TSTP Solution File: ANA002-4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA002-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 17:13:46 EDT 2023

% Result   : Unsatisfiable 11.73s 11.91s
% Output   : CNFRefutation 11.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   75 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :  170 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  164 (  59   ~; 105   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   6   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   78 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    f: $i > $i ).

tff(decl_25,type,
    n0: $i ).

tff(decl_26,type,
    h: $i > $i ).

tff(decl_27,type,
    lower_bound: $i ).

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

tff(decl_29,type,
    k: $i > $i ).

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

tff(decl_31,type,
    g: $i > $i ).

cnf(continuity2,axiom,
    ( less_than_or_equal(f(X1),n0)
    | less_than_or_equal(X2,h(X1))
    | ~ less_than_or_equal(X2,X1)
    | ~ less_than_or_equal(f(X2),n0)
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).

cnf(crossover3_and_g_function2,axiom,
    ( less_than_or_equal(f(g(X1)),n0)
    | less_than_or_equal(l,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover3_and_g_function2) ).

cnf(crossover1,axiom,
    ( less_than_or_equal(X1,l)
    | ~ less_than_or_equal(X1,upper_bound)
    | ~ less_than_or_equal(f(X1),n0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover1) ).

cnf(crossover2_and_g_function1,axiom,
    ( less_than_or_equal(g(X1),upper_bound)
    | less_than_or_equal(l,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover2_and_g_function1) ).

cnf(crossover4_and_g_function3,axiom,
    ( less_than_or_equal(l,X1)
    | ~ less_than_or_equal(g(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover4_and_g_function3) ).

cnf(lower_mapping,hypothesis,
    less_than_or_equal(f(lower_bound),n0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_mapping) ).

cnf(the_interval,hypothesis,
    less_than_or_equal(lower_bound,upper_bound),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_interval) ).

cnf(totality_of_less,axiom,
    ( less_than_or_equal(X1,X2)
    | less_than_or_equal(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_less) ).

cnf(transitivity_of_less,axiom,
    ( less_than_or_equal(X1,X2)
    | ~ less_than_or_equal(X1,X3)
    | ~ less_than_or_equal(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).

cnf(continuity1,axiom,
    ( less_than_or_equal(f(X1),n0)
    | ~ less_than_or_equal(X1,h(X1))
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).

cnf(continuity4,axiom,
    ( less_than_or_equal(n0,f(X1))
    | less_than_or_equal(k(X1),X2)
    | ~ less_than_or_equal(X1,X2)
    | ~ less_than_or_equal(n0,f(X2))
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity4) ).

cnf(prove_there_is_x_which_crosses,negated_conjecture,
    ( ~ less_than_or_equal(f(l),n0)
    | ~ less_than_or_equal(n0,f(l)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).

cnf(reflexivity_of_less,axiom,
    less_than_or_equal(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_less) ).

cnf(interpolation1,axiom,
    ( less_than_or_equal(X1,X2)
    | ~ less_than_or_equal(X1,q(X2,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interpolation1) ).

cnf(upper_mapping,hypothesis,
    less_than_or_equal(n0,f(upper_bound)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_mapping) ).

cnf(interpolation2,axiom,
    ( less_than_or_equal(X2,X1)
    | ~ less_than_or_equal(q(X1,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interpolation2) ).

cnf(continuity3,axiom,
    ( less_than_or_equal(n0,f(X1))
    | ~ less_than_or_equal(k(X1),X1)
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity3) ).

cnf(c_0_17,axiom,
    ( less_than_or_equal(f(X1),n0)
    | less_than_or_equal(X2,h(X1))
    | ~ less_than_or_equal(X2,X1)
    | ~ less_than_or_equal(f(X2),n0)
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    continuity2 ).

cnf(c_0_18,axiom,
    ( less_than_or_equal(f(g(X1)),n0)
    | less_than_or_equal(l,X1) ),
    crossover3_and_g_function2 ).

cnf(c_0_19,axiom,
    ( less_than_or_equal(X1,l)
    | ~ less_than_or_equal(X1,upper_bound)
    | ~ less_than_or_equal(f(X1),n0) ),
    crossover1 ).

cnf(c_0_20,axiom,
    ( less_than_or_equal(g(X1),upper_bound)
    | less_than_or_equal(l,X1) ),
    crossover2_and_g_function1 ).

cnf(c_0_21,axiom,
    ( less_than_or_equal(l,X1)
    | ~ less_than_or_equal(g(X1),X1) ),
    crossover4_and_g_function3 ).

