TSTP Solution File: NUM926+5 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n025.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 09:37:54 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 26 unt; 0 def)
% Number of atoms : 70 ( 39 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 51 ( 23 ~; 20 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 52 ( 4 sgn 28 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( t = one_one(int)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
( ord_less(int,one_one(int),t)
=> ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_37_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_37_nat__1__add__1) ).
fof(fact_54_Numeral1__eq1__nat,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_54_Numeral1__eq1__nat) ).
fof(fact_34_zpower__zadd__distrib,axiom,
! [X8,X9,X15] : power_power(int,X8,plus_plus(nat,X9,X15)) = times_times(int,power_power(int,X8,X9),power_power(int,X8,X15)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_34_zpower__zadd__distrib) ).
fof(fact_86_number__of__is__id,axiom,
! [X18] : number_number_of(int,X18) = X18,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_86_number__of__is__id) ).
fof(fact_85_zmult__commute,axiom,
! [X15,X11] : times_times(int,X15,X11) = times_times(int,X11,X15),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_85_zmult__commute) ).
fof(fact_25_zle__antisym,axiom,
! [X15,X11] :
( ord_less_eq(int,X15,X11)
=> ( ord_less_eq(int,X11,X15)
=> X15 = X11 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_25_zle__antisym) ).
fof(fact_0_tpos,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_0_tpos) ).
fof(fact_22_zless__le,axiom,
! [X16,X17] :
( ord_less(int,X16,X17)
<=> ( ord_less_eq(int,X16,X17)
& X16 != X17 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_22_zless__le) ).
fof(fact_23_zless__linear,axiom,
! [X8,X9] :
( ord_less(int,X8,X9)
| X8 = X9
| ord_less(int,X9,X8) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_23_zless__linear) ).
fof(c_0_12,negated_conjecture,
~ ? [X4,X5] : plus_plus(int,power_power(int,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X5,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_13,plain,
( t != one_one(int)
| plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])])]) ).
fof(c_0_14,negated_conjecture,
! [X6,X7] : plus_plus(int,power_power(int,X6,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X7,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_15,plain,
( ~ ord_less(int,one_one(int),t)
| plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06])])])])]) ).
cnf(c_0_16,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_37_nat__1__add__1]) ).
cnf(c_0_17,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_54_Numeral1__eq1__nat]) ).
fof(c_0_18,plain,
! [X16,X17,X18] : power_power(int,X16,plus_plus(nat,X17,X18)) = times_times(int,power_power(int,X16,X17),power_power(int,X16,X18)),
inference(variable_rename,[status(thm)],[fact_34_zpower__zadd__distrib]) ).
fof(c_0_19,plain,
! [X19] : number_number_of(int,X19) = X19,
inference(variable_rename,[status(thm)],[fact_86_number__of__is__id]) ).
fof(c_0_20,plain,
! [X16,X17] : times_times(int,X16,X17) = times_times(int,X17,X16),
inference(variable_rename,[status(thm)],[fact_85_zmult__commute]) ).
fof(c_0_21,plain,
! [X16,X17] :
( ~ ord_less_eq(int,X16,X17)
| ~ ord_less_eq(int,X17,X16)
| X16 = X17 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_zle__antisym])]) ).
cnf(c_0_22,plain,
( plus_plus(int,power_power(int,esk1_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk2_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| t != one_one(int) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X2,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( plus_plus(int,power_power(int,esk3_0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,esk4_0,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_26,plain,
power_power(int,X1,plus_plus(nat,X2,X3)) = times_times(int,power_power(int,X1,X2),power_power(int,X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
times_times(int,X1,X2) = times_times(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( X1 = X2
| ~ ord_less_eq(int,X2,X1)
| ~ ord_less_eq(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
ord_less_eq(int,one_one(int),t),
inference(split_conjunct,[status(thm)],[fact_0_tpos]) ).
cnf(c_0_31,plain,
one_one(int) != t,
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_32,plain,
! [X18,X19,X18,X19] :
( ( ord_less_eq(int,X18,X19)
| ~ ord_less(int,X18,X19) )
& ( X18 != X19
| ~ ord_less(int,X18,X19) )
& ( ~ ord_less_eq(int,X18,X19)
| X18 = X19
| ord_less(int,X18,X19) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_zless__le])])])])]) ).
