%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN008-1 : 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 : n018.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 01:54:22 EDT 2023

% Result   : Unsatisfiable 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   45 (  17 unt;  10 typ;   0 def)
%            Number of atoms       :   72 (   8 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   77 (  40   ~;  37   |;   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    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   64 (   3 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,
    b: $i ).

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

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

tff(decl_31,type,
    bQc: $i ).

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/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_property) ).

cnf(closure,axiom,
    quotient(X1,X2,divide(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',closure) ).

cnf(quotient_less_equal,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).

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

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).

cnf(less_equal_quotient,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).

cnf(bQc,hypothesis,
    quotient(b,c,bQc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bQc) ).

cnf(well_defined,axiom,
    ( X3 = X4
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',well_defined) ).

cnf(aQc,hypothesis,
    quotient(a,c,aQc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aQc) ).

cnf(prove_aQcLEbQc,negated_conjecture,
    ~ less_equal(aQc,bQc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aQcLEbQc) ).

cnf(c_0_11,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_12,axiom,
    quotient(X1,X2,divide(X1,X2)),
    closure ).

cnf(c_0_13,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    quotient_less_equal ).

cnf(c_0_14,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_15,plain,
    ( less_equal(divide(X1,X2),X3)
    | ~ quotient(X4,X5,X3)
    | ~ quotient(X6,X5,X2)
    | ~ quotient(X7,X5,X1)
    | ~ quotient(X7,X6,X4) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

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

cnf(c_0_17,hypothesis,
    less_equal(a,b),
    aLEb ).

cnf(c_0_18,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,zero)
    | ~ quotient(X4,X5,X2)
    | ~ quotient(X3,X5,X1) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,hypothesis,
    quotient(a,b,zero),
    inference(spm,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_20,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_21,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    less_equal_quotient ).

cnf(c_0_22,hypothesis,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(b,X3,X2)
    | ~ quotient(a,X3,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,hypothesis,
    quotient(b,c,bQc),
    bQc ).

cnf(c_0_24,plain,
    ( X1 = X2
    | ~ quotient(X2,X1,zero)
    | ~ less_equal(X1,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,hypothesis,
    ( less_equal(divide(X1,bQc),zero)
    | ~ quotient(a,c,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,axiom,
    ( X3 = X4
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X1,X2,X4) ),
    well_defined ).

cnf(c_0_27,hypothesis,
    quotient(a,c,aQc),
    aQc ).

cnf(c_0_28,hypothesis,
    ( divide(X1,bQc) = zero
    | ~ quotient(a,c,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16])]) ).

cnf(c_0_29,hypothesis,
    ( X1 = aQc
    | ~ quotient(a,c,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,negated_conjecture,
    ~ less_equal(aQc,bQc),
    prove_aQcLEbQc ).

cnf(c_0_31,hypothesis,
    ( quotient(X1,bQc,zero)
    | ~ quotient(a,c,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_28]) ).

cnf(c_0_32,hypothesis,
    divide(a,c) = aQc,
    inference(spm,[status(thm)],[c_0_29,c_0_12]) ).

cnf(c_0_33,negated_conjecture,
    ~ quotient(aQc,bQc,zero),
    inference(spm,[status(thm)],[c_0_30,c_0_21]) ).

cnf(c_0_34,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_32]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : HEN008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n018.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 13:46:13 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.015000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.018000 s
%------------------------------------------------------------------------------