TSTP Solution File: LCL903+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : LCL903+1 : TPTP v8.1.0. Released v5.5.0.
% 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 : Sun Jul 17 10:18:33 EDT 2022

% Result   : Theorem 0.20s 1.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   73 (  47 unt;   0 def)
%            Number of atoms       :  106 (  39 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   62 (  29   ~;  26   |;   2   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  135 (  16 sgn  47   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(sos_07,axiom,
    ! [X9,X10,X11] :
      ( '>='('+'(X9,X10),X11)
    <=> '>='(X10,'==>'(X9,X11)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_07) ).

fof(sos_13,axiom,
    ! [X1] : '==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_13) ).

fof(sos_08,axiom,
    ! [X1] : '>='(X1,'0'),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_08) ).

fof(sos_12,axiom,
    ! [X1] : '+'(X1,'1') = '1',
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_12) ).

fof(sos_03,axiom,
    ! [X1] : '+'(X1,'0') = X1,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_03) ).

fof(sos_02,axiom,
    ! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_02) ).

fof(sos_04,axiom,
    ! [X1] : '>='(X1,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_04) ).

fof(sos_06,axiom,
    ! [X7,X8] :
      ( ( '>='(X7,X8)
        & '>='(X8,X7) )
     => X7 = X8 ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_06) ).

fof(sos_09,axiom,
    ! [X12,X13,X14] :
      ( '>='(X12,X13)
     => '>='('+'(X12,X14),'+'(X13,X14)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_09) ).

fof(sos_11,axiom,
    ! [X18,X19,X20] :
      ( '>='(X18,X19)
     => '>='('==>'(X20,X18),'==>'(X20,X19)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_11) ).

fof(sos_10,axiom,
    ! [X15,X16,X17] :
      ( '>='(X15,X16)
     => '>='('==>'(X16,X17),'==>'(X15,X17)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sos_10) ).

fof(goals_14,conjecture,
    ! [X21] : '+'(X21,X21) = X21,
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals_14) ).

fof(c_0_12,plain,
    ! [X12,X13,X14,X12,X13,X14] :
      ( ( ~ '>='('+'(X12,X13),X14)
        | '>='(X13,'==>'(X12,X14)) )
      & ( ~ '>='(X13,'==>'(X12,X14))
        | '>='('+'(X12,X13),X14) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])])]) ).

fof(c_0_13,plain,
    ! [X2] : '==>'('==>'('==>'(X2,'1'),X2),X2) = '0',
    inference(variable_rename,[status(thm)],[sos_13]) ).

fof(c_0_14,plain,
    ! [X2] : '>='(X2,'0'),
    inference(variable_rename,[status(thm)],[sos_08]) ).

cnf(c_0_15,plain,
    ( '>='('+'(X1,X2),X3)
    | ~ '>='(X2,'==>'(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    '==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    '>='(X1,'0'),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,plain,
    ! [X2] : '+'(X2,'1') = '1',
    inference(variable_rename,[status(thm)],[sos_12]) ).

fof(c_0_19,plain,
    ! [X2] : '+'(X2,'0') = X2,
    inference(variable_rename,[status(thm)],[sos_03]) ).

fof(c_0_20,plain,
    ! [X3,X4] : '+'(X3,X4) = '+'(X4,X3),
    inference(variable_rename,[status(thm)],[sos_02]) ).

fof(c_0_21,plain,
    ! [X2] : '>='(X2,X2),
    inference(variable_rename,[status(thm)],[sos_04]) ).

fof(c_0_22,plain,
    ! [X9,X10] :
      ( ~ '>='(X9,X10)
      | ~ '>='(X10,X9)
      | X9 = X10 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).

cnf(c_0_23,plain,
    '>='('+'('==>'('==>'(X1,'1'),X1),X2),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

cnf(c_0_24,plain,
    '+'(X1,'1') = '1',
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_25,plain,
    ! [X15,X16,X17] :
      ( ~ '>='(X15,X16)
      | '>='('+'(X15,X17),'+'(X16,X17)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])])]) ).

cnf(c_0_26,plain,
    '+'(X1,'0') = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_27,plain,
    '+'(X1,X2) = '+'(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    ( '>='(X1,'==>'(X2,X3))
    | ~ '>='('+'(X2,X1),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_29,plain,
    '>='(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    ( X1 = X2
    | ~ '>='(X2,X1)
    | ~ '>='(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_31,plain,
    '>='('1',X1),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

fof(c_0_32,plain,
    ! [X21,X22,X23] :
      ( ~ '>='(X21,X22)
      | '>='('==>'(X23,X21),'==>'(X23,X22)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])])])]) ).

