TSTP Solution File: GEO043-2 by CSE

TSTP Solution File: GEO043-2 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GEO043-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 22:45:43 EDT 2023

% Result   : Unsatisfiable 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   44 (  18 unt;  14 typ;   0 def)
%            Number of atoms       :   47 (  12 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   36 (  19   ~;  17   |;   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  :   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   :   58 (   8 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,
    w: $i ).

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

cnf(identity_for_betweeness,axiom,
    ( X1 = X2
    | ~ between(X1,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).

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/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).

cnf(identity_for_equidistance,axiom,
    ( X1 = X2
    | ~ equidistant(X1,X2,X3,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).

cnf(segment_construction2,axiom,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).

cnf(w_between_u_and_x,hypothesis,
    between(u,w,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).

cnf(segment_construction1,axiom,
    between(X1,X2,extension(X1,X2,X3,X4)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).

cnf(v_between_u_and_w,hypothesis,
    between(u,v,w),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).

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/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).

cnf(prove_w_between_v_and_x,negated_conjecture,
    ~ between(v,w,x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_w_between_v_and_x) ).

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

cnf(c_0_10,axiom,
    ( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    inner_pasch2 ).

cnf(c_0_11,axiom,
    ( X1 = X2
    | ~ equidistant(X1,X2,X3,X3) ),
    identity_for_equidistance ).

cnf(c_0_12,axiom,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
    segment_construction2 ).

cnf(c_0_13,plain,
    ( inner_pasch(X1,X2,X3,X1,X4) = X1
    | ~ between(X4,X1,X3)
    | ~ between(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    between(u,w,x),
    w_between_u_and_x ).

cnf(c_0_15,axiom,
    between(X1,X2,extension(X1,X2,X3,X4)),
    segment_construction1 ).

cnf(c_0_16,plain,
    extension(X1,X2,X3,X3) = X2,
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,hypothesis,
    ( inner_pasch(w,X1,x,w,u) = w
    | ~ between(w,X1,x) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    between(X1,X2,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,hypothesis,
    between(u,v,w),
    v_between_u_and_w ).

cnf(c_0_20,axiom,
    ( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
    | ~ between(X1,X2,X3)
    | ~ between(X4,X5,X3) ),
    inner_pasch1 ).

cnf(c_0_21,hypothesis,
    inner_pasch(w,x,x,w,u) = w,
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,hypothesis,
    ( inner_pasch(v,X1,w,v,u) = v
    | ~ between(v,X1,w) ),
    inference(spm,[status(thm)],[c_0_13,c_0_19]) ).

cnf(c_0_23,hypothesis,
    between(x,w,u),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14]),c_0_18])]) ).

cnf(c_0_24,hypothesis,
    inner_pasch(v,w,w,v,u) = v,
    inference(spm,[status(thm)],[c_0_22,c_0_18]) ).

cnf(c_0_25,hypothesis,
    ( inner_pasch(w,X1,u,w,x) = w
    | ~ between(w,X1,u) ),
    inference(spm,[status(thm)],[c_0_13,c_0_23]) ).

cnf(c_0_26,hypothesis,
    between(w,v,u),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24]),c_0_19]),c_0_18])]) ).

cnf(c_0_27,hypothesis,
    inner_pasch(w,v,u,w,x) = w,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_28,negated_conjecture,
    ~ between(v,w,x),
    prove_w_between_v_and_x ).

cnf(c_0_29,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_23]),c_0_26])]),c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GEO043-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n027.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   : Wed Aug 30 00:03:23 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.009000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.012000 s
%------------------------------------------------------------------------------