TSTP Solution File: GEO049-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO049-2 : 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 : n008.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 22:45:46 EDT 2023

% Result   : Unsatisfiable 142.40s 142.50s
% Output   : CNFRefutation 142.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   95 (  40 unt;  16 typ;   0 def)
%            Number of atoms       :  160 (  28 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  146 (  65   ~;  81   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (   7   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   14 (  14 usr;   9 con; 0-6 aty)
%            Number of variables   :  211 (  22 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,
    u1: $i ).

tff(decl_35,type,
    v1: $i ).

tff(decl_36,type,
    w: $i ).

tff(decl_37,type,
    w1: $i ).

cnf(identity_for_equidistance,axiom,
    ( X1 = X2
    | ~ equidistant(X1,X2,X3,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).

cnf(segment_construction2,axiom,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).

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

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

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(segment_construction1,axiom,
    between(X1,X2,extension(X1,X2,X3,X4)),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).

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(outer_five_segment,axiom,
    ( X1 = X2
    | equidistant(X5,X7,X6,X8)
    | ~ equidistant(X1,X2,X3,X4)
    | ~ equidistant(X2,X5,X4,X6)
    | ~ equidistant(X1,X7,X3,X8)
    | ~ equidistant(X2,X7,X4,X8)
    | ~ between(X1,X2,X5)
    | ~ between(X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).

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

cnf(v_to_w_equals_v1_to_w1,hypothesis,
    equidistant(v,w,v1,w1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).

cnf(u_to_w_equals_u1_to_w1,hypothesis,
    equidistant(u,w,u1,w1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).

cnf(u_to_v_equals_u1_to_v1,hypothesis,
    equidistant(u,v,u1,v1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).

cnf(v_between_u_and_w,hypothesis,
    between(u,v,w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).

cnf(prove_v1_between_u1_and_w1,negated_conjecture,
    ~ between(u1,v1,w1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v1_between_u1_and_w1) ).

cnf(c_0_14,axiom,
    ( X1 = X2
    | ~ equidistant(X1,X2,X3,X3) ),
    identity_for_equidistance ).

cnf(c_0_15,axiom,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
    segment_construction2 ).

cnf(c_0_16,axiom,
    ( equidistant(X3,X4,X5,X6)
    | ~ equidistant(X1,X2,X3,X4)
    | ~ equidistant(X1,X2,X5,X6) ),
    transitivity_for_equidistance ).

cnf(c_0_17,axiom,
    equidistant(X1,X2,X2,X1),
    reflexivity_for_equidistance ).

cnf(c_0_18,axiom,
    ( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    inner_pasch2 ).

cnf(c_0_19,axiom,
    between(X1,X2,extension(X1,X2,X3,X4)),
    segment_construction1 ).

cnf(c_0_20,plain,
    extension(X1,X2,X3,X3) = X2,
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,plain,
    ( equidistant(X1,X2,X3,X4)
    | ~ equidistant(X4,X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,axiom,
    ( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    inner_pasch1 ).

cnf(c_0_23,plain,
    ( between(X1,inner_pasch(X2,X3,extension(X4,X1,X5,X6),X1,X4),X2)
    | ~ between(X2,X3,extension(X4,X1,X5,X6)) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    between(X1,X2,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,axiom,
    ( X1 = X2
    | equidistant(X5,X7,X6,X8)
    | ~ equidistant(X1,X2,X3,X4)
    | ~ equidistant(X2,X5,X4,X6)
    | ~ equidistant(X1,X7,X3,X8)
    | ~ equidistant(X2,X7,X4,X8)
    | ~ between(X1,X2,X5)
    | ~ between(X3,X4,X6) ),
    outer_five_segment ).

cnf(c_0_26,plain,
    equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
    inference(spm,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_27,plain,
    ( between(X1,inner_pasch(X2,X1,extension(X3,X4,X5,X6),X4,X3),X3)
    | ~ between(X2,X1,extension(X3,X4,X5,X6)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_19]) ).

cnf(c_0_28,axiom,
    ( X1 = X2
    | ~ between(X1,X2,X1) ),
    identity_for_betweeness ).

cnf(c_0_29,plain,
    between(X1,inner_pasch(X2,extension(X3,X1,X4,X5),extension(X3,X1,X4,X5),X1,X3),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,hypothesis,
    equidistant(v,w,v1,w1),
    v_to_w_equals_v1_to_w1 ).

