TSTP Solution File: GRP190-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP190-2 : 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 : n008.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 00:17:39 EDT 2023

% Result   : Unsatisfiable 0.22s 0.79s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   71 (  64 unt;   7 typ;   0 def)
%            Number of atoms       :   64 (  63 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    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (  10 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,
    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_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(glb_absorbtion,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).

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

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

cnf(p39c_1,hypothesis,
    least_upper_bound(a,b) = a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39c_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(idempotence_of_gld,axiom,
    greatest_lower_bound(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).

cnf(prove_p39c,negated_conjecture,
    greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p39c) ).

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,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_18,plain,
    multiply(inverse(inverse(X1)),identity) = X1,
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

cnf(c_0_19,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_17,c_0_17]) ).

cnf(c_0_20,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).

cnf(c_0_22,axiom,
    multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_glb1 ).

cnf(c_0_23,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_24,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_15,c_0_21]) ).

cnf(c_0_25,plain,
    greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_23]) ).

cnf(c_0_26,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    glb_absorbtion ).

cnf(c_0_27,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_28,axiom,
    least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
    lub_absorbtion ).

cnf(c_0_29,plain,
    multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
    inference(spm,[status(thm)],[c_0_14,c_0_24]) ).

cnf(c_0_30,axiom,
    multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
    monotony_glb2 ).

cnf(c_0_31,plain,
    multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_23]) ).

cnf(c_0_32,plain,
    greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_33,plain,
    least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_28,c_0_23]) ).

cnf(c_0_34,plain,
    multiply(X1,multiply(inverse(X1),X2)) = X2,
    inference(spm,[status(thm)],[c_0_17,c_0_21]) ).

cnf(c_0_35,plain,
    multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_20]) ).

cnf(c_0_36,plain,
    greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_16]),c_0_23]) ).

cnf(c_0_37,plain,
    multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
    inference(spm,[status(thm)],[c_0_31,c_0_23]) ).

cnf(c_0_38,plain,
    greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_23]) ).

cnf(c_0_39,axiom,
    least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
    associativity_of_lub ).

cnf(c_0_40,hypothesis,
    least_upper_bound(a,b) = a,
    p39c_1 ).

cnf(c_0_41,axiom,
    multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_lub1 ).

cnf(c_0_42,plain,
    inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_43,plain,
    multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_23]) ).

cnf(c_0_44,plain,
    greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_15]) ).

cnf(c_0_45,plain,
    least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_27]) ).

cnf(c_0_46,hypothesis,
    least_upper_bound(a,least_upper_bound(b,X1)) = least_upper_bound(a,X1),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_47,plain,
    least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_20]),c_0_27]) ).

cnf(c_0_48,plain,
    multiply(X1,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,inverse(X1))),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_49,plain,
    least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(X1,identity)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_27]) ).

cnf(c_0_50,plain,
    multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_35]),c_0_21]) ).

cnf(c_0_51,hypothesis,
    least_upper_bound(b,least_upper_bound(a,X1)) = least_upper_bound(a,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39]),c_0_45]) ).

cnf(c_0_52,plain,
    multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)),
    inference(spm,[status(thm)],[c_0_41,c_0_17]) ).

cnf(c_0_53,plain,
    least_upper_bound(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) = inverse(greatest_lower_bound(identity,inverse(X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_27]),c_0_49]),c_0_48]) ).

cnf(c_0_54,plain,
    multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_35]) ).

cnf(c_0_55,plain,
    multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
    inference(spm,[status(thm)],[c_0_30,c_0_50]) ).

cnf(c_0_56,hypothesis,
    greatest_lower_bound(b,least_upper_bound(a,X1)) = b,
    inference(spm,[status(thm)],[c_0_26,c_0_51]) ).

cnf(c_0_57,plain,
    least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_bound(X2,inverse(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(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]),c_0_16]),c_0_54]),c_0_55]),c_0_16]) ).

cnf(c_0_58,hypothesis,
    greatest_lower_bound(b,inverse(greatest_lower_bound(X1,inverse(a)))) = b,
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_59,hypothesis,
    least_upper_bound(inverse(b),greatest_lower_bound(X1,inverse(a))) = inverse(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_27]) ).

cnf(c_0_60,axiom,
    greatest_lower_bound(X1,X1) = X1,
    idempotence_of_gld ).

cnf(c_0_61,hypothesis,
    least_upper_bound(inverse(a),inverse(b)) = inverse(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_27]) ).

cnf(c_0_62,negated_conjecture,
    greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
    prove_p39c ).

cnf(c_0_63,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_61]),c_0_62]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : GRP190-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n008.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Aug 28 21:57:47 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.59  start to proof: theBenchmark
% 0.22/0.79  % Version  : CSE_E---1.5
% 0.22/0.79  % Problem  : theBenchmark.p
% 0.22/0.79  % Proof found
% 0.22/0.79  % SZS status Theorem for theBenchmark.p
% 0.22/0.79  % SZS output start Proof
% See solution above
% 0.22/0.80  % Total time : 0.184000 s
% 0.22/0.80  % SZS output end Proof
% 0.22/0.80  % Total time : 0.187000 s
%------------------------------------------------------------------------------