TSTP Solution File: LCL500+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n014.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 : 600s
% DateTime : Sun Jul 17 09:26:26 EDT 2022
% Result : Theorem 9.66s 2.59s
% Output : CNFRefutation 9.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 67 ( 34 unt; 0 def)
% Number of atoms : 123 ( 17 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 96 ( 40 ~; 38 |; 8 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 97 ( 6 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
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/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(rosser_kn2,conjecture,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(c_0_18,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])])])])]) ).
fof(c_0_19,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])])])]) ).
cnf(c_0_20,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_22,plain,
( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
| ~ r5 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
cnf(c_0_24,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_20,c_0_21])]) ).
cnf(c_0_25,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_22,c_0_23])]) ).
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])])]) ).
cnf(c_0_27,plain,
( is_a_theorem(implies(or(X1,X2),or(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
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,
! [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])])])]) ).
fof(c_0_31,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])])])]) ).
fof(c_0_32,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_33,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(spm,[status(thm)],[c_0_24,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,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_37,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
fof(c_0_39,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_40,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_45,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_47,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
fof(c_0_48,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])])]) ).
fof(c_0_49,negated_conjecture,
~ kn2,
inference(assume_negation,[status(cth)],[rosser_kn2]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(or(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_52,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_53,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
fof(c_0_55,plain,
! [X73,X74] :
( ( ~ kn2
| is_a_theorem(implies(and(X73,X74),X73)) )
& ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])]) ).
fof(c_0_56,negated_conjecture,
~ kn2,
inference(fof_simplification,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_58,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_59,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_34]),c_0_54])]) ).
cnf(c_0_60,plain,
( kn2
| ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
~ kn2,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_64,plain,
~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)),
inference(sr,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL500+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 06:16:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42 # ENIGMATIC: Selected SinE mode:
% 0.20/0.43 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.20/0.43 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.20/0.43 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 9.66/2.59 # ENIGMATIC: Solved by autoschedule:
% 9.66/2.59 # No SInE strategy applied
% 9.66/2.59 # Trying AutoSched0 for 150 seconds
% 9.66/2.59 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 9.66/2.59 # and selection function SelectComplexExceptUniqMaxHorn.
% 9.66/2.59 #
% 9.66/2.59 # Preprocessing time : 0.029 s
% 9.66/2.59 # Presaturation interreduction done
% 9.66/2.59
% 9.66/2.59 # Proof found!
% 9.66/2.59 # SZS status Theorem
% 9.66/2.59 # SZS output start CNFRefutation
% See solution above
% 9.66/2.59 # Training examples: 0 positive, 0 negative
% 9.66/2.59
% 9.66/2.59 # -------------------------------------------------
% 9.66/2.59 # User time : 0.092 s
% 9.66/2.59 # System time : 0.015 s
% 9.66/2.59 # Total time : 0.107 s
% 9.66/2.59 # Maximum resident set size: 7124 pages
% 9.66/2.59
%------------------------------------------------------------------------------