TSTP Solution File: SWW299+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWW299+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n022.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 21 00:10:30 EDT 2022

% Result   : Theorem 1.02s 2.20s
% Output   : CNFRefutation 1.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (  11 unt;   0 def)
%            Number of atoms       :   88 (  15 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   90 (  34   ~;  33   |;  11   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;   8 con; 0-4 aty)
%            Number of variables   :   89 (  18 sgn  48   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_insert__code,axiom,
    ! [X22,X18,X28,X5] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X5),X28),X18),X22))
    <=> ( X28 = X22
        | hBOOL(hAPP(X18,X22)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_insert__code) ).

fof(fact_bot__empty__eq,axiom,
    ! [X22,X5] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X22))
    <=> hBOOL(hAPP(hAPP(c_member(X5),X22),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_bot__empty__eq) ).

fof(fact_emptyE,axiom,
    ! [X6,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_emptyE) ).

fof(fact_nonempty__iff,axiom,
    ! [X5,X18] :
      ( X18 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
    <=> ? [X3,X49] :
          ( X18 = hAPP(hAPP(c_Set_Oinsert(X5),X3),X49)
          & ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X49)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_nonempty__iff) ).

fof(conj_2,conjecture,
    ! [X300,X301] :
      ( v_P(X300,X301)
     => ? [X304,X305] :
          ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X304,v_c,X305)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
          & ! [X302] :
              ( ! [X303] :
                  ( hBOOL(hAPP(hAPP(X304,X303),X301))
                 => hBOOL(hAPP(hAPP(X305,X303),X302)) )
             => v_Q(X300,X302) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_2) ).

fof(conj_1,hypothesis,
    ! [X300,X301] :
      ( v_P(X300,X301)
     => ! [X302] :
          ( ! [X303] :
              ( hBOOL(hAPP(hAPP(v_P_H,X303),X301))
             => hBOOL(hAPP(hAPP(v_Q_H,X303),X302)) )
         => v_Q(X300,X302) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_1) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).

fof(c_0_7,plain,
    ! [X29,X30,X31,X32,X29,X30,X31,X32] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X32),X31),X30),X29))
        | X31 = X29
        | hBOOL(hAPP(X30,X29)) )
      & ( X31 != X29
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X32),X31),X30),X29)) )
      & ( ~ hBOOL(hAPP(X30,X29))
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X32),X31),X30),X29)) ) ),
    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_insert__code])])])])]) ).

fof(c_0_8,plain,
    ! [X23,X24,X23,X24] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_HOL_Obool)),X23))
        | hBOOL(hAPP(hAPP(c_member(X24),X23),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24),X23),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X24,tc_HOL_Obool)),X23)) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])])])]) ).

fof(c_0_9,plain,
    ! [X7,X8] : ~ hBOOL(hAPP(hAPP(c_member(X8),X7),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_emptyE])]) ).

cnf(c_0_10,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4))
    | X2 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X50,X51,X50,X51,X54,X55] :
      ( ( X51 = hAPP(hAPP(c_Set_Oinsert(X50),esk8_2(X50,X51)),esk9_2(X50,X51))
        | X51 = c_Orderings_Obot__class_Obot(tc_fun(X50,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X50),esk8_2(X50,X51)),esk9_2(X50,X51)))
        | X51 = c_Orderings_Obot__class_Obot(tc_fun(X50,tc_HOL_Obool)) )
      & ( X51 != hAPP(hAPP(c_Set_Oinsert(X50),X54),X55)
        | hBOOL(hAPP(hAPP(c_member(X50),X54),X55))
        | X51 != c_Orderings_Obot__class_Obot(tc_fun(X50,tc_HOL_Obool)) ) ),
    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)],[inference(fof_simplification,[status(thm)],[fact_nonempty__iff])])])])])])])]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X300,X301] :
        ( v_P(X300,X301)
       => ? [X304,X305] :
            ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X304,v_c,X305)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
            & ! [X302] :
                ( ! [X303] :
                    ( hBOOL(hAPP(hAPP(X304,X303),X301))
                   => hBOOL(hAPP(hAPP(X305,X303),X302)) )
               => v_Q(X300,X302) ) ) ),
    inference(assume_negation,[status(cth)],[conj_2]) ).

cnf(c_0_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    inference(er,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk8_2(X2,X1)),esk9_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_17,negated_conjecture,
    ! [X308,X309,X311] :
      ( v_P(esk2_0,esk3_0)
      & ( ~ hBOOL(hAPP(hAPP(X308,X311),esk3_0))
        | hBOOL(hAPP(hAPP(X309,X311),esk4_2(X308,X309)))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X308,v_c,X309)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
      & ( ~ v_Q(esk2_0,esk4_2(X308,X309))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X308,v_c,X309)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    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)],[c_0_12])])])])])])]) ).

fof(c_0_18,hypothesis,
    ! [X304,X305,X306] :
      ( ( hBOOL(hAPP(hAPP(v_P_H,esk1_3(X304,X305,X306)),X305))
        | v_Q(X304,X306)
        | ~ v_P(X304,X305) )
      & ( ~ hBOOL(hAPP(hAPP(v_Q_H,esk1_3(X304,X305,X306)),X306))
        | v_Q(X304,X306)
        | ~ v_P(X304,X305) ) ),
    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)],[conj_1])])])])])])]) ).

