%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO001-3 : 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 : n016.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 22:45:23 EDT 2023

% Result   : Unsatisfiable 0.60s 0.63s
% Output   : CNFRefutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   32 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :   30 (   3 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  14   ~;  12   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   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   :   34 (   3 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,
    b: $i ).

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

cnf(inner_pasch2,axiom,
    ( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).

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

cnf(inner_pasch1,axiom,
    ( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).

cnf(t3,axiom,
    between(X1,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).

cnf(identity_for_betweeness,axiom,
    ( X1 = X2
    | ~ between(X1,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).

cnf(prove_b_between_c_and_a,negated_conjecture,
    ~ between(c,b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_c_and_a) ).

cnf(c_0_6,axiom,
    ( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    inner_pasch2 ).

cnf(c_0_7,hypothesis,
    between(a,b,c),
    b_between_a_and_c ).

cnf(c_0_8,axiom,
    ( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    inner_pasch1 ).

cnf(c_0_9,hypothesis,
    ( between(b,inner_pasch(X1,X2,c,b,a),X1)
    | ~ between(X1,X2,c) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,axiom,
    between(X1,X2,X2),
    t3 ).

cnf(c_0_11,hypothesis,
    ( between(X1,inner_pasch(X2,X1,c,b,a),a)
    | ~ between(X2,X1,c) ),
    inference(spm,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_12,axiom,
    ( X1 = X2
    | ~ between(X1,X2,X1) ),
    identity_for_betweeness ).

cnf(c_0_13,hypothesis,
    between(b,inner_pasch(X1,c,c,b,a),X1),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    between(c,inner_pasch(X1,c,c,b,a),a),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_15,hypothesis,
    inner_pasch(b,c,c,b,a) = b,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    ~ between(c,b,a),
    prove_b_between_c_and_a ).

cnf(c_0_17,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GEO001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 29 22:28:46 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.43/0.60  start to proof: theBenchmark
% 0.60/0.63  % Version  : CSE_E---1.5
% 0.60/0.63  % Problem  : theBenchmark.p
% 0.60/0.63  % Proof found
% 0.60/0.63  % SZS status Theorem for theBenchmark.p
% 0.60/0.63  % SZS output start Proof
% See solution above
% 0.60/0.63  % Total time : 0.012000 s
% 0.60/0.63  % SZS output end Proof
% 0.60/0.63  % Total time : 0.015000 s
%------------------------------------------------------------------------------