TSTP Solution File: NUN056+2 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUN056+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n027.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 16:26:00 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 25 unt; 0 def)
% Number of atoms : 177 ( 40 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 219 ( 93 ~; 79 |; 47 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 149 ( 5 sgn 28 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(axiom_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(oneplustwoeqthree,conjecture,
? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X17] :
( r2(X17,X23)
& ? [X34] :
( r1(X34)
& r2(X34,X17) ) ) ) )
& ? [X16] :
( ? [X25] :
( r3(X25,X16,X39)
& ? [X31] :
( r1(X31)
& r2(X31,X25) ) )
& ? [X19] :
( r2(X19,X16)
& ? [X42] :
( r1(X42)
& r2(X42,X19) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',oneplustwoeqthree) ).
fof(c_0_6,plain,
! [X10,X11,X13] :
( ( r3(X10,X11,X13)
| ~ r3(X10,X11,X13) )
& ( X13 = esk12_2(X10,X11)
| ~ r3(X10,X11,X13) )
& ( r3(X10,X11,X13)
| X13 != esk12_2(X10,X11) )
& ( X13 = esk12_2(X10,X11)
| X13 != esk12_2(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_3])])])]) ).
fof(c_0_7,plain,
! [X20,X21] :
( r2(X21,esk4_2(X20,X21))
& r3(X20,esk4_2(X20,X21),esk3_2(X20,X21))
& esk3_2(X20,X21) = esk2_2(X20,X21)
& r2(esk5_2(X20,X21),esk2_2(X20,X21))
& r3(X20,X21,esk5_2(X20,X21)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_1a])])])]) ).
fof(c_0_8,plain,
! [X6,X8] :
( ( r2(X6,X8)
| ~ r2(X6,X8) )
& ( X8 = esk1_1(X6)
| ~ r2(X6,X8) )
& ( r2(X6,X8)
| X8 != esk1_1(X6) )
& ( X8 = esk1_1(X6)
| X8 != esk1_1(X6) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_2])])])]) ).
fof(c_0_9,plain,
! [X33] :
( r1(esk11_1(X33))
& r3(X33,esk11_1(X33),esk10_1(X33))
& esk10_1(X33) = X33 ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[axiom_4a])])])]) ).
fof(c_0_10,plain,
! [X4] :
( ( r1(X4)
| ~ r1(X4) )
& ( X4 = esk9_0
| ~ r1(X4) )
& ( r1(X4)
| X4 != esk9_0 )
& ( X4 = esk9_0
| X4 != esk9_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[axiom_1])])])]) ).
cnf(c_0_11,plain,
( X3 = esk12_2(X1,X2)
| ~ r3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
r3(X1,X2,esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
r3(X1,esk4_2(X1,X2),esk3_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
esk3_2(X1,X2) = esk2_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( X2 = esk1_1(X1)
| ~ r2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
r2(X1,esk4_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
r2(esk5_2(X1,X2),esk2_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
r3(X1,esk11_1(X1),esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
esk10_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( X1 = esk9_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
r1(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
esk12_2(X1,X2) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_23,plain,
r3(X1,esk4_2(X1,X2),esk2_2(X1,X2)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_24,plain,
esk4_2(X1,X2) = esk1_1(X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_25,plain,
esk2_2(X1,X2) = esk1_1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_26,plain,
r3(X1,esk11_1(X1),X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
esk11_1(X1) = esk9_0,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_28,negated_conjecture,
~ ? [X39] :
( ? [X22] :
( X39 = X22
& ? [X23] :
( r2(X23,X22)
& ? [X17] :
( r2(X17,X23)
& ? [X34] :
( r1(X34)
& r2(X34,X17) ) ) ) )
& ? [X16] :
( ? [X25] :
( r3(X25,X16,X39)
& ? [X31] :
( r1(X31)
& r2(X31,X25) ) )
& ? [X19] :
( r2(X19,X16)
& ? [X42] :
( r1(X42)
& r2(X42,X19) ) ) ) ),
inference(assume_negation,[status(cth)],[oneplustwoeqthree]) ).
cnf(c_0_29,plain,
( X1 = esk5_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_30,plain,
r3(X1,esk1_1(X2),esk1_1(esk5_2(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,plain,
r3(X1,esk9_0,X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,negated_conjecture,
! [X43,X44,X45,X46,X47,X48,X49,X50,X51,X52] :
( X43 != X44
| ~ r2(X45,X44)
| ~ r2(X46,X45)
| ~ r1(X47)
| ~ r2(X47,X46)
| ~ r3(X49,X48,X43)
| ~ r1(X50)
| ~ r2(X50,X49)
| ~ r2(X51,X48)
| ~ r1(X52)
| ~ r2(X52,X51) ),
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_28])])])])]) ).
