%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO124-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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  : 600s
% DateTime : Sat Jul 16 05:24:29 EDT 2022

% Result   : Unsatisfiable 20.78s 21.01s
% Output   : CNFRefutation 20.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   38 (  15 unt;   9 nHn;  36 RR)
%            Number of literals    :   74 (  22 equ;  33 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-4 aty)
%            Number of variables   :   35 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(between_c_defn_1,axiom,
    ( ~ between_c(A,B,C,D)
    | B != D ) ).

cnf(between_o_defn_5,axiom,
    ( ~ ordered_by(A,B,C)
    | ~ ordered_by(A,C,D)
    | between_o(A,B,C,D) ) ).

cnf(start_point_defn_7,axiom,
    ( ~ start_point(A,B)
    | incident_o(A,B) ) ).

cnf(start_point_defn_8,axiom,
    ( ~ start_point(A,B)
    | A = C
    | ~ incident_o(C,B)
    | ordered_by(B,A,C) ) ).

cnf(o3_24,axiom,
    ( ~ between_o(A,B,C,D)
    | between_c(ax2_sk4(A,D,C,B),B,C,D) ) ).

cnf(corollary_4_10_1_133,negated_conjecture,
    start_point(sk26,sk25) ).

cnf(corollary_4_10_1_134,negated_conjecture,
    start_point(sk27,sk25) ).

cnf(corollary_4_10_1_135,negated_conjecture,
    sk26 != sk27 ).

cnf(refute_0_0,plain,
    ( ~ between_o(sk25,sk27,sk26,sk27)
    | between_c(ax2_sk4(sk25,sk27,sk26,sk27),sk27,sk26,sk27) ),
    inference(subst,[],[o3_24:[bind(A,$fot(sk25)),bind(B,$fot(sk27)),bind(C,$fot(sk26)),bind(D,$fot(sk27))]]) ).

cnf(refute_0_1,plain,
    ( ~ ordered_by(sk25,B,sk26)
    | ~ ordered_by(sk25,sk26,sk27)
    | between_o(sk25,B,sk26,sk27) ),
    inference(subst,[],[between_o_defn_5:[bind(A,$fot(sk25)),bind(C,$fot(sk26)),bind(D,$fot(sk27))]]) ).

cnf(refute_0_2,plain,
    ( ~ start_point(sk27,sk25)
    | incident_o(sk27,sk25) ),
    inference(subst,[],[start_point_defn_7:[bind(A,$fot(sk27)),bind(B,$fot(sk25))]]) ).

cnf(refute_0_3,plain,
    incident_o(sk27,sk25),
    inference(resolve,[$cnf( start_point(sk27,sk25) )],[corollary_4_10_1_134,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ incident_o(X_7931,sk25)
    | ~ start_point(sk26,sk25)
    | sk26 = X_7931
    | ordered_by(sk25,sk26,X_7931) ),
    inference(subst,[],[start_point_defn_8:[bind(A,$fot(sk26)),bind(B,$fot(sk25)),bind(C,$fot(X_7931))]]) ).

cnf(refute_0_5,plain,
    ( ~ incident_o(X_7931,sk25)
    | sk26 = X_7931
    | ordered_by(sk25,sk26,X_7931) ),
    inference(resolve,[$cnf( start_point(sk26,sk25) )],[corollary_4_10_1_133,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ incident_o(sk27,sk25)
    | sk26 = sk27
    | ordered_by(sk25,sk26,sk27) ),
    inference(subst,[],[refute_0_5:[bind(X_7931,$fot(sk27))]]) ).

cnf(refute_0_7,plain,
    ( sk26 = sk27
    | ordered_by(sk25,sk26,sk27) ),
    inference(resolve,[$cnf( incident_o(sk27,sk25) )],[refute_0_3,refute_0_6]) ).

cnf(refute_0_8,plain,
    ordered_by(sk25,sk26,sk27),
    inference(resolve,[$cnf( $equal(sk26,sk27) )],[refute_0_7,corollary_4_10_1_135]) ).

cnf(refute_0_9,plain,
    ( ~ ordered_by(sk25,B,sk26)
    | between_o(sk25,B,sk26,sk27) ),
    inference(resolve,[$cnf( ordered_by(sk25,sk26,sk27) )],[refute_0_8,refute_0_1]) ).