cnf(c_0_31,plain,
    ( X1 = X2
    | equidistant(X3,extension(X4,X2,X5,X6),X7,X6)
    | ~ between(X8,X5,X7)
    | ~ between(X1,X2,X3)
    | ~ equidistant(X1,extension(X4,X2,X5,X6),X8,X6)
    | ~ equidistant(X2,X3,X5,X7)
    | ~ equidistant(X1,X2,X8,X5) ),
    inference(spm,[status(thm)],[c_0_25,c_0_15]) ).

cnf(c_0_32,plain,
    equidistant(X1,X1,X2,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_20]) ).

cnf(c_0_33,plain,
    equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
    inference(spm,[status(thm)],[c_0_21,c_0_26]) ).

cnf(c_0_34,plain,
    between(extension(X1,X2,X3,X4),inner_pasch(X5,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2,X1),X1),
    inference(spm,[status(thm)],[c_0_27,c_0_24]) ).

cnf(c_0_35,plain,
    inner_pasch(X1,extension(X2,X1,X3,X4),extension(X2,X1,X3,X4),X1,X2) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,hypothesis,
    equidistant(v1,w1,w,v),
    inference(spm,[status(thm)],[c_0_21,c_0_30]) ).

cnf(c_0_37,plain,
    ( extension(X1,X2,X3,X4) = X2
    | equidistant(X5,extension(X1,X2,X3,X4),X6,X4)
    | ~ between(extension(X1,X2,X3,X4),X2,X5)
    | ~ between(X4,X3,X6)
    | ~ equidistant(X2,X5,X3,X6) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).

cnf(c_0_38,plain,
    between(extension(X1,X2,X3,X4),X2,X1),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,hypothesis,
    equidistant(w,v,w1,v1),
    inference(spm,[status(thm)],[c_0_21,c_0_36]) ).

cnf(c_0_40,plain,
    equidistant(X1,X2,X1,X2),
    inference(spm,[status(thm)],[c_0_21,c_0_17]) ).

cnf(c_0_41,hypothesis,
    equidistant(u,w,u1,w1),
    u_to_w_equals_u1_to_w1 ).

cnf(c_0_42,plain,
    ( extension(X1,X2,X3,X4) = X2
    | equidistant(X1,extension(X1,X2,X3,X4),X5,X4)
    | ~ between(X4,X3,X5)
    | ~ equidistant(X2,X1,X3,X5) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,hypothesis,
    equidistant(w1,v1,v,w),
    inference(spm,[status(thm)],[c_0_21,c_0_39]) ).

cnf(c_0_44,hypothesis,
    equidistant(u,v,u1,v1),
    u_to_v_equals_u1_to_v1 ).

cnf(c_0_45,plain,
    ( equidistant(X1,X2,X3,X4)
    | ~ equidistant(X3,X4,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_40]) ).

cnf(c_0_46,hypothesis,
    ( equidistant(X1,X2,u1,w1)
    | ~ equidistant(u,w,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_41]) ).

cnf(c_0_47,hypothesis,
    ( extension(v1,w1,v,X1) = w1
    | equidistant(v1,extension(v1,w1,v,X1),w,X1)
    | ~ between(X1,v,w) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_48,hypothesis,
    between(u,v,w),
    v_between_u_and_w ).

cnf(c_0_49,hypothesis,
    ( equidistant(X1,X2,u1,v1)
    | ~ equidistant(u,v,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_44]) ).

cnf(c_0_50,plain,
    ( X1 = X2
    | equidistant(X3,X4,X5,X2)
    | ~ between(X6,X4,X5)
    | ~ between(X1,X2,X3)
    | ~ equidistant(X2,X3,X4,X5)
    | ~ equidistant(X1,X4,X6,X2)
    | ~ equidistant(X1,X2,X6,X4) ),
    inference(spm,[status(thm)],[c_0_25,c_0_17]) ).

cnf(c_0_51,plain,
    equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
    inference(spm,[status(thm)],[c_0_45,c_0_15]) ).

cnf(c_0_52,hypothesis,
    equidistant(w,u,u1,w1),
    inference(spm,[status(thm)],[c_0_46,c_0_17]) ).

cnf(c_0_53,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | equidistant(v1,extension(v1,w1,v,u),w,u) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_54,hypothesis,
    equidistant(v,u,u1,v1),
    inference(spm,[status(thm)],[c_0_49,c_0_17]) ).

cnf(c_0_55,plain,
    ( X1 = X2
    | equidistant(X3,X4,extension(X5,X4,X2,X3),X2)
    | ~ between(X6,X4,extension(X5,X4,X2,X3))
    | ~ between(X1,X2,X3)
    | ~ equidistant(X1,X4,X6,X2)
    | ~ equidistant(X1,X2,X6,X4) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_56,hypothesis,
    ( equidistant(X1,X2,u1,w1)
    | ~ equidistant(w,u,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_52]) ).

