TSTP Solution File: SWV487+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWV487+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n018.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 : Wed Jul 20 18:16:59 EDT 2022
% Result : Theorem 0.24s 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 12 unt; 0 def)
% Number of atoms : 185 ( 42 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 198 ( 69 ~; 70 |; 36 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 102 ( 5 sgn 62 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(int_less_transitive,axiom,
! [X1,X2,X3] :
( ( int_less(X1,X2)
& int_less(X2,X3) )
=> int_less(X1,X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',int_less_transitive) ).
fof(int_leq,axiom,
! [X1,X2] :
( int_leq(X1,X2)
<=> ( int_less(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',int_leq) ).
fof(ut,conjecture,
! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ut) ).
fof(int_less_irreflexive,axiom,
! [X1,X2] :
( int_less(X1,X2)
=> X1 != X2 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',int_less_irreflexive) ).
fof(plus_and_inverse,axiom,
! [X1,X2] :
( int_less(X1,X2)
<=> ? [X3] :
( plus(X1,X3) = X2
& int_less(int_zero,X3) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',plus_and_inverse) ).
fof(one_successor_of_zero,axiom,
! [X1] :
( int_less(int_zero,X1)
<=> int_leq(int_one,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',one_successor_of_zero) ).
fof(int_less_total,axiom,
! [X1,X2] :
( int_less(X1,X2)
| int_leq(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',int_less_total) ).
fof(qiu,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',qiu) ).
fof(c_0_8,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
introduced(definition) ).
fof(c_0_9,plain,
! [X4,X5,X6] :
( ~ int_less(X4,X5)
| ~ int_less(X5,X6)
| int_less(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])]) ).
fof(c_0_10,plain,
! [X3,X4,X3,X4] :
( ( ~ int_leq(X3,X4)
| int_less(X3,X4)
| X3 = X4 )
& ( ~ int_less(X3,X4)
| int_leq(X3,X4) )
& ( X3 != X4
| int_leq(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])])])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( ( int_leq(int_one,X2)
& int_less(X2,X1)
& int_leq(X1,n) )
=> a(X1,X2) = real_zero ),
inference(assume_negation,[status(cth)],[ut]) ).
fof(c_0_12,plain,
! [X2,X1] :
( epred1_2(X1,X2)
=> ( ! [X8] :
( ( int_less(int_zero,X8)
& X1 = plus(X2,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X2) )
=> a(plus(X3,X8),X3) = real_zero ) )
& ! [X8] :
( ( int_leq(int_zero,X8)
& X2 = plus(X1,X8) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,plus(X3,X8)) = lu(X3,plus(X3,X8)) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X3,X4] :
( ~ int_less(X3,X4)
| X3 != X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_irreflexive])]) ).
cnf(c_0_14,plain,
( int_less(X1,X2)
| ~ int_less(X3,X2)
| ~ int_less(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( X1 = X2
| int_less(X1,X2)
| ~ int_leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
( int_leq(int_one,esk2_0)
& int_less(esk2_0,esk1_0)
& int_leq(esk1_0,n)
& a(esk1_0,esk2_0) != real_zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_17,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ int_less(int_zero,X11)
| X10 != plus(X9,X11)
| ~ int_leq(int_one,X12)
| ~ int_leq(X12,X9)
| a(plus(X12,X11),X12) = real_zero
| ~ epred1_2(X10,X9) )
& ( ~ int_leq(int_zero,X13)
| X9 != plus(X10,X13)
| ~ int_leq(int_one,X14)
| ~ int_leq(X14,X10)
| a(X14,plus(X14,X13)) = lu(X14,plus(X14,X13))
| ~ epred1_2(X10,X9) ) ),
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_12])])])])])]) ).
fof(c_0_18,plain,
! [X4,X5,X4,X5,X7] :
( ( plus(X4,esk3_2(X4,X5)) = X5
| ~ int_less(X4,X5) )
& ( int_less(int_zero,esk3_2(X4,X5))
| ~ int_less(X4,X5) )
& ( plus(X4,X7) != X5
| ~ int_less(int_zero,X7)
| int_less(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_inverse])])])])])])]) ).
cnf(c_0_19,plain,
( X1 != X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( X1 = X2
| int_less(X3,X2)
| ~ int_less(X3,X1)
| ~ int_leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
int_leq(esk1_0,n),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
int_less(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( a(plus(X3,X4),X3) = real_zero
| ~ epred1_2(X1,X2)
| ~ int_leq(X3,X2)
| ~ int_leq(int_one,X3)
| X1 != plus(X2,X4)
| ~ int_less(int_zero,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( plus(X1,esk3_2(X1,X2)) = X2
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( int_less(int_zero,esk3_2(X1,X2))
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( int_leq(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_27,plain,
! [X2,X2] :
( ( ~ int_less(int_zero,X2)
| int_leq(int_one,X2) )
& ( ~ int_leq(int_one,X2)
| int_less(int_zero,X2) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])])])]) ).
