TSTP Solution File: ALG074+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.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 16:47:35 EDT 2022
% Result : Theorem 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 20 unt; 0 def)
% Number of atoms : 129 ( 47 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 130 ( 46 ~; 37 |; 25 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 34 !; 4 ?)
% 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',co1) ).
fof(ax3,axiom,
? [X1] :
( sorti1(X1)
& ? [X2] :
( sorti1(X2)
& op1(X2,X1) != op1(X1,X2)
& op1(op1(X1,X2),X2) = X1
& op1(op1(X1,X2),X1) != X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax3) ).
fof(ax1,axiom,
! [X1] :
( sorti1(X1)
=> ! [X2] :
( sorti1(X2)
=> sorti1(op1(X1,X2)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax1) ).
fof(ax2,axiom,
! [X1] :
( sorti2(X1)
=> ! [X2] :
( sorti2(X2)
=> sorti2(op2(X1,X2)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax2) ).
fof(ax4,axiom,
~ ? [X1] :
( sorti2(X1)
& ? [X2] :
( sorti2(X2)
& op2(X2,X1) != op2(X1,X2)
& op2(op2(X1,X2),X2) = X1
& op2(op2(X1,X2),X1) != X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',ax4) ).
fof(c_0_5,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_6,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_5])])])])]) ).
fof(c_0_7,plain,
( sorti1(esk1_0)
& sorti1(esk2_0)
& op1(esk2_0,esk1_0) != op1(esk1_0,esk2_0)
& op1(op1(esk1_0,esk2_0),esk2_0) = esk1_0
& op1(op1(esk1_0,esk2_0),esk1_0) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[ax3])])])]) ).
fof(c_0_8,plain,
! [X3,X4] :
( ~ sorti1(X3)
| ~ sorti1(X4)
| sorti1(op1(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)],[ax1])])])])]) ).
fof(c_0_9,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])])])])]) ).
cnf(c_0_10,negated_conjecture,
( sorti2(h(X1))
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
sorti1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( sorti1(op1(X1,X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( h(op1(X1,X2)) = op2(h(X1),h(X2))
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
sorti1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
( j(h(X1)) = X1
| ~ sorti1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( sorti2(op2(X1,X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
sorti2(h(esk2_0)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( sorti1(op1(X1,esk2_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( h(op1(X1,esk2_0)) = op2(h(X1),h(esk2_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( j(op2(X1,X2)) = op1(j(X1),j(X2))
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
sorti2(h(esk1_0)),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
j(h(esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( sorti2(op2(X1,h(esk2_0)))
| ~ sorti2(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
sorti1(op1(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_25,negated_conjecture,
h(op1(esk1_0,esk2_0)) = op2(h(esk1_0),h(esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
fof(c_0_26,plain,
! [X3,X4] :
( ~ sorti2(X3)
| ~ sorti2(X4)
| op2(X4,X3) = op2(X3,X4)
| op2(op2(X3,X4),X4) != X3
| op2(op2(X3,X4),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)],[ax4])])])])]) ).
cnf(c_0_27,plain,
op1(op1(esk1_0,esk2_0),esk2_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( j(op2(X1,h(esk1_0))) = op1(j(X1),esk1_0)
| ~ sorti2(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
sorti2(op2(h(esk1_0),h(esk2_0))),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_30,negated_conjecture,
j(op2(h(esk1_0),h(esk2_0))) = op1(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_25]) ).
cnf(c_0_31,plain,
( op2(op2(X1,X2),X1) = X2
| op2(X2,X1) = op2(X1,X2)
| op2(op2(X1,X2),X2) != X1
| ~ sorti2(X2)
| ~ sorti2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
op2(op2(h(esk1_0),h(esk2_0)),h(esk2_0)) = h(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_24]),c_0_27]),c_0_25]) ).
cnf(c_0_33,plain,
( sorti1(op1(X1,esk1_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( h(op1(X1,esk1_0)) = op2(h(X1),h(esk1_0))
| ~ sorti1(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_35,negated_conjecture,
j(op2(op2(h(esk1_0),h(esk2_0)),h(esk1_0))) = op1(op1(esk1_0,esk2_0),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( op2(h(esk1_0),h(esk2_0)) = op2(h(esk2_0),h(esk1_0))
| op2(op2(h(esk1_0),h(esk2_0)),h(esk1_0)) = h(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]),c_0_21])]) ).
cnf(c_0_37,negated_conjecture,
j(h(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_38,plain,
op1(op1(esk1_0,esk2_0),esk1_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_39,plain,
sorti1(op1(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_33,c_0_11]) ).
cnf(c_0_40,negated_conjecture,
h(op1(esk2_0,esk1_0)) = op2(h(esk2_0),h(esk1_0)),
inference(spm,[status(thm)],[c_0_34,c_0_11]) ).
cnf(c_0_41,negated_conjecture,
op2(h(esk1_0),h(esk2_0)) = op2(h(esk2_0),h(esk1_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_42,negated_conjecture,
j(op2(h(esk2_0),h(esk1_0))) = op1(esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_39]),c_0_40]) ).
cnf(c_0_43,plain,
op1(esk2_0,esk1_0) != op1(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_41]),c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.12 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 04:18:25 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.22/1.41 # Preprocessing time : 0.014 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 45
% 0.22/1.41 # Proof object clause steps : 34
% 0.22/1.41 # Proof object formula steps : 11
% 0.22/1.41 # Proof object conjectures : 25
% 0.22/1.41 # Proof object clause conjectures : 22
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 12
% 0.22/1.41 # Proof object initial formulas used : 5
% 0.22/1.41 # Proof object generating inferences : 21
% 0.22/1.41 # Proof object simplifying inferences : 14
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 5
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 14
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 14
% 0.22/1.41 # Processed clauses : 339
% 0.22/1.41 # ...of these trivial : 24
% 0.22/1.41 # ...subsumed : 22
% 0.22/1.41 # ...remaining for further processing : 293
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 0
% 0.22/1.41 # Backward-rewritten : 77
% 0.22/1.41 # Generated clauses : 6689
% 0.22/1.41 # ...of the previous two non-trivial : 6727
% 0.22/1.41 # Contextual simplify-reflections : 0
% 0.22/1.41 # Paramodulations : 6689
% 0.22/1.41 # Factorizations : 0
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 216
% 0.22/1.41 # Positive orientable unit clauses : 110
% 0.22/1.41 # Positive unorientable unit clauses: 0
% 0.22/1.41 # Negative unit clauses : 2
% 0.22/1.41 # Non-unit-clauses : 104
% 0.22/1.41 # Current number of unprocessed clauses: 4915
% 0.22/1.41 # ...number of literals in the above : 5001
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 77
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 1468
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 1468
% 0.22/1.41 # Non-unit clause-clause subsumptions : 22
% 0.22/1.41 # Unit Clause-clause subsumption calls : 121
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 692
% 0.22/1.41 # BW rewrite match successes : 15
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 132673
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.072 s
% 0.22/1.41 # System time : 0.004 s
% 0.22/1.41 # Total time : 0.076 s
% 0.22/1.41 # Maximum resident set size: 8064 pages
% 0.22/23.41 eprover: CPU time limit exceeded, terminating
% 0.22/23.41 eprover: CPU time limit exceeded, terminating
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------