cnf(c_0_33,plain,
esk5_2(X1,esk1_1(X2)) = esk1_1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
esk12_2(X1,esk9_0) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( ~ r2(X1,X2)
| ~ r1(X1)
| ~ r2(X2,X3)
| ~ r2(X4,X5)
| ~ r1(X4)
| ~ r3(X5,X3,X6)
| ~ r2(X7,X8)
| ~ r1(X7)
| ~ r2(X8,X9)
| ~ r2(X9,X10)
| X6 != X10 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
r3(X1,esk1_1(esk1_1(X2)),esk1_1(esk1_1(esk5_2(X1,X2)))),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_37,plain,
esk5_2(X1,esk9_0) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_38,negated_conjecture,
( ~ r3(X1,X2,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r2(X7,X1)
| ~ r2(X8,X2)
| ~ r2(X9,X8)
| ~ r1(X6)
| ~ r1(X7)
| ~ r1(X9) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
r3(X1,esk1_1(esk1_1(esk9_0)),esk1_1(esk1_1(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
( r2(X2,X1)
| X1 != esk1_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_41,negated_conjecture,
( ~ r2(X1,esk1_1(esk1_1(esk9_0)))
| ~ r2(X2,esk1_1(esk1_1(X3)))
| ~ r2(X4,X2)
| ~ r2(X5,X4)
| ~ r2(X6,X3)
| ~ r2(X7,X1)
| ~ r1(X5)
| ~ r1(X6)
| ~ r1(X7) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
r2(X1,esk1_1(X1)),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_43,negated_conjecture,
( ~ r2(X1,esk1_1(esk1_1(X2)))
| ~ r2(X3,esk1_1(esk9_0))
| ~ r2(X4,X1)
| ~ r2(X5,X4)
| ~ r2(X6,X2)
| ~ r1(X5)
| ~ r1(X6)
| ~ r1(X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
( ~ r2(X1,esk1_1(esk9_0))
| ~ r2(X2,esk1_1(X3))
| ~ r2(X4,X2)
| ~ r2(X5,X3)
| ~ r1(X4)
| ~ r1(X5)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_45,plain,
r1(esk9_0),
inference(rw,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_46,negated_conjecture,
( ~ r2(X1,esk1_1(X2))
| ~ r2(X3,X1)
| ~ r2(X4,X2)
| ~ r1(X3)
| ~ r1(X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_45])]) ).
cnf(c_0_47,negated_conjecture,
( ~ r2(X1,X2)
| ~ r2(X3,X2)
| ~ r1(X1)
| ~ r1(X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ r2(X1,esk1_1(X2))
| ~ r1(X2)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
~ r1(X1),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_50,plain,
$false,
inference(sr,[status(thm)],[c_0_45,c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN056+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 2 03:16:34 EDT 2022
% 0.13/0.33 % 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 : 0.016 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 : 51
% 0.22/1.40 # Proof object clause steps : 38
% 0.22/1.40 # Proof object formula steps : 13
% 0.22/1.40 # Proof object conjectures : 12
% 0.22/1.40 # Proof object clause conjectures : 9
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 13
% 0.22/1.40 # Proof object initial formulas used : 6
% 0.22/1.40 # Proof object generating inferences : 16
% 0.22/1.40 # Proof object simplifying inferences : 12
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 12
% 0.22/1.40 # Removed by relevancy pruning/SinE : 3
% 0.22/1.40 # Initial clauses : 27
% 0.22/1.40 # Removed in clause preprocessing : 8
% 0.22/1.40 # Initial clauses in saturation : 19
% 0.22/1.40 # Processed clauses : 454
% 0.22/1.40 # ...of these trivial : 1
% 0.22/1.40 # ...subsumed : 231
% 0.22/1.40 # ...remaining for further processing : 222
% 0.22/1.40 # Other redundant clauses eliminated : 37
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 2
% 0.22/1.40 # Backward-rewritten : 14
% 0.22/1.40 # Generated clauses : 2423
% 0.22/1.40 # ...of the previous two non-trivial : 2219
% 0.22/1.40 # Contextual simplify-reflections : 95
% 0.22/1.40 # Paramodulations : 2330
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 61
% 0.22/1.40 # Current number of processed clauses : 171
% 0.22/1.40 # Positive orientable unit clauses : 18
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 3
% 0.22/1.40 # Non-unit-clauses : 150
% 0.22/1.40 # Current number of unprocessed clauses: 851
% 0.22/1.40 # ...number of literals in the above : 4160
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 50
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 19117
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 6664
% 0.22/1.40 # Non-unit clause-clause subsumptions : 297
% 0.22/1.40 # Unit Clause-clause subsumption calls : 86
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 27
% 0.22/1.40 # BW rewrite match successes : 9
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 37921
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.099 s
% 0.22/1.40 # System time : 0.004 s
% 0.22/1.40 # Total time : 0.103 s
% 0.22/1.40 # Maximum resident set size: 4700 pages
%------------------------------------------------------------------------------