cnf(c_0_28,plain,
~ int_less(X1,X1),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( n = esk1_0
| int_less(X1,n)
| ~ int_less(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,plain,
( int_leq(X1,X2)
| ~ int_less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
( int_less(X1,esk1_0)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
fof(c_0_32,plain,
! [X3,X4] :
( int_less(X3,X4)
| int_leq(X4,X3) ),
inference(variable_rename,[status(thm)],[int_less_total]) ).
cnf(c_0_33,plain,
( a(plus(X1,esk3_2(X2,X3)),X1) = real_zero
| ~ epred1_2(X3,X2)
| ~ int_less(X2,X3)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24])]),c_0_25]) ).
cnf(c_0_34,plain,
int_leq(X1,X1),
inference(er,[status(thm)],[c_0_26]) ).
fof(c_0_35,hypothesis,
! [X1,X2] :
( ( int_leq(int_one,X1)
& int_leq(X1,n)
& int_leq(int_one,X2)
& int_leq(X2,n) )
=> epred1_2(X1,X2) ),
inference(apply_def,[status(thm)],[qiu,c_0_8]) ).
cnf(c_0_36,plain,
( int_leq(int_one,X1)
| ~ int_less(int_zero,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( n = esk1_0
| ~ int_less(n,esk1_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( int_leq(X1,esk1_0)
| ~ int_less(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
( int_leq(X1,X2)
| int_less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
a(esk1_0,esk2_0) != real_zero,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_41,plain,
( a(X1,X2) = real_zero
| ~ epred1_2(X1,X2)
| ~ int_less(X2,X1)
| ~ int_leq(int_one,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_34])]) ).
cnf(c_0_42,negated_conjecture,
int_leq(int_one,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_43,hypothesis,
! [X3,X4] :
( ~ int_leq(int_one,X3)
| ~ int_leq(X3,n)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,n)
| epred1_2(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
cnf(c_0_44,negated_conjecture,
( int_leq(int_one,esk1_0)
| ~ int_less(int_zero,esk2_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_45,plain,
( int_less(int_zero,X1)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_46,negated_conjecture,
( n = esk1_0
| ~ int_leq(n,esk1_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_47,negated_conjecture,
( int_leq(esk2_0,X1)
| int_leq(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
~ epred1_2(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_22]),c_0_42])]) ).
cnf(c_0_49,hypothesis,
( epred1_2(X1,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,negated_conjecture,
int_leq(int_one,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_42])]) ).
cnf(c_0_51,negated_conjecture,
( n = esk1_0
| int_leq(esk2_0,n) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,hypothesis,
~ int_leq(esk2_0,n),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_21]),c_0_42]),c_0_50])]) ).
cnf(c_0_53,negated_conjecture,
n = esk1_0,
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
int_leq(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_55,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV487+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n018.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
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 07:07:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.015 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 56
% 0.24/1.41 # Proof object clause steps : 35
% 0.24/1.41 # Proof object formula steps : 21
% 0.24/1.41 # Proof object conjectures : 19
% 0.24/1.41 # Proof object clause conjectures : 16
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 16
% 0.24/1.41 # Proof object initial formulas used : 8
% 0.24/1.41 # Proof object generating inferences : 15
% 0.24/1.41 # Proof object simplifying inferences : 19
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 13
% 0.24/1.41 # Removed by relevancy pruning/SinE : 1
% 0.24/1.41 # Initial clauses : 22
% 0.24/1.41 # Removed in clause preprocessing : 0
% 0.24/1.41 # Initial clauses in saturation : 22
% 0.24/1.41 # Processed clauses : 1364
% 0.24/1.41 # ...of these trivial : 3
% 0.24/1.41 # ...subsumed : 946
% 0.24/1.41 # ...remaining for further processing : 415
% 0.24/1.41 # Other redundant clauses eliminated : 44
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 22
% 0.24/1.41 # Backward-rewritten : 69
% 0.24/1.41 # Generated clauses : 12819
% 0.24/1.41 # ...of the previous two non-trivial : 11037
% 0.24/1.41 # Contextual simplify-reflections : 1000
% 0.24/1.41 # Paramodulations : 12716
% 0.24/1.41 # Factorizations : 50
% 0.24/1.41 # Equation resolutions : 50
% 0.24/1.41 # Current number of processed clauses : 319
% 0.24/1.41 # Positive orientable unit clauses : 12
% 0.24/1.41 # Positive unorientable unit clauses: 1
% 0.24/1.41 # Negative unit clauses : 6
% 0.24/1.41 # Non-unit-clauses : 300
% 0.24/1.41 # Current number of unprocessed clauses: 7635
% 0.24/1.41 # ...number of literals in the above : 37107
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 94
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 24949
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 13446
% 0.24/1.41 # Non-unit clause-clause subsumptions : 1934
% 0.24/1.41 # Unit Clause-clause subsumption calls : 459
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 19
% 0.24/1.41 # BW rewrite match successes : 6
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 151091
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.233 s
% 0.24/1.41 # System time : 0.007 s
% 0.24/1.41 # Total time : 0.240 s
% 0.24/1.41 # Maximum resident set size: 10704 pages
% 0.24/23.41 eprover: CPU time limit exceeded, terminating
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49 eprover: No such file or directory
%------------------------------------------------------------------------------