TSTP Solution File: GEO202+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n014.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 04:04:38 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   57 (  20 unt;   0 def)
%            Number of atoms       :  135 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  118 (  40   ~;  60   |;   8   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  103 (   5 sgn  62   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [X1,X2,X3] :
      ( ( distinct_points(X1,X2)
        & distinct_points(X1,X3)
        & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
     => equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',con) ).

fof(ceq3,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).

fof(apart4,axiom,
    ! [X1,X2,X3] :
      ( distinct_points(X1,X2)
     => ( distinct_points(X1,X3)
        | distinct_points(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).

fof(cu1,axiom,
    ! [X1,X2,X4,X5] :
      ( ( distinct_points(X1,X2)
        & distinct_lines(X4,X5) )
     => ( apart_point_and_line(X1,X4)
        | apart_point_and_line(X1,X5)
        | apart_point_and_line(X2,X4)
        | apart_point_and_line(X2,X5) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).

fof(apart1,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).

fof(ci1,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).

fof(apart3,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).

fof(ci2,axiom,
    ! [X1,X2] :
      ( distinct_points(X1,X2)
     => ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).

fof(ceq2,axiom,
    ! [X1,X2,X3] :
      ( apart_point_and_line(X1,X2)
     => ( distinct_lines(X2,X3)
        | apart_point_and_line(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).

fof(p1,axiom,
    ! [X1,X2] :
      ( distinct_lines(X1,X2)
     => convergent_lines(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).

fof(cp2,axiom,
    ! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).

fof(ax6,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).

fof(cp1,axiom,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( distinct_points(X1,X2)
          & distinct_points(X1,X3)
          & convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
       => equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_14,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | distinct_lines(X5,X6)
      | convergent_lines(X4,X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])])])]) ).

fof(c_0_15,negated_conjecture,
    ( distinct_points(esk1_0,esk2_0)
    & distinct_points(esk1_0,esk3_0)
    & convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
    & ~ equal_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

fof(c_0_16,plain,
    ! [X4,X5,X6] :
      ( ~ distinct_points(X4,X5)
      | distinct_points(X4,X6)
      | distinct_points(X5,X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])])])]) ).

fof(c_0_17,plain,
    ! [X6,X7,X8,X9] :
      ( ~ distinct_points(X6,X7)
      | ~ distinct_lines(X8,X9)
      | apart_point_and_line(X6,X8)
      | apart_point_and_line(X6,X9)
      | apart_point_and_line(X7,X8)
      | apart_point_and_line(X7,X9) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).

cnf(c_0_18,plain,
    ( convergent_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_20,plain,
    ! [X2] : ~ distinct_points(X2,X2),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[apart1])]) ).

cnf(c_0_21,plain,
    ( distinct_points(X1,X2)
    | distinct_points(X3,X2)
    | ~ distinct_points(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    distinct_points(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,plain,
    ( apart_point_and_line(X1,X2)
    | apart_point_and_line(X1,X3)
    | apart_point_and_line(X4,X2)
    | apart_point_and_line(X4,X3)
    | ~ distinct_lines(X3,X2)
    | ~ distinct_points(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,negated_conjecture,
    ( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    ( distinct_points(esk1_0,X1)
    | distinct_points(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_27,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X3,line_connecting(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ci1])])]) ).

cnf(c_0_28,negated_conjecture,
    ( apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(X2,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(X1,X3)
    | apart_point_and_line(X2,X3)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X3)
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    distinct_points(esk3_0,esk1_0),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,X1)
    | apart_point_and_line(esk3_0,X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_32,plain,
    ! [X2] : ~ convergent_lines(X2,X2),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[apart3])]) ).

cnf(c_0_33,negated_conjecture,
    ( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk3_0,line_connecting(esk1_0,X1))
    | convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,X1))
    | ~ distinct_points(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    distinct_points(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_35,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_36,plain,
    ! [X3,X4] :
      ( ~ distinct_points(X3,X4)
      | ~ apart_point_and_line(X4,line_connecting(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ci2])])]) ).

cnf(c_0_37,negated_conjecture,
    ( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
    | apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).

fof(c_0_38,plain,
    ! [X4,X5,X6] :
      ( ~ apart_point_and_line(X4,X5)
      | distinct_lines(X5,X6)
      | apart_point_and_line(X4,X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])])])]) ).

