TSTP Solution File: KLE034+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE034+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n015.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 05:25:47 EDT 2023

% Result   : Theorem 0.21s 0.66s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   66 (  37 unt;  14 typ;   0 def)
%            Number of atoms       :   97 (  48 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   68 (  23   ~;  19   |;  20   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   72 (   2 sgn;  46   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    test: $i > $o ).

tff(decl_28,type,
    complement: ( $i * $i ) > $o ).

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

tff(decl_30,type,
    esk1_1: $i > $i ).

tff(decl_31,type,
    esk2_0: $i ).

tff(decl_32,type,
    esk3_0: $i ).

tff(decl_33,type,
    esk4_0: $i ).

tff(decl_34,type,
    esk5_0: $i ).

tff(decl_35,type,
    esk6_0: $i ).

fof(goals,conjecture,
    ! [X4,X5,X6,X7,X8] :
      ( ( test(X7)
        & test(X6)
        & test(X8)
        & leq(multiplication(multiplication(X6,X4),c(X7)),zero)
        & leq(multiplication(multiplication(X7,X5),c(X8)),zero) )
     => leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(multiplicative_associativity,axiom,
    ! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).

fof(additive_identity,axiom,
    ! [X1] : addition(X1,zero) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).

fof(additive_commutativity,axiom,
    ! [X1,X2] : addition(X1,X2) = addition(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).

fof(test_3,axiom,
    ! [X4,X5] :
      ( test(X4)
     => ( c(X4) = X5
      <=> complement(X4,X5) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).

fof(left_distributivity,axiom,
    ! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).

fof(test_2,axiom,
    ! [X4,X5] :
      ( complement(X5,X4)
    <=> ( multiplication(X4,X5) = zero
        & multiplication(X5,X4) = zero
        & addition(X4,X5) = one ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).

fof(left_annihilation,axiom,
    ! [X1] : multiplication(zero,X1) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).

fof(multiplicative_left_identity,axiom,
    ! [X1] : multiplication(one,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X4,X5,X6,X7,X8] :
        ( ( test(X7)
          & test(X6)
          & test(X8)
          & leq(multiplication(multiplication(X6,X4),c(X7)),zero)
          & leq(multiplication(multiplication(X7,X5),c(X8)),zero) )
       => leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_12,negated_conjecture,
    ( test(esk5_0)
    & test(esk4_0)
    & test(esk6_0)
    & leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
    & leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero)
    & ~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_13,plain,
    ! [X16,X17,X18] : multiplication(X16,multiplication(X17,X18)) = multiplication(multiplication(X16,X17),X18),
    inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).

fof(c_0_14,plain,
    ! [X29,X30] :
      ( ( ~ leq(X29,X30)
        | addition(X29,X30) = X30 )
      & ( addition(X29,X30) != X30
        | leq(X29,X30) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

cnf(c_0_15,negated_conjecture,
    leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_17,plain,
    ! [X14] : addition(X14,zero) = X14,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

fof(c_0_18,plain,
    ! [X9,X10] : addition(X9,X10) = addition(X10,X9),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_19,plain,
    ! [X37,X38] :
      ( ( c(X37) != X38
        | complement(X37,X38)
        | ~ test(X37) )
      & ( ~ complement(X37,X38)
        | c(X37) = X38
        | ~ test(X37) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).

cnf(c_0_20,negated_conjecture,
    leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_21,plain,
    ! [X24,X25,X26] : multiplication(addition(X24,X25),X26) = addition(multiplication(X24,X26),multiplication(X25,X26)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

cnf(c_0_22,plain,
    ( addition(X1,X2) = X2
    | ~ leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,negated_conjecture,
    leq(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero),
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_24,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_26,plain,
    ! [X35,X36] :
      ( ( multiplication(X35,X36) = zero
        | ~ complement(X36,X35) )
      & ( multiplication(X36,X35) = zero
        | ~ complement(X36,X35) )
      & ( addition(X35,X36) = one
        | ~ complement(X36,X35) )
      & ( multiplication(X35,X36) != zero
        | multiplication(X36,X35) != zero
        | addition(X35,X36) != one
        | complement(X36,X35) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).

cnf(c_0_27,plain,
    ( complement(X1,X2)
    | c(X1) != X2
    | ~ test(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,negated_conjecture,
    leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
    inference(rw,[status(thm)],[c_0_20,c_0_16]) ).

fof(c_0_29,plain,
    ! [X28] : multiplication(zero,X28) = zero,
    inference(variable_rename,[status(thm)],[left_annihilation]) ).

cnf(c_0_30,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_31,negated_conjecture,
    multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_32,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_33,plain,
    ( addition(X1,X2) = one
    | ~ complement(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_34,plain,
    ( complement(X1,c(X1))
    | ~ test(X1) ),
    inference(er,[status(thm)],[c_0_27]) ).

fof(c_0_35,plain,
    ! [X20] : multiplication(one,X20) = X20,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

cnf(c_0_36,negated_conjecture,
    multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_24]) ).

cnf(c_0_37,plain,
    multiplication(zero,X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_38,negated_conjecture,
    multiplication(addition(esk5_0,X1),multiplication(esk3_0,c(esk6_0))) = multiplication(X1,multiplication(esk3_0,c(esk6_0))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

cnf(c_0_39,plain,
    ( addition(X1,c(X1)) = one
    | ~ test(X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_25]) ).

cnf(c_0_40,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_41,negated_conjecture,
    test(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_42,plain,
    ! [X15] : addition(X15,X15) = X15,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

cnf(c_0_43,negated_conjecture,
    ~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_44,negated_conjecture,
    multiplication(esk4_0,multiplication(esk2_0,multiplication(c(esk5_0),X1))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_36]),c_0_37]),c_0_16]) ).

cnf(c_0_45,negated_conjecture,
    multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0))) = multiplication(esk3_0,c(esk6_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).

cnf(c_0_46,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_47,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    ~ leq(multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))),zero),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_16]),c_0_16]) ).

cnf(c_0_49,negated_conjecture,
    multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) = zero,
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_50,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE034+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n015.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   : Tue Aug 29 12:04:11 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.66  % Version  : CSE_E---1.5
% 0.21/0.66  % Problem  : theBenchmark.p
% 0.21/0.66  % Proof found
% 0.21/0.66  % SZS status Theorem for theBenchmark.p
% 0.21/0.66  % SZS output start Proof
% See solution above
% 0.21/0.67  % Total time : 0.071000 s
% 0.21/0.67  % SZS output end Proof
% 0.21/0.67  % Total time : 0.074000 s
%------------------------------------------------------------------------------