%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO217+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 : Wed Aug 30 22:47:11 EDT 2023

% Result   : Theorem 0.15s 0.48s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   58 (  16 unt;  19 typ;   0 def)
%            Number of atoms       :   74 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   60 (  25   ~;  23   |;   5   &)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  16   >;  14   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   55 (   0 sgn;  34   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    distinct_points: ( $i * $i ) > $o ).

tff(decl_23,type,
    distinct_lines: ( $i * $i ) > $o ).

tff(decl_24,type,
    convergent_lines: ( $i * $i ) > $o ).

tff(decl_25,type,
    line_connecting: ( $i * $i ) > $i ).

tff(decl_26,type,
    apart_point_and_line: ( $i * $i ) > $o ).

tff(decl_27,type,
    intersection_point: ( $i * $i ) > $i ).

tff(decl_28,type,
    parallel_through_point: ( $i * $i ) > $i ).

tff(decl_29,type,
    unorthogonal_lines: ( $i * $i ) > $o ).

tff(decl_30,type,
    orthogonal_through_point: ( $i * $i ) > $i ).

tff(decl_31,type,
    point: $i > $o ).

tff(decl_32,type,
    line: $i > $o ).

tff(decl_33,type,
    equal_points: ( $i * $i ) > $o ).

tff(decl_34,type,
    equal_lines: ( $i * $i ) > $o ).

tff(decl_35,type,
    parallel_lines: ( $i * $i ) > $o ).

tff(decl_36,type,
    incident_point_and_line: ( $i * $i ) > $o ).

tff(decl_37,type,
    orthogonal_lines: ( $i * $i ) > $o ).

tff(decl_38,type,
    esk1_0: $i ).

tff(decl_39,type,
    esk2_0: $i ).

tff(decl_40,type,
    esk3_0: $i ).

fof(con,conjecture,
    ! [X6,X7,X8] :
      ( ( parallel_lines(X6,X7)
        & parallel_lines(X6,X8) )
     => parallel_lines(X7,X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(a3,axiom,
    ! [X1,X2] :
      ( parallel_lines(X1,X2)
    <=> ~ convergent_lines(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).

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(apart2,axiom,
    ! [X1] : ~ distinct_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).

fof(apart5,axiom,
    ! [X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( distinct_lines(X1,X3)
        | distinct_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).

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

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

fof(c_0_7,negated_conjecture,
    ~ ! [X6,X7,X8] :
        ( ( parallel_lines(X6,X7)
          & parallel_lines(X6,X8) )
       => parallel_lines(X7,X8) ),
    inference(assume_negation,[status(cth)],[con]) ).

fof(c_0_8,plain,
    ! [X1,X2] :
      ( parallel_lines(X1,X2)
    <=> ~ convergent_lines(X1,X2) ),
    inference(fof_simplification,[status(thm)],[a3]) ).

fof(c_0_9,negated_conjecture,
    ( parallel_lines(esk1_0,esk2_0)
    & parallel_lines(esk1_0,esk3_0)
    & ~ parallel_lines(esk2_0,esk3_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_10,plain,
    ! [X86,X87] :
      ( ( ~ parallel_lines(X86,X87)
        | ~ convergent_lines(X86,X87) )
      & ( convergent_lines(X86,X87)
        | parallel_lines(X86,X87) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).

fof(c_0_11,plain,
    ! [X41,X42,X43] :
      ( ~ convergent_lines(X41,X42)
      | distinct_lines(X42,X43)
      | convergent_lines(X41,X43) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).

cnf(c_0_12,negated_conjecture,
    ~ parallel_lines(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( convergent_lines(X1,X2)
    | parallel_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X1] : ~ distinct_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart2]) ).

fof(c_0_15,plain,
    ! [X17,X18,X19] :
      ( ~ distinct_lines(X17,X18)
      | distinct_lines(X17,X19)
      | distinct_lines(X18,X19) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).

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

cnf(c_0_17,negated_conjecture,
    convergent_lines(esk2_0,esk3_0),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

fof(c_0_18,plain,
    ! [X12] : ~ distinct_lines(X12,X12),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

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

cnf(c_0_20,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | distinct_lines(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_21,plain,
    ! [X44,X45] :
      ( ~ distinct_lines(X44,X45)
      | convergent_lines(X44,X45) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).

cnf(c_0_22,plain,
    ~ distinct_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | distinct_lines(esk3_0,X2)
    | distinct_lines(X1,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,plain,
    ( ~ parallel_lines(X1,X2)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_25,negated_conjecture,
    parallel_lines(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_26,plain,
    ( convergent_lines(X1,X2)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | distinct_lines(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    ~ convergent_lines(esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    convergent_lines(esk2_0,esk1_0),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_31,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart3]) ).

cnf(c_0_32,negated_conjecture,
    parallel_lines(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_33,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | distinct_lines(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_30]) ).

fof(c_0_34,plain,
    ! [X13] : ~ convergent_lines(X13,X13),
    inference(variable_rename,[status(thm)],[c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    ~ convergent_lines(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_24,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( convergent_lines(esk2_0,X1)
    | convergent_lines(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_33]) ).

cnf(c_0_37,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : GEO217+3 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Aug 29 22:17:02 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.15/0.47  start to proof: theBenchmark
% 0.15/0.48  % Version  : CSE_E---1.5
% 0.15/0.48  % Problem  : theBenchmark.p
% 0.15/0.48  % Proof found
% 0.15/0.48  % SZS status Theorem for theBenchmark.p
% 0.15/0.48  % SZS output start Proof
% See solution above
% 0.15/0.49  % Total time : 0.007000 s
% 0.15/0.49  % SZS output end Proof
% 0.15/0.49  % Total time : 0.011000 s
%------------------------------------------------------------------------------