cnf(c_0_33,plain,
    ( '>='('+'(X1,X2),'+'(X3,X2))
    | ~ '>='(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_34,plain,
    '+'('0',X1) = X1,
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_35,plain,
    '>='(X1,'==>'(X2,'+'(X2,X1))),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,plain,
    ( X1 = '1'
    | ~ '>='(X1,'1') ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,plain,
    '>='('+'(X1,'==>'(X1,X2)),X2),
    inference(spm,[status(thm)],[c_0_15,c_0_29]) ).

cnf(c_0_38,plain,
    ( '>='('==>'(X1,X2),'==>'(X1,X3))
    | ~ '>='(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_39,plain,
    '>='('+'(X1,X2),X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_17])]) ).

cnf(c_0_40,plain,
    ( '0' = X1
    | ~ '>='('0',X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_17]) ).

cnf(c_0_41,plain,
    '>='(X1,'==>'(X2,'==>'(X3,'+'(X3,'+'(X2,X1))))),
    inference(spm,[status(thm)],[c_0_28,c_0_35]) ).

cnf(c_0_42,plain,
    ( '+'(X1,X2) = '+'(X3,X2)
    | ~ '>='('+'(X1,X2),'+'(X3,X2))
    | ~ '>='(X3,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_33]) ).

cnf(c_0_43,plain,
    '+'(X1,'==>'(X1,'1')) = '1',
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_44,plain,
    ( '==>'(X1,X2) = '==>'(X1,X3)
    | ~ '>='('==>'(X1,X2),'==>'(X1,X3))
    | ~ '>='(X3,X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_38]) ).

cnf(c_0_45,plain,
    '>='('==>'('==>'(X1,'1'),X1),X1),
    inference(spm,[status(thm)],[c_0_23,c_0_26]) ).

cnf(c_0_46,plain,
    '>='(X1,'==>'(X2,X1)),
    inference(spm,[status(thm)],[c_0_28,c_0_39]) ).

cnf(c_0_47,plain,
    '==>'(X1,'==>'(X2,'+'(X2,X1))) = '0',
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_26]) ).

cnf(c_0_48,plain,
    ( '+'(X1,'==>'(X2,'1')) = '1'
    | ~ '>='(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_31])]) ).

cnf(c_0_49,plain,
    '>='('==>'(X1,'1'),'==>'(X1,X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_31])]) ).

cnf(c_0_50,plain,
    '==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_37])]) ).

cnf(c_0_51,plain,
    '==>'('==>'(X1,'1'),X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_45]),c_0_46])]) ).

cnf(c_0_52,plain,
    '==>'(X1,'==>'(X2,'+'(X1,X2))) = '0',
    inference(spm,[status(thm)],[c_0_47,c_0_27]) ).

cnf(c_0_53,plain,
    '+'('==>'(X1,'1'),'==>'('==>'(X1,X2),'1')) = '1',
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_54,plain,
    '==>'('==>'(X1,'1'),'1') = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_27]),c_0_43]) ).

cnf(c_0_55,plain,
    ( '>='(X1,'==>'(X2,X3))
    | ~ '>='('+'(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_28,c_0_27]) ).

cnf(c_0_56,plain,
    '==>'('==>'(X1,'1'),'==>'(X1,X2)) = '0',
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).

cnf(c_0_57,plain,
    '>='(X1,'==>'('==>'(X1,'1'),X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_43]),c_0_31])]) ).

fof(c_0_58,plain,
    ! [X18,X19,X20] :
      ( ~ '>='(X18,X19)
      | '>='('==>'(X19,X20),'==>'(X18,X20)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])])]) ).

cnf(c_0_59,plain,
    '==>'(X1,'==>'('==>'(X1,'1'),X2)) = '0',
    inference(spm,[status(thm)],[c_0_56,c_0_54]) ).

cnf(c_0_60,plain,
    ( '==>'('==>'(X1,'1'),X2) = X1
    | ~ '>='(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_51]),c_0_57])]) ).

cnf(c_0_61,plain,
    ( '>='('==>'(X1,X2),'==>'(X3,X2))
    | ~ '>='(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

fof(c_0_62,negated_conjecture,
    ~ ! [X21] : '+'(X21,X21) = X21,
    inference(assume_negation,[status(cth)],[goals_14]) ).

cnf(c_0_63,plain,
    ( X1 = '0'
    | ~ '>='('==>'(X1,X2),X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_54]) ).

cnf(c_0_64,plain,
    '>='('==>'('==>'(X1,'+'(X1,X2)),X3),'==>'(X2,X3)),
    inference(spm,[status(thm)],[c_0_61,c_0_35]) ).

cnf(c_0_65,plain,
    ( '>='('+'(X1,X2),'+'(X3,X1))
    | ~ '>='(X2,X3) ),
    inference(spm,[status(thm)],[c_0_33,c_0_27]) ).

fof(c_0_66,negated_conjecture,
    '+'(esk1_0,esk1_0) != esk1_0,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])]) ).

