TSTP Solution File: KLE132+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE132+1 : 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 : n010.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 05:26:30 EDT 2023

% Result   : Theorem 0.19s 0.72s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   83 (  61 unt;  19 typ;   0 def)
%            Number of atoms       :   70 (  69 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   4   ~;   0   |;   2   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :   16 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  15   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   4 con; 0-2 aty)
%            Number of variables   :   93 (   1 sgn;  51   !;   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,
    antidomain: $i > $i ).

tff(decl_28,type,
    domain: $i > $i ).

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

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

tff(decl_31,type,
    c: $i > $i ).

tff(decl_32,type,
    domain_difference: ( $i * $i ) > $i ).

tff(decl_33,type,
    forward_diamond: ( $i * $i ) > $i ).

tff(decl_34,type,
    backward_diamond: ( $i * $i ) > $i ).

tff(decl_35,type,
    forward_box: ( $i * $i ) > $i ).

tff(decl_36,type,
    backward_box: ( $i * $i ) > $i ).

tff(decl_37,type,
    divergence: $i > $i ).

tff(decl_38,type,
    star: $i > $i ).

tff(decl_39,type,
    esk1_0: $i ).

tff(decl_40,type,
    esk2_0: $i ).

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(domain1,axiom,
    ! [X4] : multiplication(antidomain(X4),X4) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).

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(domain3,axiom,
    ! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).

fof(goals,conjecture,
    ! [X4] :
      ( ! [X5] : addition(forward_diamond(X4,domain(X5)),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))
     => ! [X6] :
          ( addition(domain(X6),forward_diamond(X4,domain(X6))) = forward_diamond(X4,domain(X6))
         => domain(X6) = zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(forward_diamond,axiom,
    ! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).

fof(domain4,axiom,
    ! [X4] : domain(X4) = antidomain(antidomain(X4)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).

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

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

fof(domain_difference,axiom,
    ! [X4,X5] : domain_difference(X4,X5) = multiplication(domain(X4),antidomain(X5)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',domain_difference) ).

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

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

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

fof(c_0_14,plain,
    ! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
    inference(variable_rename,[status(thm)],[left_distributivity]) ).

fof(c_0_15,plain,
    ! [X29] : multiplication(antidomain(X29),X29) = zero,
    inference(variable_rename,[status(thm)],[domain1]) ).

fof(c_0_16,plain,
    ! [X12] : addition(X12,zero) = X12,
    inference(variable_rename,[status(thm)],[additive_identity]) ).

cnf(c_0_17,plain,
    multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    multiplication(antidomain(X1),X1) = zero,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    addition(X1,zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_20,plain,
    ! [X7,X8] : addition(X7,X8) = addition(X8,X7),
    inference(variable_rename,[status(thm)],[additive_commutativity]) ).

fof(c_0_21,plain,
    ! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
    inference(variable_rename,[status(thm)],[domain3]) ).

fof(c_0_22,negated_conjecture,
    ~ ! [X4] :
        ( ! [X5] : addition(forward_diamond(X4,domain(X5)),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))
       => ! [X6] :
            ( addition(domain(X6),forward_diamond(X4,domain(X6))) = forward_diamond(X4,domain(X6))
           => domain(X6) = zero ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_23,plain,
    ! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
    inference(variable_rename,[status(thm)],[forward_diamond]) ).

fof(c_0_24,plain,
    ! [X33] : domain(X33) = antidomain(antidomain(X33)),
    inference(variable_rename,[status(thm)],[domain4]) ).

fof(c_0_25,plain,
    ! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
    inference(variable_rename,[status(thm)],[right_distributivity]) ).

cnf(c_0_26,plain,
    multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_27,plain,
    addition(X1,X2) = addition(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_28,plain,
    addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_29,plain,
    ! [X18] : multiplication(one,X18) = X18,
    inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).

fof(c_0_30,plain,
    ! [X40,X41] : domain_difference(X40,X41) = multiplication(domain(X40),antidomain(X41)),
    inference(variable_rename,[status(thm)],[domain_difference]) ).

fof(c_0_31,negated_conjecture,
    ! [X55] :
      ( addition(forward_diamond(esk1_0,domain(X55)),forward_diamond(star(esk1_0),domain_difference(domain(X55),forward_diamond(esk1_0,domain(X55))))) = forward_diamond(star(esk1_0),domain_difference(domain(X55),forward_diamond(esk1_0,domain(X55))))
      & addition(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))) = forward_diamond(esk1_0,domain(esk2_0))
      & domain(esk2_0) != zero ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).

