TSTP Solution File: NUM490+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM490+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 09:33:00 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 22 unt; 0 def)
% Number of atoms : 143 ( 40 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 172 ( 76 ~; 70 |; 17 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 1 sgn 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefDiff) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMulComm) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAMDistr) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefLE) ).
fof(m__1951,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1951) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1837) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1883) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1870) ).
fof(m__,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB) ).
fof(m__1924,hypothesis,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1924) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).
fof(c_0_12,plain,
! [X4,X5,X6,X6] :
( ( aNaturalNumber0(X6)
| X6 != sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,X6) = X5
| X6 != sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| sdtpldt0(X4,X6) != X5
| X6 = sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])])]) ).
fof(c_0_13,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_14,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,sdtpldt0(X5,X6)) = sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtasdt0(sdtpldt0(X5,X6),X4) = sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_15,plain,
( aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| X3 != sdtmndt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk2_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,esk2_2(X4,X5)) = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| sdtpldt0(X4,X7) != X5
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])])]) ).
cnf(c_0_17,hypothesis,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1951]) ).
cnf(c_0_18,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_20,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_21,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
cnf(c_0_24,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_26,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_27,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_29,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_30,hypothesis,
sdtpldt0(sdtasdt0(xm,xp),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_31,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X3,X1)) = sdtasdt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_32,hypothesis,
xn = sdtpldt0(xp,xr),
inference(split_conjunct,[status(thm)],[m__1924]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_19]),c_0_25])]) ).
fof(c_0_34,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( X1 = sdtmndt0(X2,X3)
| sdtpldt0(X3,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_20]),c_0_19]),c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_36]) ).
cnf(c_0_40,hypothesis,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xm,xn),
inference(rw,[status(thm)],[c_0_17,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
sdtmndt0(sdtasdt0(xm,xn),sdtasdt0(xp,xm)) != sdtasdt0(xr,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_18]),c_0_25]),c_0_20])]) ).
fof(c_0_42,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_43,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_44,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,hypothesis,
~ aNaturalNumber0(sdtasdt0(xr,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_20]),c_0_19])]) ).
cnf(c_0_46,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_44]),c_0_20]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM490+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n018.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 : Tue Jul 5 11:44:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.019 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 47
% 0.24/1.42 # Proof object clause steps : 27
% 0.24/1.42 # Proof object formula steps : 20
% 0.24/1.42 # Proof object conjectures : 5
% 0.24/1.42 # Proof object clause conjectures : 2
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 15
% 0.24/1.42 # Proof object initial formulas used : 12
% 0.24/1.42 # Proof object generating inferences : 10
% 0.24/1.42 # Proof object simplifying inferences : 25
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 47
% 0.24/1.42 # Removed by relevancy pruning/SinE : 2
% 0.24/1.42 # Initial clauses : 79
% 0.24/1.42 # Removed in clause preprocessing : 3
% 0.24/1.42 # Initial clauses in saturation : 76
% 0.24/1.42 # Processed clauses : 2773
% 0.24/1.42 # ...of these trivial : 113
% 0.24/1.42 # ...subsumed : 1800
% 0.24/1.42 # ...remaining for further processing : 860
% 0.24/1.42 # Other redundant clauses eliminated : 50
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 100
% 0.24/1.42 # Backward-rewritten : 148
% 0.24/1.42 # Generated clauses : 25204
% 0.24/1.42 # ...of the previous two non-trivial : 23323
% 0.24/1.42 # Contextual simplify-reflections : 481
% 0.24/1.42 # Paramodulations : 25123
% 0.24/1.42 # Factorizations : 1
% 0.24/1.42 # Equation resolutions : 80
% 0.24/1.42 # Current number of processed clauses : 611
% 0.24/1.42 # Positive orientable unit clauses : 131
% 0.24/1.42 # Positive unorientable unit clauses: 0
% 0.24/1.42 # Negative unit clauses : 52
% 0.24/1.42 # Non-unit-clauses : 428
% 0.24/1.42 # Current number of unprocessed clauses: 16231
% 0.24/1.42 # ...number of literals in the above : 79846
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 248
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 115740
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 55256
% 0.24/1.42 # Non-unit clause-clause subsumptions : 1456
% 0.24/1.42 # Unit Clause-clause subsumption calls : 4213
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 38
% 0.24/1.42 # BW rewrite match successes : 38
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 478270
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.426 s
% 0.24/1.42 # System time : 0.019 s
% 0.24/1.42 # Total time : 0.445 s
% 0.24/1.42 # Maximum resident set size: 19504 pages
%------------------------------------------------------------------------------