cnf(c_0_67,plain,
    ( '+'(X1,'==>'(X1,X2)) = X2
    | ~ '>='(X2,'+'(X1,'==>'(X1,X2))) ),
    inference(spm,[status(thm)],[c_0_30,c_0_37]) ).

cnf(c_0_68,plain,
    '==>'(X1,'+'(X1,X1)) = '0',
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_69,plain,
    '>='('+'(X1,X2),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_34]),c_0_17])]) ).

cnf(c_0_70,negated_conjecture,
    '+'(esk1_0,esk1_0) != esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_71,plain,
    '+'(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_26]),c_0_26]),c_0_69])]) ).

cnf(c_0_72,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LCL903+1 : TPTP v8.1.0. Released v5.5.0.
% 0.11/0.11  % Command  : run_ET %s %d
% 0.11/0.32  % Computer : n019.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Mon Jul  4 04:13:38 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.20/1.39  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.20/1.39  # Preprocessing time       : 0.008 s
% 0.20/1.39  
% 0.20/1.39  # Proof found!
% 0.20/1.39  # SZS status Theorem
% 0.20/1.39  # SZS output start CNFRefutation
% See solution above
% 0.20/1.39  # Proof object total steps             : 73
% 0.20/1.39  # Proof object clause steps            : 48
% 0.20/1.39  # Proof object formula steps           : 25
% 0.20/1.39  # Proof object conjectures             : 5
% 0.20/1.39  # Proof object clause conjectures      : 2
% 0.20/1.39  # Proof object formula conjectures     : 3
% 0.20/1.39  # Proof object initial clauses used    : 13
% 0.20/1.39  # Proof object initial formulas used   : 12
% 0.20/1.39  # Proof object generating inferences   : 34
% 0.20/1.39  # Proof object simplifying inferences  : 29
% 0.20/1.39  # Training examples: 0 positive, 0 negative
% 0.20/1.39  # Parsed axioms                        : 14
% 0.20/1.39  # Removed by relevancy pruning/SinE    : 0
% 0.20/1.39  # Initial clauses                      : 15
% 0.20/1.39  # Removed in clause preprocessing      : 0
% 0.20/1.39  # Initial clauses in saturation        : 15
% 0.20/1.39  # Processed clauses                    : 3266
% 0.20/1.39  # ...of these trivial                  : 918
% 0.20/1.39  # ...subsumed                          : 1735
% 0.20/1.39  # ...remaining for further processing  : 613
% 0.20/1.39  # Other redundant clauses eliminated   : 0
% 0.20/1.39  # Clauses deleted for lack of memory   : 0
% 0.20/1.39  # Backward-subsumed                    : 9
% 0.20/1.39  # Backward-rewritten                   : 25
% 0.20/1.39  # Generated clauses                    : 118504
% 0.20/1.39  # ...of the previous two non-trivial   : 68415
% 0.20/1.39  # Contextual simplify-reflections      : 147
% 0.20/1.39  # Paramodulations                      : 118501
% 0.20/1.39  # Factorizations                       : 0
% 0.20/1.39  # Equation resolutions                 : 0
% 0.20/1.39  # Current number of processed clauses  : 578
% 0.20/1.39  #    Positive orientable unit clauses  : 249
% 0.20/1.39  #    Positive unorientable unit clauses: 4
% 0.20/1.39  #    Negative unit clauses             : 2
% 0.20/1.39  #    Non-unit-clauses                  : 323
% 0.20/1.39  # Current number of unprocessed clauses: 63520
% 0.20/1.39  # ...number of literals in the above   : 114703
% 0.20/1.39  # Current number of archived formulas  : 0
% 0.20/1.39  # Current number of archived clauses   : 34
% 0.20/1.39  # Clause-clause subsumption calls (NU) : 17864
% 0.20/1.39  # Rec. Clause-clause subsumption calls : 17617
% 0.20/1.39  # Non-unit clause-clause subsumptions  : 1241
% 0.20/1.39  # Unit Clause-clause subsumption calls : 2245
% 0.20/1.39  # Rewrite failures with RHS unbound    : 0
% 0.20/1.39  # BW rewrite match attempts            : 3429
% 0.20/1.39  # BW rewrite match successes           : 44
% 0.20/1.39  # Condensation attempts                : 0
% 0.20/1.39  # Condensation successes               : 0
% 0.20/1.39  # Termbank termtop insertions          : 1382057
% 0.20/1.39  
% 0.20/1.39  # -------------------------------------------------
% 0.20/1.39  # User time                : 0.689 s
% 0.20/1.39  # System time              : 0.036 s
% 0.20/1.39  # Total time               : 0.725 s
% 0.20/1.39  # Maximum resident set size: 67472 pages
%------------------------------------------------------------------------------