cnf(c_0_22,hypothesis,
    less_than_or_equal(f(lower_bound),n0),
    lower_mapping ).

cnf(c_0_23,hypothesis,
    less_than_or_equal(lower_bound,upper_bound),
    the_interval ).

cnf(c_0_24,plain,
    ( less_than_or_equal(g(X1),h(X2))
    | less_than_or_equal(f(X2),n0)
    | less_than_or_equal(l,X1)
    | ~ less_than_or_equal(g(X1),X2)
    | ~ less_than_or_equal(X2,upper_bound)
    | ~ less_than_or_equal(lower_bound,X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,plain,
    ( less_than_or_equal(g(X1),l)
    | less_than_or_equal(l,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]) ).

cnf(c_0_26,plain,
    less_than_or_equal(l,upper_bound),
    inference(spm,[status(thm)],[c_0_21,c_0_20]) ).

cnf(c_0_27,hypothesis,
    less_than_or_equal(lower_bound,l),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_23])]) ).

cnf(c_0_28,axiom,
    ( less_than_or_equal(X1,X2)
    | less_than_or_equal(X2,X1) ),
    totality_of_less ).

cnf(c_0_29,plain,
    ( less_than_or_equal(g(X1),h(l))
    | less_than_or_equal(f(l),n0)
    | less_than_or_equal(l,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).

cnf(c_0_30,plain,
    ( less_than_or_equal(n0,f(X1))
    | less_than_or_equal(X1,l)
    | ~ less_than_or_equal(X1,upper_bound) ),
    inference(spm,[status(thm)],[c_0_19,c_0_28]) ).

cnf(c_0_31,axiom,
    ( less_than_or_equal(X1,X2)
    | ~ less_than_or_equal(X1,X3)
    | ~ less_than_or_equal(X3,X2) ),
    transitivity_of_less ).

cnf(c_0_32,axiom,
    ( less_than_or_equal(f(X1),n0)
    | ~ less_than_or_equal(X1,h(X1))
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    continuity1 ).

cnf(c_0_33,plain,
    ( less_than_or_equal(f(l),n0)
    | less_than_or_equal(l,h(l)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_29]) ).

cnf(c_0_34,axiom,
    ( less_than_or_equal(n0,f(X1))
    | less_than_or_equal(k(X1),X2)
    | ~ less_than_or_equal(X1,X2)
    | ~ less_than_or_equal(n0,f(X2))
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    continuity4 ).

cnf(c_0_35,plain,
    ( less_than_or_equal(n0,f(X1))
    | less_than_or_equal(upper_bound,X1)
    | less_than_or_equal(X1,l) ),
    inference(spm,[status(thm)],[c_0_30,c_0_28]) ).

cnf(c_0_36,plain,
    ( less_than_or_equal(X1,X2)
    | less_than_or_equal(X3,X1)
    | ~ less_than_or_equal(X3,X2) ),
    inference(spm,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ less_than_or_equal(f(l),n0)
    | ~ less_than_or_equal(n0,f(l)) ),
    prove_there_is_x_which_crosses ).

cnf(c_0_38,plain,
    less_than_or_equal(f(l),n0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26]),c_0_27])]) ).

cnf(c_0_39,plain,
    ( less_than_or_equal(n0,f(X1))
    | less_than_or_equal(k(X1),X2)
    | less_than_or_equal(X2,l)
    | less_than_or_equal(upper_bound,X2)
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_40,hypothesis,
    ( less_than_or_equal(X1,l)
    | ~ less_than_or_equal(X1,lower_bound) ),
    inference(spm,[status(thm)],[c_0_31,c_0_27]) ).

cnf(c_0_41,axiom,
    less_than_or_equal(X1,X1),
    reflexivity_of_less ).

cnf(c_0_42,negated_conjecture,
    ~ less_than_or_equal(n0,f(l)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).

cnf(c_0_43,hypothesis,
    ( less_than_or_equal(k(l),X1)
    | less_than_or_equal(upper_bound,X1)
    | less_than_or_equal(X1,l) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),c_0_42]),c_0_28]) ).

cnf(c_0_44,axiom,
    ( less_than_or_equal(X1,X2)
    | ~ less_than_or_equal(X1,q(X2,X1)) ),
    interpolation1 ).

cnf(c_0_45,plain,
    ( less_than_or_equal(X1,X2)
    | less_than_or_equal(X2,X3)
    | less_than_or_equal(X3,X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_28]) ).