cnf(c_0_39,plain,
    ( ~ apart_point_and_line(X1,line_connecting(X2,X1))
    | ~ distinct_points(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_40,negated_conjecture,
    ( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0))
    | apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_37]),c_0_22])]) ).

fof(c_0_41,plain,
    ! [X3,X4] :
      ( ~ distinct_lines(X3,X4)
      | convergent_lines(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).

cnf(c_0_42,plain,
    ( apart_point_and_line(X1,X2)
    | distinct_lines(X3,X2)
    | ~ apart_point_and_line(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,negated_conjecture,
    apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_22])]) ).

fof(c_0_44,plain,
    ! [X3,X4] : ~ apart_point_and_line(X3,parallel_through_point(X4,X3)),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[cp2])]) ).

cnf(c_0_45,plain,
    ( convergent_lines(X1,X2)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_46,negated_conjecture,
    ( apart_point_and_line(esk3_0,X1)
    | distinct_lines(line_connecting(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_47,plain,
    ! [X4,X5,X6] :
      ( ~ convergent_lines(X4,X5)
      | convergent_lines(X4,X6)
      | convergent_lines(X5,X6) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])]) ).

cnf(c_0_48,plain,
    ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_49,negated_conjecture,
    ( apart_point_and_line(esk3_0,X1)
    | convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_50,plain,
    ! [X3,X4] : ~ convergent_lines(parallel_through_point(X4,X3),X4),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[cp1])]) ).

cnf(c_0_51,plain,
    ( convergent_lines(X1,X2)
    | convergent_lines(X3,X2)
    | ~ convergent_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_52,negated_conjecture,
    convergent_lines(line_connecting(esk1_0,esk2_0),parallel_through_point(X1,esk3_0)),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_53,plain,
    ~ convergent_lines(parallel_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_54,negated_conjecture,
    ( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
    | convergent_lines(parallel_through_point(X2,esk3_0),X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    convergent_lines(line_connecting(esk1_0,esk2_0),X1),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_56,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_35,c_0_55]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO202+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n014.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jun 17 17:06:19 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41  # Preprocessing time       : 0.017 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 57
% 0.23/1.41  # Proof object clause steps            : 30
% 0.23/1.41  # Proof object formula steps           : 27
% 0.23/1.41  # Proof object conjectures             : 21
% 0.23/1.41  # Proof object clause conjectures      : 18
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 15
% 0.23/1.41  # Proof object initial formulas used   : 13
% 0.23/1.41  # Proof object generating inferences   : 15
% 0.23/1.41  # Proof object simplifying inferences  : 5
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 36
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 4
% 0.23/1.41  # Initial clauses                      : 42
% 0.23/1.41  # Removed in clause preprocessing      : 0
% 0.23/1.41  # Initial clauses in saturation        : 42
% 0.23/1.41  # Processed clauses                    : 680
% 0.23/1.41  # ...of these trivial                  : 4
% 0.23/1.41  # ...subsumed                          : 339
% 0.23/1.41  # ...remaining for further processing  : 337
% 0.23/1.41  # Other redundant clauses eliminated   : 0
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 75
% 0.23/1.41  # Backward-rewritten                   : 69
% 0.23/1.41  # Generated clauses                    : 7022
% 0.23/1.41  # ...of the previous two non-trivial   : 6346
% 0.23/1.41  # Contextual simplify-reflections      : 115
% 0.23/1.41  # Paramodulations                      : 6572
% 0.23/1.41  # Factorizations                       : 450
% 0.23/1.41  # Equation resolutions                 : 0
% 0.23/1.41  # Current number of processed clauses  : 193
% 0.23/1.41  #    Positive orientable unit clauses  : 29
% 0.23/1.41  #    Positive unorientable unit clauses: 0
% 0.23/1.41  #    Negative unit clauses             : 8
% 0.23/1.41  #    Non-unit-clauses                  : 156
% 0.23/1.41  # Current number of unprocessed clauses: 1548
% 0.23/1.41  # ...number of literals in the above   : 8836
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 144
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 27173
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 8683
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 463
% 0.23/1.41  # Unit Clause-clause subsumption calls : 1427
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 24
% 0.23/1.41  # BW rewrite match successes           : 24
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 128884
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.194 s
% 0.23/1.41  # System time              : 0.002 s
% 0.23/1.41  # Total time               : 0.196 s
% 0.23/1.41  # Maximum resident set size: 7800 pages
%------------------------------------------------------------------------------