TSTP Solution File: HEN011-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN011-3 : 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 : n024.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 01:54:27 EDT 2023

% Result   : Unsatisfiable 0.86s 0.93s
% Output   : CNFRefutation 0.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   95 (  70 unt;  10 typ;   0 def)
%            Number of atoms       :  104 (  77 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   41 (  22   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Maximal term depth    :    5 (   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    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :   81 (  24 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 ).

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

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

tff(decl_31,type,
    g: $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(identity_is_largest,axiom,
    less_equal(X1,identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).

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(identity_divide_b,hypothesis,
    divide(identity,b) = d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_b) ).

cnf(identity_divide_d,hypothesis,
    divide(identity,d) = g,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_d) ).

cnf(identity_divide_a,hypothesis,
    divide(identity,a) = c,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).

cnf(identity_divide_c,hypothesis,
    divide(identity,c) = e,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_c) ).

cnf(prove_commutativity,negated_conjecture,
    divide(c,g) != divide(d,e),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).

cnf(c_0_12,axiom,
    ( divide(X1,X2) = zero
    | ~ less_equal(X1,X2) ),
    quotient_less_equal1 ).

cnf(c_0_13,axiom,
    less_equal(divide(X1,X2),X1),
    quotient_smaller_than_numerator ).

cnf(c_0_14,axiom,
    less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
    quotient_property ).

cnf(c_0_15,plain,
    divide(divide(X1,X2),X1) = zero,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_17,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_18,axiom,
    less_equal(X1,identity),
    identity_is_largest ).

cnf(c_0_19,axiom,
    ( less_equal(X1,X2)
    | divide(X1,X2) != zero ),
    quotient_less_equal2 ).

cnf(c_0_20,plain,
    less_equal(divide(divide(X1,X1),divide(X2,X1)),zero),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,plain,
    divide(zero,X1) = zero,
    inference(spm,[status(thm)],[c_0_12,c_0_16]) ).

cnf(c_0_22,plain,
    ( divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X3),X2)
    | ~ less_equal(divide(divide(X1,X3),X2),divide(divide(X1,X2),divide(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_23,hypothesis,
    divide(identity,b) = d,
    identity_divide_b ).

cnf(c_0_24,plain,
    divide(X1,identity) = zero,
    inference(spm,[status(thm)],[c_0_12,c_0_18]) ).

cnf(c_0_25,plain,
    ( divide(X1,X2) = X1
    | ~ less_equal(X1,divide(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_13]) ).

cnf(c_0_26,plain,
    ( X1 = X2
    | divide(X2,X1) != zero
    | ~ less_equal(X1,X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_19]) ).

cnf(c_0_27,plain,
    less_equal(divide(divide(X1,X1),zero),zero),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,hypothesis,
    divide(identity,d) = g,
    identity_divide_d ).

cnf(c_0_29,hypothesis,
    divide(divide(X1,b),d) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_21]),c_0_24]),c_0_21]),c_0_16])]) ).

cnf(c_0_30,plain,
    ( divide(X1,X2) = X1
    | divide(X1,divide(X1,X2)) != zero ),
    inference(spm,[status(thm)],[c_0_25,c_0_19]) ).

cnf(c_0_31,plain,
    divide(divide(X1,X1),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21])]) ).

cnf(c_0_32,hypothesis,
    less_equal(divide(divide(X1,d),g),zero),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_28]),c_0_24]),c_0_21]) ).

cnf(c_0_33,hypothesis,
    divide(identity,a) = c,
    identity_divide_a ).

cnf(c_0_34,hypothesis,
    divide(divide(X1,d),divide(b,d)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_16])]) ).

cnf(c_0_35,plain,
    ( divide(divide(X1,X2),zero) = divide(divide(X1,zero),X2)
    | ~ less_equal(divide(divide(X1,zero),X2),divide(divide(X1,X2),zero)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_21]) ).

cnf(c_0_36,plain,
    divide(X1,X1) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31])]) ).

cnf(c_0_37,plain,
    divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
    inference(spm,[status(thm)],[c_0_12,c_0_14]) ).

cnf(c_0_38,hypothesis,
    divide(divide(X1,d),g) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_16])]) ).

cnf(c_0_39,hypothesis,
    divide(divide(X1,a),c) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_24]),c_0_21]),c_0_24]),c_0_21]),c_0_16])]) ).

cnf(c_0_40,hypothesis,
    divide(identity,c) = e,
    identity_divide_c ).

cnf(c_0_41,plain,
    ( X1 = X2
    | divide(X2,X1) != zero
    | divide(X1,X2) != zero ),
    inference(spm,[status(thm)],[c_0_26,c_0_19]) ).

cnf(c_0_42,hypothesis,
    divide(g,divide(b,d)) = zero,
    inference(spm,[status(thm)],[c_0_34,c_0_28]) ).

cnf(c_0_43,plain,
    divide(divide(X1,divide(X1,zero)),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16])]) ).

cnf(c_0_44,hypothesis,
    divide(divide(divide(X1,g),divide(d,g)),zero) = zero,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_45,hypothesis,
    divide(divide(X1,c),divide(a,c)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_39]),c_0_16])]) ).

cnf(c_0_46,hypothesis,
    less_equal(divide(divide(X1,c),e),zero),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_40]),c_0_24]),c_0_21]) ).

cnf(c_0_47,hypothesis,
    divide(b,d) = g,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38])]) ).

cnf(c_0_48,plain,
    divide(X1,divide(X1,zero)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_43]),c_0_43])]) ).

cnf(c_0_49,hypothesis,
    divide(divide(X1,g),divide(d,g)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_44]),c_0_21])]) ).

