TSTP Solution File: GRP172-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP172-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n009.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 00:17:27 EDT 2023

% Result   : Unsatisfiable 0.48s 0.64s
% Output   : CNFRefutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   54 (  47 unt;   7 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    :    4 (   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   :   67 (  11 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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).

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

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

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

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

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

cnf(p04d_1,hypothesis,
    greatest_lower_bound(identity,a) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p04d_1) ).

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

cnf(p04d_2,hypothesis,
    greatest_lower_bound(identity,b) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p04d_2) ).

cnf(prove_p04d,negated_conjecture,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p04d) ).

cnf(c_0_12,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_13,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_14,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_15,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_16,plain,
    multiply(inverse(inverse(X1)),identity) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_13]) ).

cnf(c_0_17,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_15]) ).

cnf(c_0_18,axiom,
    multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_lub1 ).

cnf(c_0_19,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_21,axiom,
    least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
    lub_absorbtion ).

cnf(c_0_22,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_23,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    glb_absorbtion ).

cnf(c_0_24,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_18,c_0_19]),c_0_20]) ).

cnf(c_0_25,plain,
    least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,hypothesis,
    greatest_lower_bound(identity,a) = identity,
    p04d_1 ).

cnf(c_0_27,axiom,
    greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
    associativity_of_glb ).

cnf(c_0_28,hypothesis,
    greatest_lower_bound(identity,b) = identity,
    p04d_2 ).

cnf(c_0_29,plain,
    greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_23,c_0_20]) ).

cnf(c_0_30,plain,
    greatest_lower_bound(X1,multiply(X1,least_upper_bound(X2,identity))) = X1,
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_31,hypothesis,
    least_upper_bound(a,identity) = a,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,hypothesis,
    greatest_lower_bound(identity,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,X1),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_33,plain,
    greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_27]) ).

cnf(c_0_34,plain,
    greatest_lower_bound(X1,multiply(X1,least_upper_bound(identity,X2))) = X1,
    inference(spm,[status(thm)],[c_0_30,c_0_20]) ).

cnf(c_0_35,hypothesis,
    least_upper_bound(identity,a) = a,
    inference(rw,[status(thm)],[c_0_31,c_0_20]) ).

cnf(c_0_36,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).

cnf(c_0_37,plain,
    least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
    inference(spm,[status(thm)],[c_0_25,c_0_27]) ).

cnf(c_0_38,hypothesis,
    greatest_lower_bound(identity,greatest_lower_bound(X1,b)) = greatest_lower_bound(identity,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]) ).

cnf(c_0_39,hypothesis,
    greatest_lower_bound(X1,multiply(X1,a)) = X1,
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_13,c_0_36]) ).

cnf(c_0_41,hypothesis,
    least_upper_bound(b,greatest_lower_bound(identity,X1)) = b,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,hypothesis,
    greatest_lower_bound(identity,inverse(a)) = inverse(a),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_13]),c_0_22]) ).

cnf(c_0_43,plain,
    multiply(X1,least_upper_bound(X2,inverse(X1))) = least_upper_bound(identity,multiply(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_40]),c_0_20]) ).

cnf(c_0_44,hypothesis,
    least_upper_bound(b,inverse(a)) = b,
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_45,negated_conjecture,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    prove_p04d ).

cnf(c_0_46,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP172-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 22:37:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.48/0.62  start to proof: theBenchmark
% 0.48/0.64  % Version  : CSE_E---1.5
% 0.48/0.64  % Problem  : theBenchmark.p
% 0.48/0.64  % Proof found
% 0.48/0.64  % SZS status Theorem for theBenchmark.p
% 0.48/0.64  % SZS output start Proof
% See solution above
% 0.61/0.65  % Total time : 0.019000 s
% 0.61/0.65  % SZS output end Proof
% 0.61/0.65  % Total time : 0.022000 s
%------------------------------------------------------------------------------