TSTP Solution File: GRP181-4 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP181-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 00:17:32 EDT 2023

% Result   : Unsatisfiable 6.59s 6.74s
% Output   : CNFRefutation 6.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   55 (  47 unt;   8 typ;   0 def)
%            Number of atoms       :   47 (  46 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   61 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    identity: $i ).

tff(decl_23,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_24,type,
    inverse: $i > $i ).

tff(decl_25,type,
    greatest_lower_bound: ( $i * $i ) > $i ).

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

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

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

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

cnf(associativity,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X1),X1) = identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(p12x_3,hypothesis,
    inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_3) ).

cnf(p12x_2,hypothesis,
    inverse(inverse(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).

cnf(monotony_glb1,axiom,
    multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).

cnf(symmetry_of_glb,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).

cnf(p12x_6,hypothesis,
    inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_6) ).

cnf(p12x_1,hypothesis,
    inverse(identity) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).

cnf(monotony_lub1,axiom,
    multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).

cnf(p12x_4,hypothesis,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).

cnf(p12x_5,hypothesis,
    least_upper_bound(a,c) = least_upper_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_5) ).

cnf(symmetry_of_lub,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).

cnf(prove_p12x,negated_conjecture,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12x) ).

cnf(c_0_14,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_15,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_16,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_17,hypothesis,
    inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
    p12x_3 ).

cnf(c_0_18,hypothesis,
    inverse(inverse(X1)) = X1,
    p12x_2 ).

cnf(c_0_19,axiom,
    multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_glb1 ).

cnf(c_0_20,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_21,hypothesis,
    inverse(greatest_lower_bound(X1,X2)) = least_upper_bound(inverse(X1),inverse(X2)),
    p12x_6 ).

cnf(c_0_22,hypothesis,
    inverse(identity) = identity,
    p12x_1 ).

cnf(c_0_23,axiom,
    multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_lub1 ).

cnf(c_0_24,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_25,hypothesis,
    inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,plain,
    greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_20]) ).

cnf(c_0_27,hypothesis,
    inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,hypothesis,
    multiply(inverse(X1),identity) = inverse(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_16]) ).

cnf(c_0_29,plain,
    multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,hypothesis,
    least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_25]) ).

cnf(c_0_31,hypothesis,
    multiply(X1,identity) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_18]) ).

cnf(c_0_32,hypothesis,
    multiply(X1,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = least_upper_bound(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_18]),c_0_18]),c_0_31]) ).

cnf(c_0_33,hypothesis,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
    p12x_4 ).

cnf(c_0_34,hypothesis,
    least_upper_bound(a,c) = least_upper_bound(b,c),
    p12x_5 ).

cnf(c_0_35,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_36,hypothesis,
    multiply(X1,multiply(inverse(greatest_lower_bound(X2,X1)),X2)) = least_upper_bound(X1,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_20]) ).

cnf(c_0_37,hypothesis,
    greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_20]),c_0_20]) ).

cnf(c_0_38,hypothesis,
    least_upper_bound(c,a) = least_upper_bound(c,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_35]) ).

cnf(c_0_39,hypothesis,
    multiply(a,multiply(inverse(greatest_lower_bound(c,b)),c)) = least_upper_bound(c,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_35]),c_0_38]) ).

cnf(c_0_40,hypothesis,
    multiply(inverse(greatest_lower_bound(c,b)),c) = multiply(inverse(a),least_upper_bound(c,b)),
    inference(spm,[status(thm)],[c_0_24,c_0_39]) ).

cnf(c_0_41,hypothesis,
    multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_18]) ).

cnf(c_0_42,hypothesis,
    multiply(b,multiply(inverse(a),least_upper_bound(c,b))) = least_upper_bound(c,b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_35]) ).

cnf(c_0_43,hypothesis,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_15,c_0_18]) ).

cnf(c_0_44,hypothesis,
    inverse(a) = inverse(b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_14]),c_0_43]),c_0_31]) ).

cnf(c_0_45,negated_conjecture,
    a != b,
    prove_p12x ).

cnf(c_0_46,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_44]),c_0_18]),c_0_45]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GRP181-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.04/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n029.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   : Mon Aug 28 20:47:56 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.53/0.56  start to proof: theBenchmark
% 6.59/6.74  % Version  : CSE_E---1.5
% 6.59/6.74  % Problem  : theBenchmark.p
% 6.59/6.74  % Proof found
% 6.59/6.74  % SZS status Theorem for theBenchmark.p
% 6.59/6.74  % SZS output start Proof
% See solution above
% 6.59/6.74  % Total time : 6.156000 s
% 6.59/6.74  % SZS output end Proof
% 6.59/6.74  % Total time : 6.160000 s
%------------------------------------------------------------------------------