TSTP Solution File: HAL006+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : HAL006+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n020.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 : Sat Jul 16 12:45:12 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (   6 unt;   0 def)
%            Number of atoms       :  104 (  26 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  121 (  50   ~;  44   |;  19   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :   66 (   0 sgn  30   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(subtract_distribution,axiom,
    ! [X1,X2,X3] :
      ( morphism(X1,X2,X3)
     => ! [X5,X6] :
          ( ( element(X5,X2)
            & element(X6,X2) )
         => apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).

fof(lemma12,conjecture,
    ! [X19] :
      ( element(X19,e)
     => ? [X21,X24] :
          ( element(X21,b)
          & element(X24,b)
          & apply(g,subtract(b,X21,X24)) = X19 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lemma12) ).

fof(g_morphism,axiom,
    morphism(g,b,e),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',g_morphism) ).

fof(lemma8,axiom,
    ! [X19] :
      ( element(X19,e)
     => ? [X21,X22,X23] :
          ( element(X21,b)
          & element(X22,e)
          & subtract(e,apply(g,X21),X19) = X22
          & element(X23,a)
          & apply(gamma,apply(f,X23)) = X22
          & apply(g,apply(alpha,X23)) = X22 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lemma8) ).

fof(subtract_cancellation,axiom,
    ! [X2,X5,X6] :
      ( ( element(X5,X2)
        & element(X6,X2) )
     => subtract(X2,X5,subtract(X2,X5,X6)) = X6 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).

fof(morphism,axiom,
    ! [X1,X2,X3] :
      ( morphism(X1,X2,X3)
     => ( ! [X4] :
            ( element(X4,X2)
           => element(apply(X1,X4),X3) )
        & apply(X1,zero(X2)) = zero(X3) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).

fof(alpha_morphism,axiom,
    morphism(alpha,a,b),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',alpha_morphism) ).

fof(c_0_7,plain,
    ! [X7,X8,X9,X10,X11] :
      ( ~ morphism(X7,X8,X9)
      | ~ element(X10,X8)
      | ~ element(X11,X8)
      | apply(X7,subtract(X8,X10,X11)) = subtract(X9,apply(X7,X10),apply(X7,X11)) ),
    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)],[subtract_distribution])])])])]) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X19] :
        ( element(X19,e)
       => ? [X21,X24] :
            ( element(X21,b)
            & element(X24,b)
            & apply(g,subtract(b,X21,X24)) = X19 ) ),
    inference(assume_negation,[status(cth)],[lemma12]) ).

cnf(c_0_9,plain,
    ( apply(X1,subtract(X2,X3,X4)) = subtract(X5,apply(X1,X3),apply(X1,X4))
    | ~ element(X4,X2)
    | ~ element(X3,X2)
    | ~ morphism(X1,X2,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,plain,
    morphism(g,b,e),
    inference(split_conjunct,[status(thm)],[g_morphism]) ).

fof(c_0_11,plain,
    ! [X24] :
      ( ( element(esk4_1(X24),b)
        | ~ element(X24,e) )
      & ( element(esk5_1(X24),e)
        | ~ element(X24,e) )
      & ( subtract(e,apply(g,esk4_1(X24)),X24) = esk5_1(X24)
        | ~ element(X24,e) )
      & ( element(esk6_1(X24),a)
        | ~ element(X24,e) )
      & ( apply(gamma,apply(f,esk6_1(X24))) = esk5_1(X24)
        | ~ element(X24,e) )
      & ( apply(g,apply(alpha,esk6_1(X24))) = esk5_1(X24)
        | ~ element(X24,e) ) ),
    inference(distribute,[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)],[lemma8])])])])])]) ).

fof(c_0_12,negated_conjecture,
    ! [X26,X27] :
      ( element(esk1_0,e)
      & ( ~ element(X26,b)
        | ~ element(X27,b)
        | apply(g,subtract(b,X26,X27)) != esk1_0 ) ),
    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_8])])])])])]) ).

cnf(c_0_13,plain,
    ( subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2))
    | ~ element(X2,b)
    | ~ element(X1,b) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( apply(g,apply(alpha,esk6_1(X1))) = esk5_1(X1)
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_15,plain,
    ! [X7,X8,X9] :
      ( ~ element(X8,X7)
      | ~ element(X9,X7)
      | subtract(X7,X8,subtract(X7,X8,X9)) = X9 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).

