TSTP Solution File: GRP181-3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP181-3 : 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 : n025.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 0.85s 0.91s
% Output   : CNFRefutation 0.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   49 (  41 unt;   8 typ;   0 def)
%            Number of atoms       :   41 (  40 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   :   53 (   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(monotony_glb2,axiom,
    multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).

cnf(p12x_4,hypothesis,
    inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).

cnf(p12x_2,hypothesis,
    least_upper_bound(a,c) = least_upper_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).

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(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(p12x_1,hypothesis,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).

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

cnf(c_0_11,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_12,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_13,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_14,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

cnf(c_0_15,axiom,
    multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
    monotony_glb2 ).

cnf(c_0_16,plain,
    multiply(inverse(inverse(X1)),identity) = X1,
    inference(spm,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_17,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_14,c_0_14]) ).

cnf(c_0_18,plain,
    multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_12]) ).

cnf(c_0_19,hypothesis,
    inverse(least_upper_bound(X1,X2)) = greatest_lower_bound(inverse(X1),inverse(X2)),
    p12x_4 ).

cnf(c_0_20,hypothesis,
    least_upper_bound(a,c) = least_upper_bound(b,c),
    p12x_2 ).

cnf(c_0_21,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_22,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,axiom,
    multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_glb1 ).

cnf(c_0_24,hypothesis,
    multiply(inverse(least_upper_bound(X1,X2)),X1) = greatest_lower_bound(identity,multiply(inverse(X2),X1)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_25,hypothesis,
    least_upper_bound(c,a) = least_upper_bound(c,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).

cnf(c_0_26,hypothesis,
    greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
    p12x_1 ).

cnf(c_0_27,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_28,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_22]) ).

cnf(c_0_29,plain,
    multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
    inference(spm,[status(thm)],[c_0_23,c_0_14]) ).

cnf(c_0_30,hypothesis,
    greatest_lower_bound(identity,multiply(inverse(a),c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_24]) ).

cnf(c_0_31,hypothesis,
    greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).

cnf(c_0_32,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_12,c_0_28]) ).

cnf(c_0_33,hypothesis,
    multiply(a,greatest_lower_bound(identity,multiply(inverse(b),c))) = greatest_lower_bound(c,b),
    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_29,c_0_30]),c_0_28]),c_0_28]),c_0_22]),c_0_27]),c_0_31]) ).

cnf(c_0_34,plain,
    multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
    inference(spm,[status(thm)],[c_0_11,c_0_32]) ).

cnf(c_0_35,hypothesis,
    greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(a),greatest_lower_bound(c,b)),
    inference(spm,[status(thm)],[c_0_14,c_0_33]) ).

cnf(c_0_36,plain,
    multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_34]),c_0_22]) ).

cnf(c_0_37,hypothesis,
    multiply(b,multiply(inverse(a),greatest_lower_bound(c,b))) = greatest_lower_bound(c,b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_35]),c_0_28]),c_0_28]),c_0_22]),c_0_27]) ).

cnf(c_0_38,hypothesis,
    inverse(a) = inverse(b),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_11]),c_0_32]),c_0_22]) ).

cnf(c_0_39,negated_conjecture,
    a != b,
    prove_p12x ).

cnf(c_0_40,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_28]),c_0_39]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : GRP181-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Aug 28 23:41:10 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.16/0.56  start to proof: theBenchmark
% 0.85/0.91  % Version  : CSE_E---1.5
% 0.85/0.91  % Problem  : theBenchmark.p
% 0.85/0.91  % Proof found
% 0.85/0.91  % SZS status Theorem for theBenchmark.p
% 0.85/0.91  % SZS output start Proof
% See solution above
% 0.85/0.92  % Total time : 0.349000 s
% 0.85/0.92  % SZS output end Proof
% 0.85/0.92  % Total time : 0.351000 s
%------------------------------------------------------------------------------