cnf(c_0_32,plain,
    forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_33,plain,
    domain(X1) = antidomain(antidomain(X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,plain,
    multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_35,plain,
    ! [X17] : multiplication(X17,one) = X17,
    inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).

cnf(c_0_36,plain,
    multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_37,plain,
    addition(antidomain(X1),antidomain(antidomain(X1))) = one,
    inference(rw,[status(thm)],[c_0_28,c_0_27]) ).

cnf(c_0_38,plain,
    multiplication(one,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_39,plain,
    domain_difference(X1,X2) = multiplication(domain(X1),antidomain(X2)),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

fof(c_0_40,plain,
    ! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
    inference(variable_rename,[status(thm)],[additive_associativity]) ).

cnf(c_0_41,negated_conjecture,
    addition(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))) = forward_diamond(esk1_0,domain(esk2_0)),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_42,plain,
    forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).

cnf(c_0_43,plain,
    multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_19]) ).

cnf(c_0_44,plain,
    multiplication(X1,one) = X1,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_45,plain,
    multiplication(antidomain(antidomain(X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

cnf(c_0_46,negated_conjecture,
    addition(forward_diamond(esk1_0,domain(X1)),forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1))))) = forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1)))),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_47,plain,
    domain_difference(X1,X2) = multiplication(antidomain(antidomain(X1)),antidomain(X2)),
    inference(rw,[status(thm)],[c_0_39,c_0_33]) ).

cnf(c_0_48,plain,
    addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_49,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_33]),c_0_33]),c_0_33]),c_0_42]),c_0_42]) ).

cnf(c_0_50,plain,
    antidomain(antidomain(antidomain(X1))) = antidomain(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_44]),c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1))))))),antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))) = antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_47]),c_0_47]) ).

cnf(c_0_52,plain,
    antidomain(one) = zero,
    inference(spm,[status(thm)],[c_0_44,c_0_18]) ).

cnf(c_0_53,plain,
    addition(zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_19,c_0_27]) ).

fof(c_0_54,plain,
    ! [X25] : multiplication(X25,zero) = zero,
    inference(variable_rename,[status(thm)],[right_annihilation]) ).

cnf(c_0_55,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),X1)) = addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_50]) ).

cnf(c_0_56,negated_conjecture,
    addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(X1))))),addition(antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),antidomain(multiplication(esk1_0,antidomain(antidomain(X1)))))))))),X2)) = addition(antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),antidomain(multiplication(esk1_0,antidomain(antidomain(X1)))))))))),X2),
    inference(rw,[status(thm)],[inference(rw,[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_48,c_0_51]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]),c_0_50]) ).

cnf(c_0_57,negated_conjecture,
    multiplication(antidomain(antidomain(esk2_0)),antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = zero,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_49]),c_0_18]),c_0_50]) ).

cnf(c_0_58,plain,
    antidomain(zero) = one,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_52]),c_0_53]) ).

cnf(c_0_59,plain,
    multiplication(X1,zero) = zero,
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_60,negated_conjecture,
    domain(esk2_0) != zero,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_61,negated_conjecture,
    addition(antidomain(antidomain(esk2_0)),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_55,c_0_56]),c_0_57]),c_0_58]),c_0_52]),c_0_59]),c_0_58]),c_0_52]),c_0_53]),c_0_57]),c_0_58]),c_0_52]),c_0_59]),c_0_58]),c_0_52]),c_0_53]) ).

cnf(c_0_62,negated_conjecture,
    antidomain(antidomain(esk2_0)) != zero,
    inference(rw,[status(thm)],[c_0_60,c_0_33]) ).

cnf(c_0_63,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_61]),c_0_62]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : KLE132+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 11:48:03 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.72  % Version  : CSE_E---1.5
% 0.19/0.72  % Problem  : theBenchmark.p
% 0.19/0.72  % Proof found
% 0.19/0.72  % SZS status Theorem for theBenchmark.p
% 0.19/0.72  % SZS output start Proof
% See solution above
% 0.19/0.72  % Total time : 0.148000 s
% 0.19/0.72  % SZS output end Proof
% 0.19/0.72  % Total time : 0.152000 s
%------------------------------------------------------------------------------