TSTP Solution File: ALG202+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% 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 : 600s
% DateTime : Thu Jul 14 16:50:17 EDT 2022
% Result : Theorem 0.12s 1.32s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 78 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 87 ( 30 ~; 21 |; 14 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',co1) ).
fof(ax2,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax2) ).
fof(ax4,axiom,
~ ! [X1] :
( sorti2(X1)
=> op2(X1,X1) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax4) ).
fof(ax3,axiom,
! [X1] :
( sorti1(X1)
=> op1(X1,X1) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ax3) ).
fof(c_0_4,negated_conjecture,
~ ( ( ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) )
& ! [X2] :
( sorti2(X2)
=> sorti1(j(X2)) ) )
=> ~ ( ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
& ! [X5] :
( sorti2(X5)
=> ! [X6] :
( sorti2(X6)
=> j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
& ! [X7] :
( sorti2(X7)
=> h(j(X7)) = X7 )
& ! [X8] :
( sorti1(X8)
=> j(h(X8)) = X8 ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_5,negated_conjecture,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( ~ sorti1(X9)
| sorti2(h(X9)) )
& ( ~ sorti2(X10)
| sorti1(j(X10)) )
& ( ~ sorti1(X11)
| ~ sorti1(X12)
| h(op1(X11,X12)) = op2(h(X11),h(X12)) )
& ( ~ sorti2(X13)
| ~ sorti2(X14)
| j(op2(X13,X14)) = op1(j(X13),j(X14)) )
& ( ~ sorti2(X15)
| h(j(X15)) = X15 )
& ( ~ sorti1(X16)
| j(h(X16)) = X16 ) ),
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_4])])])])]) ).
fof(c_0_6,plain,
! [X3,X4] :
( ~ sorti2(X3)
| ~ sorti2(X4)
| sorti2(op2(X3,X4)) ),
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)],[ax2])])])])]) ).
fof(c_0_7,plain,
( sorti2(esk1_0)
& op2(esk1_0,esk1_0) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).
cnf(c_0_8,negated_conjecture,
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
op2(esk1_0,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( op2(X1,X2) = h(op1(j(X1),j(X2)))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_13,plain,
sorti2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,plain,
! [X2] :
( ~ sorti1(X2)
| op1(X2,X2) = X2 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])]) ).
cnf(c_0_15,negated_conjecture,
h(op1(j(esk1_0),j(esk1_0))) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,plain,
( op1(X1,X1) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( h(j(esk1_0)) != esk1_0
| ~ sorti1(j(esk1_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,negated_conjecture,
~ sorti1(j(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_8]),c_0_13])]) ).
cnf(c_0_19,negated_conjecture,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ALG202+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.08 % Command : run_ET %s %d
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Wed Jun 8 10:49:06 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.12/1.32 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.12/1.32 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.12/1.32 # Preprocessing time : 0.008 s
% 0.12/1.32
% 0.12/1.32 # Proof found!
% 0.12/1.32 # SZS status Theorem
% 0.12/1.32 # SZS output start CNFRefutation
% See solution above
% 0.12/1.32 # Proof object total steps : 21
% 0.12/1.32 # Proof object clause steps : 12
% 0.12/1.32 # Proof object formula steps : 9
% 0.12/1.32 # Proof object conjectures : 11
% 0.12/1.32 # Proof object clause conjectures : 8
% 0.12/1.32 # Proof object formula conjectures : 3
% 0.12/1.32 # Proof object initial clauses used : 7
% 0.12/1.32 # Proof object initial formulas used : 4
% 0.12/1.32 # Proof object generating inferences : 5
% 0.12/1.32 # Proof object simplifying inferences : 7
% 0.12/1.32 # Training examples: 0 positive, 0 negative
% 0.12/1.32 # Parsed axioms : 5
% 0.12/1.32 # Removed by relevancy pruning/SinE : 0
% 0.12/1.32 # Initial clauses : 11
% 0.12/1.32 # Removed in clause preprocessing : 0
% 0.12/1.32 # Initial clauses in saturation : 11
% 0.12/1.32 # Processed clauses : 24
% 0.12/1.32 # ...of these trivial : 0
% 0.12/1.32 # ...subsumed : 2
% 0.12/1.32 # ...remaining for further processing : 22
% 0.12/1.32 # Other redundant clauses eliminated : 0
% 0.12/1.32 # Clauses deleted for lack of memory : 0
% 0.12/1.32 # Backward-subsumed : 0
% 0.12/1.32 # Backward-rewritten : 0
% 0.12/1.32 # Generated clauses : 64
% 0.12/1.32 # ...of the previous two non-trivial : 54
% 0.12/1.32 # Contextual simplify-reflections : 8
% 0.12/1.32 # Paramodulations : 64
% 0.12/1.32 # Factorizations : 0
% 0.12/1.32 # Equation resolutions : 0
% 0.12/1.32 # Current number of processed clauses : 22
% 0.12/1.32 # Positive orientable unit clauses : 1
% 0.12/1.32 # Positive unorientable unit clauses: 0
% 0.12/1.32 # Negative unit clauses : 3
% 0.12/1.32 # Non-unit-clauses : 18
% 0.12/1.32 # Current number of unprocessed clauses: 41
% 0.12/1.32 # ...number of literals in the above : 179
% 0.12/1.32 # Current number of archived formulas : 0
% 0.12/1.32 # Current number of archived clauses : 0
% 0.12/1.32 # Clause-clause subsumption calls (NU) : 67
% 0.12/1.32 # Rec. Clause-clause subsumption calls : 67
% 0.12/1.32 # Non-unit clause-clause subsumptions : 10
% 0.12/1.32 # Unit Clause-clause subsumption calls : 1
% 0.12/1.32 # Rewrite failures with RHS unbound : 0
% 0.12/1.32 # BW rewrite match attempts : 0
% 0.12/1.32 # BW rewrite match successes : 0
% 0.12/1.32 # Condensation attempts : 0
% 0.12/1.32 # Condensation successes : 0
% 0.12/1.32 # Termbank termtop insertions : 1890
% 0.12/1.32
% 0.12/1.32 # -------------------------------------------------
% 0.12/1.32 # User time : 0.009 s
% 0.12/1.32 # System time : 0.000 s
% 0.12/1.32 # Total time : 0.009 s
% 0.12/1.32 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------