%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 22:45:26 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   31 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :   26 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   21 (  12   ~;   9   |;   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  :   34 (   8   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-6 aty)
%            Number of variables   :   12 (   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,
    reflection: ( $i * $i ) > $i ).

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

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

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

cnf(t1,axiom,
    ( between(X3,X2,X1)
    | ~ between(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).

cnf(c_between_a_and_d,hypothesis,
    between(a,c,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_between_a_and_d) ).

cnf(prove_not_between_others,negated_conjecture,
    ( between(c,a,d)
    | between(a,d,c) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_between_others) ).

cnf(b3,axiom,
    ( X2 = X3
    | ~ between(X1,X2,X3)
    | ~ between(X1,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).

cnf(a_not_c,hypothesis,
    a != c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_c) ).

cnf(c_not_d,hypothesis,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_not_d) ).

cnf(c_0_6,axiom,
    ( between(X3,X2,X1)
    | ~ between(X1,X2,X3) ),
    t1 ).

cnf(c_0_7,hypothesis,
    between(a,c,d),
    c_between_a_and_d ).

cnf(c_0_8,negated_conjecture,
    ( between(c,a,d)
    | between(a,d,c) ),
    prove_not_between_others ).

cnf(c_0_9,axiom,
    ( X2 = X3
    | ~ between(X1,X2,X3)
    | ~ between(X1,X3,X2) ),
    b3 ).

cnf(c_0_10,hypothesis,
    between(d,c,a),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,hypothesis,
    a != c,
    a_not_c ).

cnf(c_0_12,hypothesis,
    c != d,
    c_not_d ).

cnf(c_0_13,negated_conjecture,
    ( between(a,d,c)
    | between(d,a,c) ),
    inference(spm,[status(thm)],[c_0_6,c_0_8]) ).

cnf(c_0_14,hypothesis,
    ~ between(d,a,c),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_15,hypothesis,
    ~ between(a,d,c),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GEO006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 23:21:07 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.006000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.009000 s
%------------------------------------------------------------------------------