cnf(c_0_57,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | equidistant(w,u,extension(v1,w1,v,u),v1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_53]) ).

cnf(c_0_58,hypothesis,
    ( equidistant(X1,X2,u1,v1)
    | ~ equidistant(v,u,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_54]) ).

cnf(c_0_59,plain,
    ( X1 = X2
    | equidistant(X3,X4,extension(X5,X4,X2,X3),X2)
    | ~ between(X1,X2,X3)
    | ~ equidistant(X1,X4,X5,X2)
    | ~ equidistant(X1,X2,X5,X4) ),
    inference(spm,[status(thm)],[c_0_55,c_0_19]) ).

cnf(c_0_60,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | equidistant(extension(v1,w1,v,u),v1,u1,w1) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_61,hypothesis,
    equidistant(extension(X1,X2,v,u),X2,u1,v1),
    inference(spm,[status(thm)],[c_0_58,c_0_26]) ).

cnf(c_0_62,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | equidistant(X1,v1,extension(u1,v1,w1,X1),w1)
    | ~ between(extension(v1,w1,v,u),w1,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).

cnf(c_0_63,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | equidistant(v1,v1,extension(u1,v1,w1,v1),w1) ),
    inference(spm,[status(thm)],[c_0_62,c_0_38]) ).

cnf(c_0_64,plain,
    ( equidistant(X1,X2,extension(X3,X4,X5,X6),X4)
    | ~ equidistant(X5,X6,X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_26]) ).

cnf(c_0_65,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | equidistant(extension(u1,v1,w1,v1),w1,v1,v1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_63]) ).

cnf(c_0_66,hypothesis,
    equidistant(u1,v1,extension(X1,X2,v,u),X2),
    inference(spm,[status(thm)],[c_0_64,c_0_54]) ).

cnf(c_0_67,hypothesis,
    ( extension(v1,w1,v,u) = w1
    | extension(u1,v1,w1,v1) = w1 ),
    inference(spm,[status(thm)],[c_0_14,c_0_65]) ).

cnf(c_0_68,plain,
    ( between(X1,inner_pasch(X2,X3,X1,X1,X4),X2)
    | ~ between(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_24]) ).

cnf(c_0_69,hypothesis,
    ( extension(u1,v1,w1,v1) = w1
    | equidistant(u1,v1,w1,w1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_70,plain,
    ( between(X1,inner_pasch(X2,X1,X3,X3,X4),X4)
    | ~ between(X2,X1,X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_24]) ).

cnf(c_0_71,plain,
    between(X1,inner_pasch(X2,X1,X1,X1,X3),X2),
    inference(spm,[status(thm)],[c_0_68,c_0_24]) ).

cnf(c_0_72,hypothesis,
    ( extension(u1,v1,w1,v1) = w1
    | v1 = u1 ),
    inference(spm,[status(thm)],[c_0_14,c_0_69]) ).

cnf(c_0_73,negated_conjecture,
    ~ between(u1,v1,w1),
    prove_v1_between_u1_and_w1 ).

cnf(c_0_74,plain,
    between(X1,inner_pasch(X2,X1,X1,X1,X3),X3),
    inference(spm,[status(thm)],[c_0_70,c_0_24]) ).

cnf(c_0_75,plain,
    inner_pasch(X1,X1,X1,X1,X2) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_71]) ).

cnf(c_0_76,hypothesis,
    v1 = u1,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_72]),c_0_73]) ).

cnf(c_0_77,plain,
    between(X1,X1,X2),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_78,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_76]),c_0_77])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GEO049-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.19/0.35  % Computer : n008.cluster.edu
% 0.19/0.35  % Model    : x86_64 x86_64
% 0.19/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35  % Memory   : 8042.1875MB
% 0.19/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35  % CPULimit   : 300
% 0.19/0.35  % WCLimit    : 300
% 0.19/0.35  % DateTime   : Tue Aug 29 22:35:47 EDT 2023
% 0.19/0.36  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 142.40/142.50  % Version  : CSE_E---1.5
% 142.40/142.50  % Problem  : theBenchmark.p
% 142.40/142.50  % Proof found
% 142.40/142.50  % SZS status Theorem for theBenchmark.p
% 142.40/142.50  % SZS output start Proof
% See solution above
% 142.40/142.50  % Total time : 141.774000 s
% 142.40/142.50  % SZS output end Proof
% 142.40/142.50  % Total time : 141.785000 s
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