TSTP Solution File: HEN010-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN010-2 : 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 : n026.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 01:54:25 EDT 2023

% Result   : Unsatisfiable 1.15s 1.19s
% Output   : CNFRefutation 1.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   48 (  18 unt;   9 typ;   0 def)
%            Number of atoms       :   84 (  10 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   92 (  47   ~;  45   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   73 (   6 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    zero: $i ).

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

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

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

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

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

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

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

cnf(one_inversion_equals_three,axiom,
    ( X2 = X4
    | ~ quotient(identity,X1,X2)
    | ~ quotient(identity,X2,X3)
    | ~ quotient(identity,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).

cnf(closure,axiom,
    quotient(X1,X2,divide(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).

cnf(divisor_existence,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).

cnf(identity_divide_idQ_idQa,hypothesis,
    quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).

cnf(quotient_property,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).

cnf(x_divde_zero_is_x,axiom,
    quotient(X1,zero,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).

cnf(identity_divide_idQa,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).

cnf(transitivity_of_less_equal,axiom,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).

cnf(x_divide_x_is_zero,axiom,
    quotient(X1,X1,zero),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).

cnf(identity_divide_a,hypothesis,
    quotient(identity,a,idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).

cnf(less_equal_quotient,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).

cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
    idQa != idQa_Q__idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).

cnf(c_0_13,axiom,
    ( X2 = X4
    | ~ quotient(identity,X1,X2)
    | ~ quotient(identity,X2,X3)
    | ~ quotient(identity,X3,X4) ),
    one_inversion_equals_three ).

cnf(c_0_14,axiom,
    quotient(X1,X2,divide(X1,X2)),
    closure ).

cnf(c_0_15,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    divisor_existence ).

cnf(c_0_16,hypothesis,
    quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa),
    identity_divide_idQ_idQa ).

cnf(c_0_17,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    quotient_property ).

cnf(c_0_18,axiom,
    quotient(X1,zero,X1),
    x_divde_zero_is_x ).

cnf(c_0_19,plain,
    ( X1 = divide(identity,X2)
    | ~ quotient(identity,X1,X2)
    | ~ quotient(identity,X3,X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    identity_divide_idQa ).

cnf(c_0_21,axiom,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    transitivity_of_less_equal ).

cnf(c_0_22,hypothesis,
    less_equal(idQa_Q__idQ_idQa,idQa),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_23,plain,
    ( less_equal(X1,X2)
    | ~ quotient(X3,X4,zero)
    | ~ quotient(X5,X4,X2)
    | ~ quotient(X6,X4,X1)
    | ~ quotient(X6,X3,X5) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,axiom,
    quotient(X1,X1,zero),
    x_divide_x_is_zero ).

cnf(c_0_25,hypothesis,
    ( divide(identity,idQ_idQa) = idQa
    | ~ quotient(identity,X1,idQa) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,hypothesis,
    quotient(identity,a,idQa),
    identity_divide_a ).

cnf(c_0_27,hypothesis,
    ( less_equal(X1,idQa)
    | ~ less_equal(X1,idQa_Q__idQ_idQa) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    less_equal_quotient ).

cnf(c_0_29,plain,
    ( less_equal(X1,X2)
    | ~ quotient(X3,X4,X2)
    | ~ quotient(X5,X4,X1)
    | ~ quotient(X5,X4,X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,hypothesis,
    divide(identity,idQ_idQa) = idQa,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_32,hypothesis,
    ( less_equal(X1,idQa)
    | ~ quotient(X1,idQa_Q__idQ_idQa,zero) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_33,hypothesis,
    ( less_equal(X1,idQa_Q__idQ_idQa)
    | ~ quotient(X2,idQ_idQa,idQa)
    | ~ quotient(X2,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_16]) ).

cnf(c_0_34,hypothesis,
    quotient(identity,idQ_idQa,idQa),
    inference(spm,[status(thm)],[c_0_14,c_0_30]) ).

cnf(c_0_35,hypothesis,
    ( idQa = X1
    | ~ quotient(X1,idQa_Q__idQ_idQa,zero)
    | ~ less_equal(idQa,X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,hypothesis,
    ( less_equal(X1,idQa_Q__idQ_idQa)
    | ~ quotient(identity,idQ_idQa,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    idQa != idQa_Q__idQ_idQa,
    prove_idQa_equals_idQa_Q__idQ_idQa ).

cnf(c_0_38,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24]),c_0_34])]),c_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : HEN010-2 : 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
% 0.14/0.35  % Computer : n026.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   : Thu Aug 24 13:50:32 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.22/0.58  start to proof: theBenchmark
% 1.15/1.19  % Version  : CSE_E---1.5
% 1.15/1.19  % Problem  : theBenchmark.p
% 1.15/1.19  % Proof found
% 1.15/1.19  % SZS status Theorem for theBenchmark.p
% 1.15/1.19  % SZS output start Proof
% See solution above
% 1.15/1.20  % Total time : 0.605000 s
% 1.15/1.20  % SZS output end Proof
% 1.15/1.20  % Total time : 0.608000 s
%------------------------------------------------------------------------------