TSTP Solution File: GEO007-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO007-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 0.52s 0.68s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   68 (  26 unt;  14 typ;   0 def)
%            Number of atoms       :  102 (  27 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   87 (  39   ~;  48   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   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    :   12 (  12 usr;   7 con; 0-6 aty)
%            Number of variables   :   79 (   8 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    euclid1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_26,type,
    euclid2: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_27,type,
    extension: ( $i * $i * $i * $i ) > $i ).

tff(decl_28,type,
    lower_dimension_point_1: $i ).

tff(decl_29,type,
    lower_dimension_point_2: $i ).

tff(decl_30,type,
    lower_dimension_point_3: $i ).

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

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

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

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

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

cnf(identity_for_betweeness,axiom,
    ( X1 = X2
    | ~ between(X1,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).

cnf(outer_pasch1,axiom,
    ( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).

cnf(identity_for_equidistance,axiom,
    ( X1 = X2
    | ~ equidistant(X1,X2,X3,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).

cnf(segment_construction2,axiom,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).

cnf(a_between_a_and_e,hypothesis,
    between(e,a,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_between_a_and_e) ).

cnf(segment_construction1,axiom,
    between(X1,X2,extension(X1,X2,X3,X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).

cnf(a_between_a_and_c,hypothesis,
    between(d,a,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_between_a_and_c) ).

cnf(outer_pasch2,axiom,
    ( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
    | ~ between(X1,X2,X3)
    | ~ between(X4,X3,X5) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).

cnf(connectivity_for_betweeness,axiom,
    ( X1 = X2
    | between(X1,X3,X4)
    | between(X1,X4,X3)
    | ~ between(X1,X2,X3)
    | ~ between(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',connectivity_for_betweeness) ).

cnf(a_not_c,hypothesis,
    a != c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).

cnf(transitivity_for_betweeness,axiom,
    ( between(X1,X2,X4)
    | ~ between(X1,X2,X3)
    | ~ between(X2,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).

cnf(e_not_between_d_and_a,hypothesis,
    ~ between(d,e,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_not_between_d_and_a) ).

cnf(prove_d_between_e_and_a,negated_conjecture,
    ~ between(e,d,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_between_e_and_a) ).

cnf(c_0_13,axiom,
    ( X1 = X2
    | ~ between(X1,X2,X1) ),
    identity_for_betweeness ).

cnf(c_0_14,axiom,
    ( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X3,X5) ),
    outer_pasch1 ).

cnf(c_0_15,axiom,
    ( X1 = X2
    | ~ equidistant(X1,X2,X3,X3) ),
    identity_for_equidistance ).

cnf(c_0_16,axiom,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
    segment_construction2 ).

cnf(c_0_17,plain,
    ( outer_pasch(X1,X2,X2,X3,X4) = X2
    | ~ between(X2,X4,X3)
    | ~ between(X2,X1,X4) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,hypothesis,
    between(e,a,c),
    a_between_a_and_e ).

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_15,c_0_16]) ).

cnf(c_0_21,hypothesis,
    ( outer_pasch(X1,e,e,c,a) = e
    | ~ between(e,X1,a) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    between(X1,X2,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,hypothesis,
    between(d,a,c),
    a_between_a_and_c ).

cnf(c_0_24,axiom,
    ( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
    | ~ between(X1,X2,X3)
    | ~ between(X4,X3,X5) ),
    outer_pasch2 ).

cnf(c_0_25,hypothesis,
    outer_pasch(a,e,e,c,a) = e,
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,hypothesis,
    ( outer_pasch(X1,d,d,c,a) = d
    | ~ between(d,X1,a) ),
    inference(spm,[status(thm)],[c_0_17,c_0_23]) ).

cnf(c_0_27,axiom,
    ( X1 = X2
    | between(X1,X3,X4)
    | between(X1,X4,X3)
    | ~ between(X1,X2,X3)
    | ~ between(X1,X2,X4) ),
    connectivity_for_betweeness ).

cnf(c_0_28,hypothesis,
    between(c,a,e),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18]),c_0_22])]) ).

cnf(c_0_29,hypothesis,
    a != c,
    a_not_c ).

cnf(c_0_30,hypothesis,
    outer_pasch(a,d,d,c,a) = d,
    inference(spm,[status(thm)],[c_0_26,c_0_22]) ).

