TSTP Solution File: GEO172+2 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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  : 300s
% DateTime : Mon May 20 20:01:03 EDT 2024

% Result   : Theorem 0.23s 0.56s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   46 (  20 unt;   0 def)
%            Number of atoms       :  108 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  109 (  47   ~;  45   |;   9   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   77 (   0 sgn  45   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [X1,X2,X3] :
      ( ( convergent_lines(X1,X2)
        & ~ apart_point_and_line(X3,X1)
        & ~ apart_point_and_line(X3,X2) )
     => ~ distinct_points(X3,intersection_point(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(apart3,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).

fof(apart6,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).

fof(apart5,axiom,
    ! [X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( distinct_lines(X1,X3)
        | distinct_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).

fof(ceq3,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => distinct_lines(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).

fof(apart2,axiom,
    ! [X1] : ~ distinct_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).

fof(apart1,axiom,
    ! [X1] : ~ distinct_points(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).

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/GEO008+0.ax',cu1) ).

fof(con2,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( ( apart_point_and_line(X3,X1)
          | apart_point_and_line(X3,X2) )
       => distinct_points(X3,intersection_point(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( convergent_lines(X1,X2)
          & ~ apart_point_and_line(X3,X1)
          & ~ apart_point_and_line(X3,X2) )
       => ~ distinct_points(X3,intersection_point(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).

fof(c_0_10,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart3]) ).

fof(c_0_11,plain,
    ! [X15,X16,X17] :
      ( ~ convergent_lines(X15,X16)
      | convergent_lines(X15,X17)
      | convergent_lines(X16,X17) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])])]) ).

fof(c_0_12,negated_conjecture,
    ( convergent_lines(esk1_0,esk2_0)
    & ~ apart_point_and_line(esk3_0,esk1_0)
    & ~ apart_point_and_line(esk3_0,esk2_0)
    & distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

fof(c_0_13,plain,
    ! [X12,X13,X14] :
      ( ~ distinct_lines(X12,X13)
      | distinct_lines(X12,X14)
      | distinct_lines(X13,X14) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])])]) ).

fof(c_0_14,plain,
    ! [X34,X35] :
      ( ~ convergent_lines(X34,X35)
      | distinct_lines(X34,X35) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])])]) ).

fof(c_0_15,plain,
    ! [X8] : ~ convergent_lines(X8,X8),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_10])]) ).

cnf(c_0_16,plain,
    ( convergent_lines(X1,X3)
    | convergent_lines(X2,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    convergent_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_18,plain,
    ! [X1] : ~ distinct_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart2]) ).

cnf(c_0_19,plain,
    ( distinct_lines(X1,X3)
    | distinct_lines(X2,X3)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( distinct_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    ( convergent_lines(esk1_0,X1)
    | convergent_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_23,plain,
    ! [X7] : ~ distinct_lines(X7,X7),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_18])]) ).

cnf(c_0_24,plain,
    ( distinct_lines(X1,X2)
    | distinct_lines(X3,X2)
    | ~ convergent_lines(X1,X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    convergent_lines(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_26,plain,
    ! [X1] : ~ distinct_points(X1,X1),
    inference(fof_simplification,[status(thm)],[apart1]) ).

fof(c_0_27,plain,
    ! [X24,X25,X26,X27] :
      ( ~ distinct_points(X24,X25)
      | ~ distinct_lines(X26,X27)
      | apart_point_and_line(X24,X26)
      | apart_point_and_line(X24,X27)
      | apart_point_and_line(X25,X26)
      | apart_point_and_line(X25,X27) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])])]) ).

cnf(c_0_28,plain,
    ~ distinct_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ( distinct_lines(esk1_0,X1)
    | distinct_lines(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_30,plain,
    ! [X6] : ~ distinct_points(X6,X6),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).

fof(c_0_31,plain,
    ! [X21,X22,X23] :
      ( ( ~ apart_point_and_line(X23,X21)
        | distinct_points(X23,intersection_point(X21,X22))
        | ~ convergent_lines(X21,X22) )
      & ( ~ apart_point_and_line(X23,X22)
        | distinct_points(X23,intersection_point(X21,X22))
        | ~ convergent_lines(X21,X22) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])])]) ).

cnf(c_0_32,plain,
    ( apart_point_and_line(X1,X3)
    | apart_point_and_line(X1,X4)
    | apart_point_and_line(X2,X3)
    | apart_point_and_line(X2,X4)
    | ~ distinct_points(X1,X2)
    | ~ distinct_lines(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    distinct_lines(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ~ distinct_points(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,plain,
    ( distinct_points(X1,intersection_point(X2,X3))
    | ~ apart_point_and_line(X1,X2)
    | ~ convergent_lines(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( apart_point_and_line(X1,esk2_0)
    | apart_point_and_line(X1,esk1_0)
    | apart_point_and_line(X2,esk2_0)
    | apart_point_and_line(X2,esk1_0)
    | ~ distinct_points(X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_38,negated_conjecture,
    ~ apart_point_and_line(esk3_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_39,negated_conjecture,
    ~ apart_point_and_line(esk3_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_40,plain,
    ( distinct_points(X1,intersection_point(X3,X2))
    | ~ apart_point_and_line(X1,X2)
    | ~ convergent_lines(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_41,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X1)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_42,negated_conjecture,
    ( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
    | apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]) ).

