TSTP Solution File: HEN007-3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN007-3 : 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 : n014.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 : Thu Aug 31 01:54:20 EDT 2023

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   46 (  33 unt;   7 typ;   0 def)
%            Number of atoms       :   47 (  16 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   50 (   8 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    zero: $i ).

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

tff(decl_26,type,
    a: $i ).

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

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

cnf(quotient_less_equal1,axiom,
    ( divide(X1,X2) = zero
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).

cnf(quotient_smaller_than_numerator,axiom,
    less_equal(divide(X1,X2),X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).

cnf(quotient_property,axiom,
    less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_property) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).

cnf(quotient_less_equal2,axiom,
    ( less_equal(X1,X2)
    | divide(X1,X2) != zero ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).

cnf(a_LE_b,hypothesis,
    less_equal(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).

cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
    ~ less_equal(divide(c,b),divide(c,a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).

cnf(c_0_8,axiom,
    ( divide(X1,X2) = zero
    | ~ less_equal(X1,X2) ),
    quotient_less_equal1 ).

cnf(c_0_9,axiom,
    less_equal(divide(X1,X2),X1),
    quotient_smaller_than_numerator ).

cnf(c_0_10,axiom,
    less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
    quotient_property ).

cnf(c_0_11,plain,
    divide(divide(X1,X2),X1) = zero,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_13,plain,
    less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    divide(zero,X1) = zero,
    inference(spm,[status(thm)],[c_0_8,c_0_12]) ).

cnf(c_0_15,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_16,plain,
    less_equal(divide(divide(X1,X1),zero),zero),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_17,axiom,
    ( less_equal(X1,X2)
    | divide(X1,X2) != zero ),
    quotient_less_equal2 ).

cnf(c_0_18,plain,
    divide(divide(X1,X1),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12])]) ).

cnf(c_0_19,plain,
    less_equal(divide(X1,X1),zero),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_20,plain,
    less_equal(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
    inference(spm,[status(thm)],[c_0_10,c_0_14]) ).

cnf(c_0_21,plain,
    divide(X1,X1) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_12])]) ).

cnf(c_0_22,plain,
    less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,plain,
    divide(divide(X1,divide(X1,zero)),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_22]),c_0_12])]) ).

cnf(c_0_24,plain,
    less_equal(divide(X1,divide(X1,zero)),zero),
    inference(spm,[status(thm)],[c_0_17,c_0_23]) ).

cnf(c_0_25,hypothesis,
    less_equal(a,b),
    a_LE_b ).

cnf(c_0_26,plain,
    divide(X1,divide(X1,zero)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_24]),c_0_12])]) ).

cnf(c_0_27,hypothesis,
    divide(a,b) = zero,
    inference(spm,[status(thm)],[c_0_8,c_0_25]) ).

cnf(c_0_28,plain,
    less_equal(X1,divide(X1,zero)),
    inference(spm,[status(thm)],[c_0_17,c_0_26]) ).

cnf(c_0_29,hypothesis,
    less_equal(divide(divide(X1,b),zero),divide(divide(X1,a),b)),
    inference(spm,[status(thm)],[c_0_10,c_0_27]) ).

cnf(c_0_30,plain,
    divide(X1,zero) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_28]),c_0_9])]) ).

cnf(c_0_31,hypothesis,
    less_equal(divide(X1,b),divide(divide(X1,a),b)),
    inference(rw,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_32,plain,
    less_equal(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_30]) ).

cnf(c_0_33,hypothesis,
    divide(divide(X1,b),divide(divide(X1,a),b)) = zero,
    inference(spm,[status(thm)],[c_0_8,c_0_31]) ).

cnf(c_0_34,hypothesis,
    less_equal(divide(divide(X1,b),divide(X1,a)),zero),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_14]) ).

cnf(c_0_35,hypothesis,
    divide(divide(X1,b),divide(X1,a)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_34]),c_0_30]) ).

cnf(c_0_36,negated_conjecture,
    ~ less_equal(divide(c,b),divide(c,a)),
    prove_c_divide_b_LE_c_divide_a ).

cnf(c_0_37,hypothesis,
    less_equal(divide(X1,b),divide(X1,a)),
    inference(spm,[status(thm)],[c_0_17,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : HEN007-3 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Thu Aug 24 13:31:49 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.018000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.021000 s
%------------------------------------------------------------------------------