TSTP Solution File: GRP194+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n006.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 09:01:14 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    :   34 (  10 unt;   0 def)
%            Number of atoms       :   82 (  14 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :   84 (  36   ~;  34   |;   8   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   46 (   3 sgn  22   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(left_zero,axiom,
    ! [X1,X2] :
      ( left_zero(X1,X2)
    <=> ( group_member(X2,X1)
        & ! [X3] :
            ( group_member(X3,X1)
           => multiply(X1,X2,X3) = X2 ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',left_zero) ).

fof(homomorphism1,axiom,
    ! [X2] :
      ( group_member(X2,f)
     => group_member(phi(X2),h) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',homomorphism1) ).

fof(homomorphism2,axiom,
    ! [X2,X3] :
      ( ( group_member(X2,f)
        & group_member(X3,f) )
     => multiply(h,phi(X2),phi(X3)) = phi(multiply(f,X2,X3)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',homomorphism2) ).

fof(total_function,axiom,
    ! [X1,X2,X3] :
      ( ( group_member(X2,X1)
        & group_member(X3,X1) )
     => group_member(multiply(X1,X2,X3),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP007+0.ax',total_function) ).

fof(left_zero_for_f,hypothesis,
    left_zero(f,f_left_zero),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',left_zero_for_f) ).

fof(surjective,axiom,
    ! [X2] :
      ( group_member(X2,h)
     => ? [X3] :
          ( group_member(X3,f)
          & phi(X3) = X2 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',surjective) ).

fof(prove_left_zero_h,conjecture,
    left_zero(h,phi(f_left_zero)),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_left_zero_h) ).

fof(c_0_7,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( group_member(X5,X4)
        | ~ left_zero(X4,X5) )
      & ( ~ group_member(X6,X4)
        | multiply(X4,X5,X6) = X5
        | ~ left_zero(X4,X5) )
      & ( group_member(esk1_2(X4,X5),X4)
        | ~ group_member(X5,X4)
        | left_zero(X4,X5) )
      & ( multiply(X4,X5,esk1_2(X4,X5)) != X5
        | ~ group_member(X5,X4)
        | left_zero(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)],[left_zero])])])])])])]) ).

fof(c_0_8,plain,
    ! [X3] :
      ( ~ group_member(X3,f)
      | group_member(phi(X3),h) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism1])]) ).

fof(c_0_9,plain,
    ! [X4,X5] :
      ( ~ group_member(X4,f)
      | ~ group_member(X5,f)
      | multiply(h,phi(X4),phi(X5)) = phi(multiply(f,X4,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[homomorphism2])]) ).

fof(c_0_10,plain,
    ! [X4,X5,X6] :
      ( ~ group_member(X5,X4)
      | ~ group_member(X6,X4)
      | group_member(multiply(X4,X5,X6),X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[total_function])]) ).

cnf(c_0_11,plain,
    ( multiply(X1,X2,X3) = X2
    | ~ left_zero(X1,X2)
    | ~ group_member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,hypothesis,
    left_zero(f,f_left_zero),
    inference(split_conjunct,[status(thm)],[left_zero_for_f]) ).

cnf(c_0_13,plain,
    ( group_member(X2,X1)
    | ~ left_zero(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,plain,
    ( group_member(phi(X1),h)
    | ~ group_member(X1,f) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2))
    | ~ group_member(X2,f)
    | ~ group_member(X1,f) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    ( group_member(multiply(X1,X2,X3),X1)
    | ~ group_member(X3,X1)
    | ~ group_member(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,hypothesis,
    ( multiply(f,f_left_zero,X1) = f_left_zero
    | ~ group_member(X1,f) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_18,hypothesis,
    group_member(f_left_zero,f),
    inference(spm,[status(thm)],[c_0_13,c_0_12]) ).

fof(c_0_19,plain,
    ! [X4] :
      ( ( group_member(esk2_1(X4),f)
        | ~ group_member(X4,h) )
      & ( phi(esk2_1(X4)) = X4
        | ~ group_member(X4,h) ) ),
    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)],[surjective])])])])])]) ).