cnf(c_0_43,plain,
    ( ~ apart_point_and_line(intersection_point(X1,X2),X2)
    | ~ convergent_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_17])]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% 0.13/0.15  % Command    : run_E %s %d THM
% 0.16/0.37  % Computer : n002.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sun May 19 14:21:38 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.23/0.54  Running first-order model finding
% 0.23/0.54  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.56  # Version: 3.1.0
% 0.23/0.56  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56  # Starting new_bool_3 with 300s (1) cores
% 0.23/0.56  # Starting new_bool_1 with 300s (1) cores
% 0.23/0.56  # Starting sh5l with 300s (1) cores
% 0.23/0.56  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 17858 completed with status 0
% 0.23/0.56  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.56  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56  # No SInE strategy applied
% 0.23/0.56  # Search class: FGUNF-FFSF22-SFFFFFNN
% 0.23/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.56  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.56  # Starting new_bool_3 with 136s (1) cores
% 0.23/0.56  # Starting new_bool_1 with 136s (1) cores
% 0.23/0.56  # Starting sh5l with 136s (1) cores
% 0.23/0.56  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 17864 completed with status 0
% 0.23/0.56  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.56  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56  # No SInE strategy applied
% 0.23/0.56  # Search class: FGUNF-FFSF22-SFFFFFNN
% 0.23/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.56  # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.56  # Preprocessing time       : 0.001 s
% 0.23/0.56  # Presaturation interreduction done
% 0.23/0.56  
% 0.23/0.56  # Proof found!
% 0.23/0.56  # SZS status Theorem
% 0.23/0.56  # SZS output start CNFRefutation
% See solution above
% 0.23/0.56  # Parsed axioms                        : 13
% 0.23/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.23/0.56  # Initial clauses                      : 18
% 0.23/0.56  # Removed in clause preprocessing      : 0
% 0.23/0.56  # Initial clauses in saturation        : 18
% 0.23/0.56  # Processed clauses                    : 71
% 0.23/0.56  # ...of these trivial                  : 0
% 0.23/0.56  # ...subsumed                          : 12
% 0.23/0.56  # ...remaining for further processing  : 59
% 0.23/0.56  # Other redundant clauses eliminated   : 0
% 0.23/0.56  # Clauses deleted for lack of memory   : 0
% 0.23/0.56  # Backward-subsumed                    : 0
% 0.23/0.56  # Backward-rewritten                   : 1
% 0.23/0.56  # Generated clauses                    : 114
% 0.23/0.56  # ...of the previous two non-redundant : 87
% 0.23/0.56  # ...aggressively subsumed             : 0
% 0.23/0.56  # Contextual simplify-reflections      : 0
% 0.23/0.56  # Paramodulations                      : 94
% 0.23/0.56  # Factorizations                       : 20
% 0.23/0.56  # NegExts                              : 0
% 0.23/0.56  # Equation resolutions                 : 0
% 0.23/0.56  # Disequality decompositions           : 0
% 0.23/0.56  # Total rewrite steps                  : 29
% 0.23/0.56  # ...of those cached                   : 25
% 0.23/0.56  # Propositional unsat checks           : 0
% 0.23/0.56  #    Propositional check models        : 0
% 0.23/0.56  #    Propositional check unsatisfiable : 0
% 0.23/0.56  #    Propositional clauses             : 0
% 0.23/0.56  #    Propositional clauses after purity: 0
% 0.23/0.56  #    Propositional unsat core size     : 0
% 0.23/0.56  #    Propositional preprocessing time  : 0.000
% 0.23/0.56  #    Propositional encoding time       : 0.000
% 0.23/0.56  #    Propositional solver time         : 0.000
% 0.23/0.56  #    Success case prop preproc time    : 0.000
% 0.23/0.56  #    Success case prop encoding time   : 0.000
% 0.23/0.56  #    Success case prop solver time     : 0.000
% 0.23/0.56  # Current number of processed clauses  : 40
% 0.23/0.56  #    Positive orientable unit clauses  : 5
% 0.23/0.56  #    Positive unorientable unit clauses: 0
% 0.23/0.56  #    Negative unit clauses             : 5
% 0.23/0.56  #    Non-unit-clauses                  : 30
% 0.23/0.56  # Current number of unprocessed clauses: 48
% 0.23/0.56  # ...number of literals in the above   : 200
% 0.23/0.56  # Current number of archived formulas  : 0
% 0.23/0.56  # Current number of archived clauses   : 19
% 0.23/0.56  # Clause-clause subsumption calls (NU) : 139
% 0.23/0.56  # Rec. Clause-clause subsumption calls : 96
% 0.23/0.56  # Non-unit clause-clause subsumptions  : 11
% 0.23/0.56  # Unit Clause-clause subsumption calls : 5
% 0.23/0.56  # Rewrite failures with RHS unbound    : 0
% 0.23/0.56  # BW rewrite match attempts            : 1
% 0.23/0.56  # BW rewrite match successes           : 1
% 0.23/0.56  # Condensation attempts                : 0
% 0.23/0.56  # Condensation successes               : 0
% 0.23/0.56  # Termbank termtop insertions          : 2390
% 0.23/0.56  # Search garbage collected termcells   : 217
% 0.23/0.56  
% 0.23/0.56  # -------------------------------------------------
% 0.23/0.56  # User time                : 0.007 s
% 0.23/0.56  # System time              : 0.003 s
% 0.23/0.56  # Total time               : 0.010 s
% 0.23/0.56  # Maximum resident set size: 1756 pages
% 0.23/0.56  
% 0.23/0.56  # -------------------------------------------------
% 0.23/0.56  # User time                : 0.023 s
% 0.23/0.56  # System time              : 0.007 s
% 0.23/0.56  # Total time               : 0.030 s
% 0.23/0.56  # Maximum resident set size: 1708 pages
% 0.23/0.56  % E---3.1 exiting
%------------------------------------------------------------------------------