cnf(c_0_50,hypothesis,
    divide(e,divide(a,c)) = zero,
    inference(spm,[status(thm)],[c_0_45,c_0_40]) ).

cnf(c_0_51,hypothesis,
    divide(divide(X1,c),e) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_46]),c_0_16])]) ).

cnf(c_0_52,plain,
    divide(divide(X1,X2),divide(identity,X2)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_21]),c_0_21]),c_0_16])]) ).

cnf(c_0_53,hypothesis,
    divide(g,b) = zero,
    inference(spm,[status(thm)],[c_0_15,c_0_47]) ).

cnf(c_0_54,plain,
    divide(X1,zero) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_15])]) ).

cnf(c_0_55,hypothesis,
    ( divide(d,g) = divide(X1,g)
    | divide(divide(d,g),divide(X1,g)) != zero ),
    inference(spm,[status(thm)],[c_0_41,c_0_49]) ).

cnf(c_0_56,hypothesis,
    divide(a,c) = e,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_51])]) ).

cnf(c_0_57,hypothesis,
    divide(divide(X1,e),divide(c,e)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_51]),c_0_16])]) ).

cnf(c_0_58,plain,
    ( divide(identity,X1) = divide(X2,X1)
    | divide(divide(identity,X1),divide(X2,X1)) != zero ),
    inference(spm,[status(thm)],[c_0_41,c_0_52]) ).

cnf(c_0_59,hypothesis,
    divide(divide(X1,b),divide(divide(X1,g),b)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_53]),c_0_54]) ).

cnf(c_0_60,hypothesis,
    divide(d,g) = divide(identity,g),
    inference(spm,[status(thm)],[c_0_55,c_0_52]) ).

cnf(c_0_61,hypothesis,
    divide(e,a) = zero,
    inference(spm,[status(thm)],[c_0_15,c_0_56]) ).

cnf(c_0_62,hypothesis,
    ( divide(c,e) = divide(X1,e)
    | divide(divide(c,e),divide(X1,e)) != zero ),
    inference(spm,[status(thm)],[c_0_41,c_0_57]) ).

cnf(c_0_63,hypothesis,
    divide(divide(identity,g),b) = d,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_23]) ).

cnf(c_0_64,hypothesis,
    less_equal(divide(identity,g),d),
    inference(spm,[status(thm)],[c_0_13,c_0_60]) ).

cnf(c_0_65,hypothesis,
    divide(divide(X1,a),divide(divide(X1,e),a)) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_61]),c_0_54]) ).

cnf(c_0_66,hypothesis,
    divide(c,e) = divide(identity,e),
    inference(spm,[status(thm)],[c_0_62,c_0_52]) ).

cnf(c_0_67,plain,
    divide(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)) = zero,
    inference(spm,[status(thm)],[c_0_37,c_0_15]) ).

cnf(c_0_68,hypothesis,
    divide(divide(divide(identity,X1),divide(c,X1)),divide(e,X1)) = zero,
    inference(spm,[status(thm)],[c_0_37,c_0_40]) ).

cnf(c_0_69,hypothesis,
    divide(identity,g) = d,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_63]),c_0_64])]) ).

cnf(c_0_70,hypothesis,
    divide(divide(identity,e),a) = c,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_65]),c_0_33]) ).

cnf(c_0_71,hypothesis,
    less_equal(divide(identity,e),c),
    inference(spm,[status(thm)],[c_0_13,c_0_66]) ).

cnf(c_0_72,plain,
    divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)) = zero,
    inference(rw,[status(thm)],[c_0_67,c_0_54]) ).

cnf(c_0_73,hypothesis,
    divide(divide(d,divide(c,g)),divide(e,g)) = zero,
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_74,hypothesis,
    divide(divide(divide(identity,X1),divide(d,X1)),divide(g,X1)) = zero,
    inference(spm,[status(thm)],[c_0_37,c_0_28]) ).

cnf(c_0_75,hypothesis,
    divide(identity,e) = c,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_70]),c_0_71])]) ).

cnf(c_0_76,hypothesis,
    divide(divide(d,divide(c,g)),e) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_21]),c_0_54]) ).

cnf(c_0_77,hypothesis,
    divide(divide(c,divide(d,e)),divide(g,e)) = zero,
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_78,hypothesis,
    divide(divide(d,e),divide(divide(c,g),e)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_76]),c_0_16])]) ).

cnf(c_0_79,hypothesis,
    divide(divide(c,divide(d,e)),g) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_77]),c_0_21]),c_0_54]) ).

cnf(c_0_80,hypothesis,
    divide(divide(d,e),divide(c,g)) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_78]),c_0_21]),c_0_54]) ).

cnf(c_0_81,negated_conjecture,
    divide(c,g) != divide(d,e),
    prove_commutativity ).

cnf(c_0_82,hypothesis,
    divide(divide(c,g),divide(divide(d,e),g)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_79]),c_0_16])]) ).

cnf(c_0_83,hypothesis,
    divide(divide(c,g),divide(d,e)) != zero,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_80]),c_0_81]) ).

cnf(c_0_84,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_21]),c_0_54]),c_0_83]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : HEN011-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Thu Aug 24 13:28:24 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.86/0.93  % Version  : CSE_E---1.5
% 0.86/0.93  % Problem  : theBenchmark.p
% 0.86/0.93  % Proof found
% 0.86/0.93  % SZS status Theorem for theBenchmark.p
% 0.86/0.93  % SZS output start Proof
% See solution above
% 0.86/0.94  % Total time : 0.356000 s
% 0.86/0.94  % SZS output end Proof
% 0.86/0.94  % Total time : 0.359000 s
%------------------------------------------------------------------------------