fof(c_0_16,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ element(X8,X6)
        | element(apply(X5,X8),X7)
        | ~ morphism(X5,X6,X7) )
      & ( apply(X5,zero(X6)) = zero(X7)
        | ~ morphism(X5,X6,X7) ) ),
    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)],[morphism])])])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( apply(g,subtract(b,X1,X2)) != esk1_0
    | ~ element(X2,b)
    | ~ element(X1,b) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( subtract(e,apply(g,X1),esk5_1(X2)) = apply(g,subtract(b,X1,apply(alpha,esk6_1(X2))))
    | ~ element(apply(alpha,esk6_1(X2)),b)
    | ~ element(X1,b)
    | ~ element(X2,e) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_19,plain,
    ( subtract(X1,X2,subtract(X1,X2,X3)) = X3
    | ~ element(X3,X1)
    | ~ element(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,plain,
    ( subtract(e,apply(g,esk4_1(X1)),X1) = esk5_1(X1)
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_21,plain,
    ( element(apply(X1,X4),X3)
    | ~ morphism(X1,X2,X3)
    | ~ element(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ( subtract(e,apply(g,X1),esk5_1(X2)) != esk1_0
    | ~ element(apply(alpha,esk6_1(X2)),b)
    | ~ element(X1,b)
    | ~ element(X2,e) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    ( subtract(e,apply(g,esk4_1(X1)),esk5_1(X1)) = X1
    | ~ element(apply(g,esk4_1(X1)),e)
    | ~ element(X1,e) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( element(apply(g,X1),e)
    | ~ element(X1,b) ),
    inference(spm,[status(thm)],[c_0_21,c_0_10]) ).

cnf(c_0_25,plain,
    ( element(esk4_1(X1),b)
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_26,plain,
    morphism(alpha,a,b),
    inference(split_conjunct,[status(thm)],[alpha_morphism]) ).

cnf(c_0_27,negated_conjecture,
    ( X1 != esk1_0
    | ~ element(apply(alpha,esk6_1(X1)),b)
    | ~ element(X1,e) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).

cnf(c_0_28,plain,
    ( element(apply(alpha,X1),b)
    | ~ element(X1,a) ),
    inference(spm,[status(thm)],[c_0_21,c_0_26]) ).

cnf(c_0_29,plain,
    ( element(esk6_1(X1),a)
    | ~ element(X1,e) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,negated_conjecture,
    ( X1 != esk1_0
    | ~ element(X1,e) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_31,negated_conjecture,
    element(esk1_0,e),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_30,c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : HAL006+1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun  7 21:05:21 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42  # Preprocessing time       : 0.019 s
% 0.24/1.42  
% 0.24/1.42  # Proof found!
% 0.24/1.42  # SZS status Theorem
% 0.24/1.42  # SZS output start CNFRefutation
% See solution above
% 0.24/1.42  # Proof object total steps             : 33
% 0.24/1.42  # Proof object clause steps            : 20
% 0.24/1.42  # Proof object formula steps           : 13
% 0.24/1.42  # Proof object conjectures             : 9
% 0.24/1.42  # Proof object clause conjectures      : 6
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 11
% 0.24/1.42  # Proof object initial formulas used   : 7
% 0.24/1.42  # Proof object generating inferences   : 9
% 0.24/1.42  # Proof object simplifying inferences  : 3
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 33
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 5
% 0.24/1.42  # Initial clauses                      : 52
% 0.24/1.42  # Removed in clause preprocessing      : 0
% 0.24/1.42  # Initial clauses in saturation        : 52
% 0.24/1.42  # Processed clauses                    : 553
% 0.24/1.42  # ...of these trivial                  : 8
% 0.24/1.42  # ...subsumed                          : 263
% 0.24/1.42  # ...remaining for further processing  : 282
% 0.24/1.42  # Other redundant clauses eliminated   : 2
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 13
% 0.24/1.42  # Backward-rewritten                   : 10
% 0.24/1.42  # Generated clauses                    : 2290
% 0.24/1.42  # ...of the previous two non-trivial   : 2131
% 0.24/1.42  # Contextual simplify-reflections      : 239
% 0.24/1.42  # Paramodulations                      : 2285
% 0.24/1.42  # Factorizations                       : 0
% 0.24/1.42  # Equation resolutions                 : 5
% 0.24/1.42  # Current number of processed clauses  : 259
% 0.24/1.42  #    Positive orientable unit clauses  : 25
% 0.24/1.42  #    Positive unorientable unit clauses: 0
% 0.24/1.42  #    Negative unit clauses             : 2
% 0.24/1.42  #    Non-unit-clauses                  : 232
% 0.24/1.42  # Current number of unprocessed clauses: 1527
% 0.24/1.42  # ...number of literals in the above   : 10165
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 23
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 10890
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 4105
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 499
% 0.24/1.42  # Unit Clause-clause subsumption calls : 58
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 10
% 0.24/1.42  # BW rewrite match successes           : 8
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 72131
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.128 s
% 0.24/1.42  # System time              : 0.004 s
% 0.24/1.42  # Total time               : 0.132 s
% 0.24/1.42  # Maximum resident set size: 5496 pages
% 0.24/23.46  eprover: CPU time limit exceeded, terminating
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47  eprover: No such file or directory
% 0.24/23.47  eprover: Cannot stat file /export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
% 0.24/23.50  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50  eprover: No such file or directory
%------------------------------------------------------------------------------