%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO020-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n024.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 22:45:33 EDT 2023

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   26 (   9 unt;  14 typ;   0 def)
%            Number of atoms       :   17 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (   7   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-6 aty)
%            Number of variables   :   20 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    lower_dimension_point_1: $i ).

tff(decl_27,type,
    lower_dimension_point_2: $i ).

tff(decl_28,type,
    lower_dimension_point_3: $i ).

tff(decl_29,type,
    euclid1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_30,type,
    euclid2: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_31,type,
    continuous: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_32,type,
    u: $i ).

tff(decl_33,type,
    v: $i ).

tff(decl_34,type,
    w: $i ).

tff(decl_35,type,
    x: $i ).

cnf(transitivity_for_equidistance,axiom,
    ( equidistant(X3,X4,X5,X6)
    | ~ equidistant(X1,X2,X3,X4)
    | ~ equidistant(X1,X2,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).

cnf(reflexivity_for_equidistance,axiom,
    equidistant(X1,X2,X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).

cnf(u_to_v_equals_w_to_x,hypothesis,
    equidistant(u,v,w,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).

cnf(prove_symmetry,negated_conjecture,
    ~ equidistant(x,w,u,v),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry) ).

cnf(c_0_4,axiom,
    ( equidistant(X3,X4,X5,X6)
    | ~ equidistant(X1,X2,X3,X4)
    | ~ equidistant(X1,X2,X5,X6) ),
    transitivity_for_equidistance ).

cnf(c_0_5,axiom,
    equidistant(X1,X2,X2,X1),
    reflexivity_for_equidistance ).

cnf(c_0_6,plain,
    ( equidistant(X1,X2,X3,X4)
    | ~ equidistant(X4,X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,hypothesis,
    equidistant(u,v,w,x),
    u_to_v_equals_w_to_x ).

cnf(c_0_8,hypothesis,
    equidistant(w,x,v,u),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_9,hypothesis,
    equidistant(v,u,x,w),
    inference(spm,[status(thm)],[c_0_6,c_0_8]) ).

cnf(c_0_10,negated_conjecture,
    ~ equidistant(x,w,u,v),
    prove_symmetry ).

cnf(c_0_11,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GEO020-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 29 19:04:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.006000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.009000 s
%------------------------------------------------------------------------------