cnf(refute_0_10,plain,
    ( ~ ordered_by(sk25,sk27,sk26)
    | between_o(sk25,sk27,sk26,sk27) ),
    inference(subst,[],[refute_0_9:[bind(B,$fot(sk27))]]) ).

cnf(refute_0_11,plain,
    ( ~ start_point(sk26,sk25)
    | incident_o(sk26,sk25) ),
    inference(subst,[],[start_point_defn_7:[bind(A,$fot(sk26)),bind(B,$fot(sk25))]]) ).

cnf(refute_0_12,plain,
    incident_o(sk26,sk25),
    inference(resolve,[$cnf( start_point(sk26,sk25) )],[corollary_4_10_1_133,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ incident_o(X_7931,sk25)
    | ~ start_point(sk27,sk25)
    | sk27 = X_7931
    | ordered_by(sk25,sk27,X_7931) ),
    inference(subst,[],[start_point_defn_8:[bind(A,$fot(sk27)),bind(B,$fot(sk25)),bind(C,$fot(X_7931))]]) ).

cnf(refute_0_14,plain,
    ( ~ incident_o(X_7931,sk25)
    | sk27 = X_7931
    | ordered_by(sk25,sk27,X_7931) ),
    inference(resolve,[$cnf( start_point(sk27,sk25) )],[corollary_4_10_1_134,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ incident_o(sk26,sk25)
    | sk27 = sk26
    | ordered_by(sk25,sk27,sk26) ),
    inference(subst,[],[refute_0_14:[bind(X_7931,$fot(sk26))]]) ).

cnf(refute_0_16,plain,
    ( sk27 = sk26
    | ordered_by(sk25,sk27,sk26) ),
    inference(resolve,[$cnf( incident_o(sk26,sk25) )],[refute_0_12,refute_0_15]) ).

cnf(refute_0_17,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_18,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_19,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( sk27 != sk26
    | sk26 = sk27 ),
    inference(subst,[],[refute_0_19:[bind(X,$fot(sk27)),bind(Y,$fot(sk26))]]) ).

cnf(refute_0_21,plain,
    sk27 != sk26,
    inference(resolve,[$cnf( $equal(sk26,sk27) )],[refute_0_20,corollary_4_10_1_135]) ).

cnf(refute_0_22,plain,
    ordered_by(sk25,sk27,sk26),
    inference(resolve,[$cnf( $equal(sk27,sk26) )],[refute_0_16,refute_0_21]) ).

cnf(refute_0_23,plain,
    between_o(sk25,sk27,sk26,sk27),
    inference(resolve,[$cnf( ordered_by(sk25,sk27,sk26) )],[refute_0_22,refute_0_10]) ).

cnf(refute_0_24,plain,
    between_c(ax2_sk4(sk25,sk27,sk26,sk27),sk27,sk26,sk27),
    inference(resolve,[$cnf( between_o(sk25,sk27,sk26,sk27) )],[refute_0_23,refute_0_0]) ).

cnf(refute_0_25,plain,
    ( D != D
    | ~ between_c(A,D,C,D) ),
    inference(subst,[],[between_c_defn_1:[bind(B,$fot(D))]]) ).

cnf(refute_0_26,plain,
    D = D,
    introduced(tautology,[refl,[$fot(D)]]) ).

cnf(refute_0_27,plain,
    ~ between_c(A,D,C,D),
    inference(resolve,[$cnf( $equal(D,D) )],[refute_0_26,refute_0_25]) ).

cnf(refute_0_28,plain,
    ~ between_c(ax2_sk4(sk25,sk27,sk26,sk27),sk27,sk26,sk27),
    inference(subst,[],[refute_0_27:[bind(A,$fot(ax2_sk4(sk25,sk27,sk26,sk27))),bind(C,$fot(sk26)),bind(D,$fot(sk27))]]) ).

cnf(refute_0_29,plain,
    $false,
    inference(resolve,[$cnf( between_c(ax2_sk4(sk25,sk27,sk26,sk27),sk27,sk26,sk27) )],[refute_0_24,refute_0_28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO124-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sat Jun 18 02:10:43 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 20.78/21.01  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.78/21.01  
% 20.78/21.01  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.78/21.01  
%------------------------------------------------------------------------------