cnf(c_0_20,plain,
    ( group_member(multiply(h,phi(X1),phi(X2)),h)
    | ~ group_member(X2,f)
    | ~ group_member(X1,f) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_21,hypothesis,
    ( multiply(h,phi(f_left_zero),phi(X1)) = phi(f_left_zero)
    | ~ group_member(X1,f) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_18])]) ).

fof(c_0_22,negated_conjecture,
    ~ left_zero(h,phi(f_left_zero)),
    inference(assume_negation,[status(cth)],[prove_left_zero_h]) ).

cnf(c_0_23,plain,
    ( phi(esk2_1(X1)) = X1
    | ~ group_member(X1,h) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_24,plain,
    ( group_member(esk2_1(X1),f)
    | ~ group_member(X1,h) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,hypothesis,
    ( group_member(phi(f_left_zero),h)
    | ~ group_member(X1,f) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18])]) ).

fof(c_0_26,negated_conjecture,
    ~ left_zero(h,phi(f_left_zero)),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( left_zero(X1,X2)
    | ~ group_member(X2,X1)
    | multiply(X1,X2,esk1_2(X1,X2)) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_28,hypothesis,
    ( multiply(h,phi(f_left_zero),X1) = phi(f_left_zero)
    | ~ group_member(X1,h) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_24]) ).

cnf(c_0_29,hypothesis,
    group_member(phi(f_left_zero),h),
    inference(spm,[status(thm)],[c_0_25,c_0_18]) ).

cnf(c_0_30,negated_conjecture,
    ~ left_zero(h,phi(f_left_zero)),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,hypothesis,
    ~ group_member(esk1_2(h,phi(f_left_zero)),h),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]) ).

cnf(c_0_32,plain,
    ( left_zero(X1,X2)
    | group_member(esk1_2(X1,X2),X1)
    | ~ group_member(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_33,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29])]),c_0_30]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 12:07:12 EDT 2022
% 0.13/0.34  % 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       : 0.014 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             : 34
% 0.24/1.42  # Proof object clause steps            : 20
% 0.24/1.42  # Proof object formula steps           : 14
% 0.24/1.42  # Proof object conjectures             : 4
% 0.24/1.42  # Proof object clause conjectures      : 1
% 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  : 12
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 8
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 0
% 0.24/1.42  # Initial clauses                      : 12
% 0.24/1.42  # Removed in clause preprocessing      : 0
% 0.24/1.42  # Initial clauses in saturation        : 12
% 0.24/1.42  # Processed clauses                    : 41
% 0.24/1.42  # ...of these trivial                  : 0
% 0.24/1.42  # ...subsumed                          : 4
% 0.24/1.42  # ...remaining for further processing  : 37
% 0.24/1.42  # Other redundant clauses eliminated   : 0
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 2
% 0.24/1.42  # Backward-rewritten                   : 3
% 0.24/1.42  # Generated clauses                    : 160
% 0.24/1.42  # ...of the previous two non-trivial   : 120
% 0.24/1.42  # Contextual simplify-reflections      : 9
% 0.24/1.42  # Paramodulations                      : 160
% 0.24/1.42  # Factorizations                       : 0
% 0.24/1.42  # Equation resolutions                 : 0
% 0.24/1.42  # Current number of processed clauses  : 32
% 0.24/1.42  #    Positive orientable unit clauses  : 5
% 0.24/1.42  #    Positive unorientable unit clauses: 0
% 0.24/1.42  #    Negative unit clauses             : 2
% 0.24/1.42  #    Non-unit-clauses                  : 25
% 0.24/1.42  # Current number of unprocessed clauses: 53
% 0.24/1.42  # ...number of literals in the above   : 239
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 5
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 98
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 89
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 15
% 0.24/1.42  # Unit Clause-clause subsumption calls : 0
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 6
% 0.24/1.42  # BW rewrite match successes           : 2
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 3802
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.014 s
% 0.24/1.42  # System time              : 0.005 s
% 0.24/1.42  # Total time               : 0.019 s
% 0.24/1.42  # Maximum resident set size: 2808 pages
%------------------------------------------------------------------------------