TSTP Solution File: NUM461+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM461+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n005.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 09:32:40 EDT 2022
% Result : Theorem 0.21s 1.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 152 ( 74 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 189 ( 74 ~; 83 |; 27 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 22 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xm,xl),X1) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xl,xm),X1) = sdtpldt0(xn,xm) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddAsso) ).
fof(m__873,hypothesis,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__873) ).
fof(m__840,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__840) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddComm) ).
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__840_03,hypothesis,
( xl != xn
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xl,X1) = xn )
& sdtlseqdt0(xl,xn) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__840_03) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddCanc) ).
fof(c_0_8,negated_conjecture,
~ ( sdtpldt0(xm,xl) != sdtpldt0(xm,xn)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xm,xl),X1) = sdtpldt0(xm,xn) )
| sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn)) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtpldt0(xl,xm),X1) = sdtpldt0(xn,xm) )
| sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm)) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,negated_conjecture,
! [X2,X3] :
( ( ~ aNaturalNumber0(X3)
| sdtpldt0(sdtpldt0(xl,xm),X3) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
& ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X2)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
& ( ~ aNaturalNumber0(X3)
| sdtpldt0(sdtpldt0(xl,xm),X3) != sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) )
& ( ~ sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ~ sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ) ),
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)],[c_0_8])])])])])]) ).
fof(c_0_10,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_11,negated_conjecture,
( sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(xl,xm),X2) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__873]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xl),
inference(split_conjunct,[status(thm)],[m__840]) ).
fof(c_0_15,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_16,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_17,negated_conjecture,
( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xl,sdtpldt0(xm,X1)) != sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_18,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(xl,sdtpldt0(X1,xm)) != sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13])]) ).
cnf(c_0_21,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_19]) ).
fof(c_0_22,hypothesis,
( xl != xn
& aNaturalNumber0(esk1_0)
& sdtpldt0(xl,esk1_0) = xn
& sdtlseqdt0(xl,xn) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__840_03])])])]) ).
cnf(c_0_23,negated_conjecture,
( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X2) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13]),c_0_14])]) ).
cnf(c_0_24,hypothesis,
sdtpldt0(xl,esk1_0) = xn,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_27,hypothesis,
( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_12]),c_0_14]),c_0_13])]) ).
cnf(c_0_28,hypothesis,
( sdtpldt0(xm,xn) = sdtpldt0(xm,xl)
| sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25])]) ).
cnf(c_0_29,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__840]) ).
fof(c_0_30,plain,
! [X4,X5,X6] :
( ( sdtpldt0(X4,X5) != sdtpldt0(X4,X6)
| X5 = X6
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtpldt0(X5,X4) != sdtpldt0(X6,X4)
| X5 = X6
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_31,hypothesis,
( sdtpldt0(xn,xm) = sdtpldt0(xl,xm)
| sdtpldt0(xm,xl) = sdtpldt0(xn,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_29]),c_0_13])]) ).
cnf(c_0_32,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,hypothesis,
sdtpldt0(xn,xm) = sdtpldt0(xl,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_14]),c_0_13])]) ).
cnf(c_0_34,hypothesis,
( X1 = xn
| sdtpldt0(X1,xm) != sdtpldt0(xl,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_13]),c_0_29])]) ).
cnf(c_0_35,hypothesis,
xl != xn,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_14])]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM461+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Tue Jul 5 18:49:37 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.21/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.40 # Preprocessing time : 0.017 s
% 0.21/1.40
% 0.21/1.40 # Proof found!
% 0.21/1.40 # SZS status Theorem
% 0.21/1.40 # SZS output start CNFRefutation
% See solution above
% 0.21/1.40 # Proof object total steps : 37
% 0.21/1.40 # Proof object clause steps : 22
% 0.21/1.40 # Proof object formula steps : 15
% 0.21/1.40 # Proof object conjectures : 7
% 0.21/1.40 # Proof object clause conjectures : 4
% 0.21/1.40 # Proof object formula conjectures : 3
% 0.21/1.40 # Proof object initial clauses used : 11
% 0.21/1.40 # Proof object initial formulas used : 8
% 0.21/1.40 # Proof object generating inferences : 11
% 0.21/1.40 # Proof object simplifying inferences : 28
% 0.21/1.40 # Training examples: 0 positive, 0 negative
% 0.21/1.40 # Parsed axioms : 27
% 0.21/1.40 # Removed by relevancy pruning/SinE : 3
% 0.21/1.40 # Initial clauses : 40
% 0.21/1.40 # Removed in clause preprocessing : 1
% 0.21/1.40 # Initial clauses in saturation : 39
% 0.21/1.40 # Processed clauses : 303
% 0.21/1.40 # ...of these trivial : 2
% 0.21/1.40 # ...subsumed : 140
% 0.21/1.40 # ...remaining for further processing : 161
% 0.21/1.40 # Other redundant clauses eliminated : 6
% 0.21/1.40 # Clauses deleted for lack of memory : 0
% 0.21/1.40 # Backward-subsumed : 13
% 0.21/1.40 # Backward-rewritten : 20
% 0.21/1.40 # Generated clauses : 1798
% 0.21/1.40 # ...of the previous two non-trivial : 1630
% 0.21/1.40 # Contextual simplify-reflections : 32
% 0.21/1.40 # Paramodulations : 1783
% 0.21/1.40 # Factorizations : 0
% 0.21/1.40 # Equation resolutions : 15
% 0.21/1.40 # Current number of processed clauses : 127
% 0.21/1.40 # Positive orientable unit clauses : 21
% 0.21/1.40 # Positive unorientable unit clauses: 0
% 0.21/1.40 # Negative unit clauses : 4
% 0.21/1.40 # Non-unit-clauses : 102
% 0.21/1.40 # Current number of unprocessed clauses: 1120
% 0.21/1.40 # ...number of literals in the above : 5120
% 0.21/1.40 # Current number of archived formulas : 0
% 0.21/1.40 # Current number of archived clauses : 33
% 0.21/1.40 # Clause-clause subsumption calls (NU) : 3049
% 0.21/1.40 # Rec. Clause-clause subsumption calls : 822
% 0.21/1.40 # Non-unit clause-clause subsumptions : 174
% 0.21/1.40 # Unit Clause-clause subsumption calls : 83
% 0.21/1.40 # Rewrite failures with RHS unbound : 0
% 0.21/1.40 # BW rewrite match attempts : 7
% 0.21/1.40 # BW rewrite match successes : 2
% 0.21/1.40 # Condensation attempts : 0
% 0.21/1.40 # Condensation successes : 0
% 0.21/1.40 # Termbank termtop insertions : 33712
% 0.21/1.40
% 0.21/1.40 # -------------------------------------------------
% 0.21/1.40 # User time : 0.100 s
% 0.21/1.40 # System time : 0.001 s
% 0.21/1.40 # Total time : 0.101 s
% 0.21/1.40 # Maximum resident set size: 4384 pages
%------------------------------------------------------------------------------