cnf(c_0_31,hypothesis,
    ( between(c,e,X1)
    | between(c,X1,e)
    | ~ between(c,a,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_32,hypothesis,
    between(c,a,d),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_23]),c_0_22])]) ).

cnf(c_0_33,hypothesis,
    ( between(c,d,e)
    | between(c,e,d) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_34,hypothesis,
    ( outer_pasch(X1,c,c,d,e) = c
    | between(c,d,e)
    | ~ between(c,X1,e) ),
    inference(spm,[status(thm)],[c_0_17,c_0_33]) ).

cnf(c_0_35,hypothesis,
    ( outer_pasch(e,c,c,d,e) = c
    | between(c,d,e) ),
    inference(spm,[status(thm)],[c_0_34,c_0_22]) ).

cnf(c_0_36,hypothesis,
    ( outer_pasch(e,c,c,d,e) = c
    | outer_pasch(X1,c,c,e,d) = c
    | ~ between(c,X1,d) ),
    inference(spm,[status(thm)],[c_0_17,c_0_35]) ).

cnf(c_0_37,hypothesis,
    ( outer_pasch(d,c,c,e,d) = c
    | outer_pasch(e,c,c,d,e) = c ),
    inference(spm,[status(thm)],[c_0_36,c_0_22]) ).

cnf(c_0_38,hypothesis,
    ( outer_pasch(d,c,c,e,d) = c
    | between(d,e,c)
    | ~ between(c,e,d) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_22])]) ).

cnf(c_0_39,hypothesis,
    ( outer_pasch(d,c,c,e,d) = c
    | between(c,d,e)
    | between(d,e,c) ),
    inference(spm,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_40,axiom,
    ( between(X1,X2,X4)
    | ~ between(X1,X2,X3)
    | ~ between(X2,X4,X3) ),
    transitivity_for_betweeness ).

cnf(c_0_41,hypothesis,
    ( outer_pasch(d,c,c,e,d) = c
    | outer_pasch(X1,c,c,e,d) = c
    | between(d,e,c)
    | ~ between(c,X1,d) ),
    inference(spm,[status(thm)],[c_0_17,c_0_39]) ).

cnf(c_0_42,hypothesis,
    ( between(X1,e,a)
    | ~ between(X1,e,c) ),
    inference(spm,[status(thm)],[c_0_40,c_0_18]) ).

cnf(c_0_43,hypothesis,
    ( outer_pasch(d,c,c,e,d) = c
    | between(d,e,c) ),
    inference(spm,[status(thm)],[c_0_41,c_0_22]) ).

cnf(c_0_44,hypothesis,
    ~ between(d,e,a),
    e_not_between_d_and_a ).

cnf(c_0_45,hypothesis,
    outer_pasch(d,c,c,e,d) = c,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).

cnf(c_0_46,hypothesis,
    ( between(X1,d,a)
    | ~ between(X1,d,c) ),
    inference(spm,[status(thm)],[c_0_40,c_0_23]) ).

cnf(c_0_47,hypothesis,
    ( between(e,d,c)
    | ~ between(c,d,e) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_45]),c_0_22])]) ).

cnf(c_0_48,negated_conjecture,
    ~ between(e,d,a),
    prove_d_between_e_and_a ).

cnf(c_0_49,hypothesis,
    ~ between(c,d,e),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_50,hypothesis,
    outer_pasch(e,c,c,d,e) = c,
    inference(sr,[status(thm)],[c_0_35,c_0_49]) ).

cnf(c_0_51,hypothesis,
    between(c,e,d),
    inference(sr,[status(thm)],[c_0_33,c_0_49]) ).

cnf(c_0_52,hypothesis,
    between(d,e,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_50]),c_0_22])]),c_0_51])]) ).

cnf(c_0_53,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_52]),c_0_44]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GEO007-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 20:58:51 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.52/0.68  % Version  : CSE_E---1.5
% 0.52/0.68  % Problem  : theBenchmark.p
% 0.52/0.68  % Proof found
% 0.52/0.68  % SZS status Theorem for theBenchmark.p
% 0.52/0.68  % SZS output start Proof
% See solution above
% 0.52/0.69  % Total time : 0.117000 s
% 0.52/0.69  % SZS output end Proof
% 0.52/0.69  % Total time : 0.120000 s
%------------------------------------------------------------------------------