cnf(c_0_33,plain,
( plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,power_power(int,esk3_0,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))),power_power(int,esk4_0,plus_plus(nat,number_number_of(nat,bit1(pls)),number_number_of(nat,bit1(pls)))))
| ~ ord_less(int,one_one(int),t) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_34,negated_conjecture,
plus_plus(int,times_times(int,power_power(int,X1,number_number_of(nat,bit1(pls))),power_power(int,X1,number_number_of(nat,bit1(pls)))),times_times(int,power_power(int,X2,number_number_of(nat,bit1(pls))),power_power(int,X2,number_number_of(nat,bit1(pls))))) != plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_25]),c_0_25]),c_0_26]),c_0_26]),c_0_27]),c_0_28]) ).
fof(c_0_35,plain,
! [X10,X11] :
( ord_less(int,X10,X11)
| X10 = X11
| ord_less(int,X11,X10) ),
inference(variable_rename,[status(thm)],[fact_23_zless__linear]) ).
cnf(c_0_36,plain,
~ ord_less_eq(int,t,one_one(int)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_37,plain,
( ord_less_eq(int,X1,X2)
| ~ ord_less(int,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
~ ord_less(int,one_one(int),t),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_27]),c_0_28]),c_0_26]),c_0_26]),c_0_34]) ).
cnf(c_0_39,plain,
( ord_less(int,X1,X2)
| X2 = X1
| ord_less(int,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
~ ord_less(int,t,one_one(int)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM926+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jul 7 16:31:29 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.023 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 42
% 0.22/1.40 # Proof object clause steps : 20
% 0.22/1.40 # Proof object formula steps : 22
% 0.22/1.40 # Proof object conjectures : 5
% 0.22/1.40 # Proof object clause conjectures : 2
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 12
% 0.22/1.40 # Proof object initial formulas used : 12
% 0.22/1.40 # Proof object generating inferences : 3
% 0.22/1.40 # Proof object simplifying inferences : 19
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 142
% 0.22/1.40 # Removed by relevancy pruning/SinE : 48
% 0.22/1.40 # Initial clauses : 126
% 0.22/1.40 # Removed in clause preprocessing : 2
% 0.22/1.40 # Initial clauses in saturation : 124
% 0.22/1.40 # Processed clauses : 135
% 0.22/1.40 # ...of these trivial : 5
% 0.22/1.40 # ...subsumed : 19
% 0.22/1.40 # ...remaining for further processing : 111
% 0.22/1.40 # Other redundant clauses eliminated : 1
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 3
% 0.22/1.40 # Backward-rewritten : 5
% 0.22/1.40 # Generated clauses : 435
% 0.22/1.40 # ...of the previous two non-trivial : 387
% 0.22/1.40 # Contextual simplify-reflections : 0
% 0.22/1.40 # Paramodulations : 428
% 0.22/1.40 # Factorizations : 4
% 0.22/1.40 # Equation resolutions : 3
% 0.22/1.40 # Current number of processed clauses : 102
% 0.22/1.40 # Positive orientable unit clauses : 28
% 0.22/1.40 # Positive unorientable unit clauses: 3
% 0.22/1.40 # Negative unit clauses : 8
% 0.22/1.40 # Non-unit-clauses : 63
% 0.22/1.40 # Current number of unprocessed clauses: 372
% 0.22/1.40 # ...number of literals in the above : 689
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 8
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 318
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 311
% 0.22/1.40 # Non-unit clause-clause subsumptions : 22
% 0.22/1.40 # Unit Clause-clause subsumption calls : 33
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 44
% 0.22/1.40 # BW rewrite match successes : 30
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 17700
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.032 s
% 0.22/1.40 # System time : 0.005 s
% 0.22/1.40 # Total time : 0.037 s
% 0.22/1.40 # Maximum resident set size: 3872 pages
% 0.22/23.40 eprover: CPU time limit exceeded, terminating
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.42 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.42 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/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/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/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/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
%------------------------------------------------------------------------------