cnf(c_0_46,hypothesis,
    ( less_than_or_equal(k(l),X1)
    | less_than_or_equal(X2,l)
    | less_than_or_equal(upper_bound,X2)
    | less_than_or_equal(X1,X2) ),
    inference(spm,[status(thm)],[c_0_36,c_0_43]) ).

cnf(c_0_47,hypothesis,
    less_than_or_equal(n0,f(upper_bound)),
    upper_mapping ).

cnf(c_0_48,plain,
    ( less_than_or_equal(q(X1,X2),X3)
    | less_than_or_equal(X3,X2)
    | less_than_or_equal(X2,X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_49,axiom,
    ( less_than_or_equal(X2,X1)
    | ~ less_than_or_equal(q(X1,X2),X1) ),
    interpolation2 ).

cnf(c_0_50,hypothesis,
    ( less_than_or_equal(upper_bound,q(X1,X2))
    | less_than_or_equal(q(X1,X2),l)
    | less_than_or_equal(k(l),X2)
    | less_than_or_equal(X2,X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_46]) ).

cnf(c_0_51,hypothesis,
    ( less_than_or_equal(k(X1),upper_bound)
    | less_than_or_equal(n0,f(X1))
    | ~ less_than_or_equal(X1,upper_bound)
    | ~ less_than_or_equal(lower_bound,X1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_47]) ).

cnf(c_0_52,plain,
    ( less_than_or_equal(q(X1,q(X2,X3)),X3)
    | less_than_or_equal(q(X2,X3),X1)
    | less_than_or_equal(X3,X2) ),
    inference(spm,[status(thm)],[c_0_44,c_0_48]) ).

cnf(c_0_53,hypothesis,
    ( less_than_or_equal(upper_bound,q(l,X1))
    | less_than_or_equal(k(l),X1)
    | less_than_or_equal(X1,l) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_54,hypothesis,
    ( less_than_or_equal(n0,f(l))
    | less_than_or_equal(k(l),upper_bound) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_26]),c_0_27])]) ).

cnf(c_0_55,plain,
    ( less_than_or_equal(q(X1,X2),X2)
    | less_than_or_equal(X2,X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_52]) ).

cnf(c_0_56,hypothesis,
    ( less_than_or_equal(X1,q(l,X2))
    | less_than_or_equal(k(l),X2)
    | less_than_or_equal(X2,l)
    | ~ less_than_or_equal(X1,upper_bound) ),
    inference(spm,[status(thm)],[c_0_31,c_0_53]) ).

cnf(c_0_57,hypothesis,
    less_than_or_equal(k(l),upper_bound),
    inference(sr,[status(thm)],[c_0_54,c_0_42]) ).

cnf(c_0_58,plain,
    ( less_than_or_equal(X1,X2)
    | less_than_or_equal(X3,X1)
    | ~ less_than_or_equal(X3,q(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_55]) ).

cnf(c_0_59,hypothesis,
    ( less_than_or_equal(k(l),q(l,X1))
    | less_than_or_equal(k(l),X1)
    | less_than_or_equal(X1,l) ),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_60,hypothesis,
    ( less_than_or_equal(k(l),X1)
    | less_than_or_equal(X1,l) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,hypothesis,
    ( less_than_or_equal(q(X1,k(l)),l)
    | less_than_or_equal(k(l),X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_60]) ).

cnf(c_0_62,axiom,
    ( less_than_or_equal(n0,f(X1))
    | ~ less_than_or_equal(k(X1),X1)
    | ~ less_than_or_equal(lower_bound,X1)
    | ~ less_than_or_equal(X1,upper_bound) ),
    continuity3 ).

cnf(c_0_63,hypothesis,
    less_than_or_equal(k(l),l),
    inference(spm,[status(thm)],[c_0_49,c_0_61]) ).

cnf(c_0_64,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_26]),c_0_27])]),c_0_42]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ANA002-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.36  % Computer : n020.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit   : 300
% 0.13/0.37  % WCLimit    : 300
% 0.13/0.37  % DateTime   : Fri Aug 25 18:49:00 EDT 2023
% 0.13/0.37  % CPUTime  : 
% 0.22/0.62  start to proof: theBenchmark
% 11.73/11.91  % Version  : CSE_E---1.5
% 11.73/11.91  % Problem  : theBenchmark.p
% 11.73/11.91  % Proof found
% 11.73/11.91  % SZS status Theorem for theBenchmark.p
% 11.73/11.91  % SZS output start Proof
% See solution above
% 11.73/11.91  % Total time : 11.248000 s
% 11.73/11.91  % SZS output end Proof
% 11.73/11.91  % Total time : 11.251000 s
%------------------------------------------------------------------------------