TSTP Solution File: BOO013-4 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 : Wed Aug 30 18:05:48 EDT 2023

% Result   : Unsatisfiable 0.59s 0.62s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   49 (  42 unt;   7 typ;   0 def)
%            Number of atoms       :   42 (  41 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  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   51 (   3 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    add: ( $i * $i ) > $i ).

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

tff(decl_24,type,
    additive_identity: $i ).

tff(decl_25,type,
    multiplicative_identity: $i ).

tff(decl_26,type,
    inverse: $i > $i ).

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

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

cnf(distributivity1,axiom,
    add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity1) ).

cnf(additive_inverse1,axiom,
    add(X1,inverse(X1)) = multiplicative_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).

cnf(multiplicative_id1,axiom,
    multiply(X1,multiplicative_identity) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).

cnf(multiplicative_inverse1,axiom,
    multiply(X1,inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).

cnf(additive_id1,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_id1) ).

cnf(commutativity_of_multiply,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).

cnf(distributivity2,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity2) ).

cnf(b_a_multiplicative_identity,hypothesis,
    add(a,b) = multiplicative_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).

cnf(b_an_additive_identity,hypothesis,
    multiply(a,b) = additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_an_additive_identity) ).

cnf(prove_a_inverse_is_b,negated_conjecture,
    b != inverse(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).

cnf(c_0_11,axiom,
    add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
    distributivity1 ).

cnf(c_0_12,axiom,
    add(X1,inverse(X1)) = multiplicative_identity,
    additive_inverse1 ).

cnf(c_0_13,axiom,
    multiply(X1,multiplicative_identity) = X1,
    multiplicative_id1 ).

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

cnf(c_0_15,axiom,
    multiply(X1,inverse(X1)) = additive_identity,
    multiplicative_inverse1 ).

cnf(c_0_16,axiom,
    add(X1,additive_identity) = X1,
    additive_id1 ).

cnf(c_0_17,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    commutativity_of_multiply ).

cnf(c_0_18,plain,
    add(X1,X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_19,plain,
    multiply(multiplicative_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_20,plain,
    multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
    inference(spm,[status(thm)],[c_0_11,c_0_18]) ).

cnf(c_0_21,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_22,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distributivity2 ).

cnf(c_0_23,plain,
    add(X1,multiplicative_identity) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_12]) ).

cnf(c_0_24,hypothesis,
    add(a,b) = multiplicative_identity,
    b_a_multiplicative_identity ).

cnf(c_0_25,plain,
    multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    add(X1,multiply(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_23]),c_0_13]),c_0_21]) ).

cnf(c_0_27,plain,
    add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_19]) ).

cnf(c_0_28,hypothesis,
    add(a,multiply(b,X1)) = add(a,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_24]),c_0_19]) ).

cnf(c_0_29,plain,
    add(additive_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_30,plain,
    multiply(X1,add(X2,X1)) = X1,
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,plain,
    add(X1,inverse(inverse(X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_16]) ).

cnf(c_0_32,hypothesis,
    multiply(a,b) = additive_identity,
    b_an_additive_identity ).

cnf(c_0_33,hypothesis,
    add(a,inverse(b)) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_16]) ).

cnf(c_0_34,plain,
    multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_29]) ).

cnf(c_0_35,plain,
    multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_17]) ).

cnf(c_0_36,hypothesis,
    multiply(a,add(b,X1)) = multiply(a,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_29]) ).

cnf(c_0_37,hypothesis,
    multiply(a,inverse(b)) = inverse(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_17]) ).

cnf(c_0_38,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_12]),c_0_13]),c_0_35]) ).

cnf(c_0_39,hypothesis,
    inverse(b) = a,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_12]),c_0_13]),c_0_37]) ).

cnf(c_0_40,negated_conjecture,
    b != inverse(a),
    prove_a_inverse_is_b ).

cnf(c_0_41,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Sun Aug 27 07:17:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.60  start to proof: theBenchmark
% 0.59/0.62  % Version  : CSE_E---1.5
% 0.59/0.62  % Problem  : theBenchmark.p
% 0.59/0.62  % Proof found
% 0.59/0.62  % SZS status Theorem for theBenchmark.p
% 0.59/0.62  % SZS output start Proof
% See solution above
% 0.59/0.63  % Total time : 0.011000 s
% 0.59/0.63  % SZS output end Proof
% 0.59/0.63  % Total time : 0.013000 s
%------------------------------------------------------------------------------