
~ equivalence_2,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_125,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_108,c_0_50]) ).
cnf(c_0_126,plain,
( is_a_theorem(or(and(X1,implies(X2,X3)),not(equiv(X2,X3))))
| ~ is_a_theorem(implies(implies(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_107]) ).
cnf(c_0_127,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_121]) ).
cnf(c_0_128,plain,
is_a_theorem(not(not(implies(X1,not(not(X1)))))),
inference(spm,[status(thm)],[c_0_96,c_0_122]) ).
cnf(c_0_129,plain,
~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0))),
inference(sr,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_130,plain,
( is_a_theorem(implies(equiv(X1,X2),X3))
| ~ is_a_theorem(implies(implies(X2,X1),X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_131,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_121]),c_0_121]) ).
cnf(c_0_132,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL513+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 08:51:50 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.48 Running first-order model finding
% 0.21/0.48 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.9vLVU8T1ht/E---3.1_18641.p
% 8.61/1.62 # Version: 3.1.0
% 8.61/1.62 # Preprocessing class: FSMSSLSSSSSNFFN.
% 8.61/1.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.61/1.62 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 8.61/1.62 # Starting new_bool_3 with 300s (1) cores
% 8.61/1.62 # Starting new_bool_1 with 300s (1) cores
% 8.61/1.62 # Starting sh5l with 300s (1) cores
% 8.61/1.62 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 18773 completed with status 0
% 8.61/1.62 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 8.61/1.62 # Preprocessing class: FSMSSLSSSSSNFFN.
% 8.61/1.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.61/1.62 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 8.61/1.62 # No SInE strategy applied
% 8.61/1.62 # Search class: FGUSF-FFMM21-MFFFFFNN
% 8.61/1.62 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.61/1.62 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 8.61/1.62 # Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 8.61/1.62 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 8.61/1.62 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.61/1.62 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 151s (1) cores
% 8.61/1.62 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 18793 completed with status 0
% 8.61/1.62 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 8.61/1.62 # Preprocessing class: FSMSSLSSSSSNFFN.
% 8.61/1.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.61/1.62 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 8.61/1.62 # No SInE strategy applied
% 8.61/1.62 # Search class: FGUSF-FFMM21-MFFFFFNN
% 8.61/1.62 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.61/1.62 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 8.61/1.62 # Preprocessing time : 0.003 s
% 8.61/1.62 # Presaturation interreduction done
% 8.61/1.62
% 8.61/1.62 # Proof found!
% 8.61/1.62 # SZS status Theorem
% 8.61/1.62 # SZS output start CNFRefutation
% See solution above
% 8.61/1.62 # Parsed axioms : 43
% 8.61/1.62 # Removed by relevancy pruning/SinE : 0
% 8.61/1.62 # Initial clauses : 72
% 8.61/1.62 # Removed in clause preprocessing : 0
% 8.61/1.62 # Initial clauses in saturation : 72
% 8.61/1.62 # Processed clauses : 10698
% 8.61/1.62 # ...of these trivial : 408
% 8.61/1.62 # ...subsumed : 8182
% 8.61/1.62 # ...remaining for further processing : 2108
% 8.61/1.62 # Other redundant clauses eliminated : 0
% 8.61/1.62 # Clauses deleted for lack of memory : 0
% 8.61/1.62 # Backward-subsumed : 367
% 8.61/1.62 # Backward-rewritten : 410
% 8.61/1.62 # Generated clauses : 87305
% 8.61/1.62 # ...of the previous two non-redundant : 80485
% 8.61/1.62 # ...aggressively subsumed : 0
% 8.61/1.62 # Contextual simplify-reflections : 1
% 8.61/1.62 # Paramodulations : 87305
% 8.61/1.62 # Factorizations : 0
% 8.61/1.62 # NegExts : 0
% 8.61/1.62 # Equation resolutions : 0
% 8.61/1.62 # Disequality decompositions : 0
% 8.61/1.62 # Total rewrite steps : 67698
% 8.61/1.62 # ...of those cached : 57666
% 8.61/1.62 # Propositional unsat checks : 0
% 8.61/1.62 # Propositional check models : 0
% 8.61/1.62 # Propositional check unsatisfiable : 0
% 8.61/1.62 # Propositional clauses : 0
% 8.61/1.62 # Propositional clauses after purity: 0
% 8.61/1.62 # Propositional unsat core size : 0
% 8.61/1.62 # Propositional preprocessing time : 0.000
% 8.61/1.62 # Propositional encoding time : 0.000
% 8.61/1.62 # Propositional solver time : 0.000
% 8.61/1.62 # Success case prop preproc time : 0.000
% 8.61/1.62 # Success case prop encoding time : 0.000
% 8.61/1.62 # Success case prop solver time : 0.000
% 8.61/1.62 # Current number of processed clauses : 1272
% 8.61/1.62 # Positive orientable unit clauses : 263
% 8.61/1.62 # Positive unorientable unit clauses: 3
% 8.61/1.62 # Negative unit clauses : 9
% 8.61/1.62 # Non-unit-clauses : 997
% 8.61/1.62 # Current number of unprocessed clauses: 65768
% 8.61/1.62 # ...number of literals in the above : 141280
% 8.61/1.62 # Current number of archived formulas : 0
% 8.61/1.62 # Current number of archived clauses : 836
% 8.61/1.62 # Clause-clause subsumption calls (NU) : 161870
% 8.61/1.62 # Rec. Clause-clause subsumption calls : 156825
% 8.61/1.62 # Non-unit clause-clause subsumptions : 8420
% 8.61/1.62 # Unit Clause-clause subsumption calls : 9651
% 8.61/1.62 # Rewrite failures with RHS unbound : 0
% 8.61/1.62 # BW rewrite match attempts : 3962
% 8.61/1.62 # BW rewrite match successes : 278
% 8.61/1.62 # Condensation attempts : 0
% 8.61/1.62 # Condensation successes : 0
% 8.61/1.62 # Termbank termtop insertions : 1435355
% 8.61/1.62 # Search garbage collected termcells : 1095
% 8.61/1.62
% 8.61/1.62 # -------------------------------------------------
% 8.61/1.62 # User time : 1.041 s
% 8.61/1.62 # System time : 0.049 s
% 8.61/1.62 # Total time : 1.090 s
% 8.61/1.62 # Maximum resident set size: 1944 pages
% 8.61/1.62
% 8.61/1.62 # -------------------------------------------------
% 8.61/1.62 # User time : 5.208 s
% 8.61/1.62 # System time : 0.313 s
% 8.61/1.62 # Total time : 5.520 s
% 8.61/1.62 # Maximum resident set size: 1736 pages
% 8.61/1.62 % E---3.1 exiting
%------------------------------------------------------------------------------