cnf(c_0_19,plain,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(sr,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(X1,esk8_2(X2,X1))) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( hBOOL(hAPP(hAPP(X2,X3),esk4_2(X1,X2)))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X1,v_c,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(X1,X3),esk3_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,hypothesis,
    ( v_Q(X1,X3)
    | hBOOL(hAPP(hAPP(v_P_H,esk1_3(X1,X2,X3)),X2))
    | ~ v_P(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[conj_0]) ).

cnf(c_0_24,plain,
    c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,hypothesis,
    ( v_Q(X1,X3)
    | ~ v_P(X1,X2)
    | ~ hBOOL(hAPP(hAPP(v_Q_H,esk1_3(X1,X2,X3)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    ( v_Q(X1,X2)
    | hBOOL(hAPP(hAPP(X3,esk1_3(X1,esk3_0,X2)),esk4_2(v_P_H,X3)))
    | ~ v_P(X1,esk3_0)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X1,v_c,X2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
    | ~ v_Q(esk2_0,esk4_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_29,hypothesis,
    ( v_Q(X1,esk4_2(v_P_H,v_Q_H))
    | ~ v_P(X1,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_30,negated_conjecture,
    v_P(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWW299+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.14  % Command  : run_ET %s %d
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sat Jun  4 21:59:51 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 1.02/2.20  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 1.02/2.20  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 1.02/2.20  # Preprocessing time       : 0.160 s
% 1.02/2.20  
% 1.02/2.20  # Proof found!
% 1.02/2.20  # SZS status Theorem
% 1.02/2.20  # SZS output start CNFRefutation
% See solution above
% 1.02/2.20  # Proof object total steps             : 32
% 1.02/2.20  # Proof object clause steps            : 18
% 1.02/2.20  # Proof object formula steps           : 14
% 1.02/2.20  # Proof object conjectures             : 8
% 1.02/2.20  # Proof object clause conjectures      : 5
% 1.02/2.20  # Proof object formula conjectures     : 3
% 1.02/2.20  # Proof object initial clauses used    : 10
% 1.02/2.20  # Proof object initial formulas used   : 7
% 1.02/2.20  # Proof object generating inferences   : 6
% 1.02/2.20  # Proof object simplifying inferences  : 7
% 1.02/2.20  # Training examples: 0 positive, 0 negative
% 1.02/2.20  # Parsed axioms                        : 5224
% 1.02/2.20  # Removed by relevancy pruning/SinE    : 5123
% 1.02/2.20  # Initial clauses                      : 163
% 1.02/2.20  # Removed in clause preprocessing      : 8
% 1.02/2.20  # Initial clauses in saturation        : 155
% 1.02/2.20  # Processed clauses                    : 457
% 1.02/2.20  # ...of these trivial                  : 8
% 1.02/2.20  # ...subsumed                          : 223
% 1.02/2.20  # ...remaining for further processing  : 226
% 1.02/2.20  # Other redundant clauses eliminated   : 10
% 1.02/2.20  # Clauses deleted for lack of memory   : 0
% 1.02/2.20  # Backward-subsumed                    : 11
% 1.02/2.20  # Backward-rewritten                   : 7
% 1.02/2.20  # Generated clauses                    : 2482
% 1.02/2.20  # ...of the previous two non-trivial   : 2152
% 1.02/2.20  # Contextual simplify-reflections      : 21
% 1.02/2.20  # Paramodulations                      : 2457
% 1.02/2.20  # Factorizations                       : 0
% 1.02/2.20  # Equation resolutions                 : 26
% 1.02/2.20  # Current number of processed clauses  : 203
% 1.02/2.20  #    Positive orientable unit clauses  : 26
% 1.02/2.20  #    Positive unorientable unit clauses: 6
% 1.02/2.20  #    Negative unit clauses             : 23
% 1.02/2.20  #    Non-unit-clauses                  : 148
% 1.02/2.20  # Current number of unprocessed clauses: 1769
% 1.02/2.20  # ...number of literals in the above   : 4977
% 1.02/2.20  # Current number of archived formulas  : 0
% 1.02/2.20  # Current number of archived clauses   : 18
% 1.02/2.20  # Clause-clause subsumption calls (NU) : 6824
% 1.02/2.20  # Rec. Clause-clause subsumption calls : 5516
% 1.02/2.20  # Non-unit clause-clause subsumptions  : 163
% 1.02/2.20  # Unit Clause-clause subsumption calls : 297
% 1.02/2.20  # Rewrite failures with RHS unbound    : 57
% 1.02/2.20  # BW rewrite match attempts            : 325
% 1.02/2.20  # BW rewrite match successes           : 40
% 1.02/2.20  # Condensation attempts                : 0
% 1.02/2.20  # Condensation successes               : 0
% 1.02/2.20  # Termbank termtop insertions          : 217921
% 1.02/2.20  
% 1.02/2.20  # -------------------------------------------------
% 1.02/2.20  # User time                : 0.232 s
% 1.02/2.20  # System time              : 0.003 s
% 1.02/2.20  # Total time               : 0.235 s
% 1.02/2.20  # Maximum resident set size: 15016 pages
%------------------------------------------------------------------------------