TSTP Solution File: BOO014-4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO014-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 18:05:50 EDT 2023

% Result   : Unsatisfiable 0.59s 0.71s
% Output   : CNFRefutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   66 (  59 unt;   7 typ;   0 def)
%            Number of atoms       :   59 (  58 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    :    6 (   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   :  111 (  10 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/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity1) ).

cnf(additive_inverse1,axiom,
    add(X1,inverse(X1)) = multiplicative_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).

cnf(multiplicative_id1,axiom,
    multiply(X1,multiplicative_identity) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).

cnf(multiplicative_inverse1,axiom,
    multiply(X1,inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).

cnf(additive_id1,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).

cnf(commutativity_of_multiply,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).

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

cnf(c_0_9,axiom,
    add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
    distributivity1 ).

cnf(c_0_10,axiom,
    add(X1,inverse(X1)) = multiplicative_identity,
    additive_inverse1 ).

cnf(c_0_11,axiom,
    multiply(X1,multiplicative_identity) = X1,
    multiplicative_id1 ).

cnf(c_0_12,plain,
    add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_13,axiom,
    multiply(X1,inverse(X1)) = additive_identity,
    multiplicative_inverse1 ).

cnf(c_0_14,axiom,
    add(X1,additive_identity) = X1,
    additive_id1 ).

cnf(c_0_15,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    commutativity_of_multiply ).

cnf(c_0_16,plain,
    add(X1,X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_17,plain,
    multiply(multiplicative_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

cnf(c_0_18,plain,
    multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
    inference(spm,[status(thm)],[c_0_9,c_0_16]) ).

cnf(c_0_19,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_20,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distributivity2 ).

cnf(c_0_21,plain,
    add(X1,multiplicative_identity) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17]),c_0_10]) ).

cnf(c_0_22,plain,
    multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,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_20,c_0_11]),c_0_21]),c_0_11]),c_0_19]) ).

cnf(c_0_24,plain,
    multiply(X1,add(X2,X1)) = X1,
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_25,plain,
    multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_15]) ).

cnf(c_0_26,plain,
    multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_20]) ).

cnf(c_0_27,plain,
    add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(X1,X3)),
    inference(spm,[status(thm)],[c_0_20,c_0_15]) ).

cnf(c_0_28,plain,
    add(X1,multiply(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_23,c_0_15]) ).

cnf(c_0_29,plain,
    multiply(X1,multiply(X2,add(X1,X3))) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]) ).

cnf(c_0_30,plain,
    add(X1,add(X2,X1)) = add(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_19]) ).

cnf(c_0_31,plain,
    multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_32,plain,
    multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
    inference(spm,[status(thm)],[c_0_31,c_0_15]) ).

cnf(c_0_33,plain,
    add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_17]) ).

cnf(c_0_34,plain,
    multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(multiply(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_31,c_0_23]) ).

cnf(c_0_35,plain,
    multiply(multiply(X1,X2),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_32,c_0_28]) ).

cnf(c_0_36,plain,
    add(additive_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_14,c_0_19]) ).

cnf(c_0_37,plain,
    add(X1,inverse(inverse(X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_13]),c_0_14]) ).

cnf(c_0_38,plain,
    multiply(multiply(X1,X2),X3) = multiply(multiply(X2,X3),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_34]),c_0_35]) ).

cnf(c_0_39,plain,
    multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_36]) ).

cnf(c_0_40,plain,
    multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_15]) ).

cnf(c_0_41,plain,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    inference(spm,[status(thm)],[c_0_15,c_0_38]) ).

cnf(c_0_42,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_10]),c_0_11]),c_0_40]) ).

cnf(c_0_43,plain,
    multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = additive_identity,
    inference(spm,[status(thm)],[c_0_13,c_0_41]) ).

cnf(c_0_44,plain,
    add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
    inference(spm,[status(thm)],[c_0_12,c_0_42]) ).

cnf(c_0_45,plain,
    multiply(X1,multiply(inverse(X1),X2)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_13]) ).

cnf(c_0_46,plain,
    multiply(X1,multiply(X2,inverse(X1))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_13]) ).

cnf(c_0_47,plain,
    multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_20]) ).

cnf(c_0_48,plain,
    add(X1,multiply(X2,inverse(multiply(inverse(X1),X2)))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_14]) ).

cnf(c_0_49,plain,
    add(X1,inverse(multiply(inverse(X1),X2))) = inverse(multiply(inverse(X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_14]),c_0_19]) ).

cnf(c_0_50,plain,
    multiply(inverse(X1),multiply(X2,X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_46,c_0_42]) ).

cnf(c_0_51,plain,
    add(inverse(X1),multiply(X1,X2)) = add(inverse(X1),X2),
    inference(spm,[status(thm)],[c_0_33,c_0_42]) ).

cnf(c_0_52,plain,
    multiply(X1,inverse(multiply(inverse(X2),X1))) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).

cnf(c_0_53,plain,
    add(inverse(X1),inverse(multiply(X2,X1))) = inverse(multiply(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_50]),c_0_14]),c_0_19]) ).

cnf(c_0_54,plain,
    inverse(multiply(inverse(X1),X2)) = add(inverse(X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_51]),c_0_53]) ).

cnf(c_0_55,plain,
    inverse(add(inverse(X1),X2)) = multiply(inverse(X2),X1),
    inference(spm,[status(thm)],[c_0_42,c_0_54]) ).

cnf(c_0_56,negated_conjecture,
    inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
    prove_c_inverse_is_d ).

cnf(c_0_57,plain,
    multiply(inverse(X1),inverse(X2)) = inverse(add(X2,X1)),
    inference(spm,[status(thm)],[c_0_55,c_0_42]) ).

cnf(c_0_58,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : BOO014-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun Aug 27 08:19:49 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.59/0.71  % Version  : CSE_E---1.5
% 0.59/0.71  % Problem  : theBenchmark.p
% 0.59/0.71  % Proof found
% 0.59/0.71  % SZS status Theorem for theBenchmark.p
% 0.59/0.71  % SZS output start Proof
% See solution above
% 0.59/0.71  % Total time : 0.150000 s
% 0.59/0.71  % SZS output end Proof
% 0.59/0.71  % Total time : 0.152000 s
%------------------------------------------------------------------------------