TSTP Solution File: BOO014-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO014-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 18:05:49 EDT 2023

% Result   : Unsatisfiable 0.19s 0.66s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   90 (  81 unt;   9 typ;   0 def)
%            Number of atoms       :   81 (  80 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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   89 (  17 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,
    inverse: $i > $i ).

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

tff(decl_26,type,
    additive_identity: $i ).

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

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

tff(decl_29,type,
    c: $i ).

tff(decl_30,type,
    d: $i ).

cnf(distributivity2,axiom,
    add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).

cnf(additive_inverse1,axiom,
    add(X1,inverse(X1)) = multiplicative_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).

cnf(multiplicative_id1,axiom,
    multiply(X1,multiplicative_identity) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).

cnf(multiplicative_id2,axiom,
    multiply(multiplicative_identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).

cnf(distributivity4,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).

cnf(additive_id1,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).

cnf(commutativity_of_multiply,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).

cnf(additive_id2,axiom,
    add(additive_identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).

cnf(multiplicative_inverse1,axiom,
    multiply(X1,inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).

cnf(a_inverse_times_b_inverse_is_d,hypothesis,
    multiply(inverse(a),inverse(b)) = d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse_is_d) ).

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

cnf(prove_c_inverse_is_d,negated_conjecture,
    inverse(c) != d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).

cnf(c_0_13,axiom,
    add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
    distributivity2 ).

cnf(c_0_14,axiom,
    add(X1,inverse(X1)) = multiplicative_identity,
    additive_inverse1 ).

cnf(c_0_15,axiom,
    multiply(X1,multiplicative_identity) = X1,
    multiplicative_id1 ).

cnf(c_0_16,plain,
    add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_17,axiom,
    multiply(multiplicative_identity,X1) = X1,
    multiplicative_id2 ).

cnf(c_0_18,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distributivity4 ).

cnf(c_0_19,plain,
    add(X1,multiplicative_identity) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).

cnf(c_0_20,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_21,axiom,
    add(X1,additive_identity) = X1,
    additive_id1 ).

cnf(c_0_22,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    commutativity_of_multiply ).

cnf(c_0_23,axiom,
    add(additive_identity,X1) = X1,
    additive_id2 ).

cnf(c_0_24,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_18,c_0_15]),c_0_19]),c_0_15]),c_0_20]) ).

cnf(c_0_25,plain,
    multiply(X1,add(X1,X2)) = add(X1,multiply(X2,additive_identity)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_22]) ).

cnf(c_0_26,plain,
    multiply(additive_identity,X1) = additive_identity,
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,plain,
    multiply(X1,add(X2,X1)) = add(X1,multiply(X2,additive_identity)),
    inference(spm,[status(thm)],[c_0_25,c_0_20]) ).

cnf(c_0_28,plain,
    multiply(X1,additive_identity) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]) ).

cnf(c_0_29,plain,
    add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_17]) ).

cnf(c_0_30,axiom,
    multiply(X1,inverse(X1)) = additive_identity,
    multiplicative_inverse1 ).

cnf(c_0_31,plain,
    multiply(X1,add(X2,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_21]) ).

cnf(c_0_32,plain,
    add(X1,inverse(inverse(X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21]) ).

cnf(c_0_33,plain,
    multiply(X1,add(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_28]),c_0_21]) ).

cnf(c_0_34,plain,
    multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_23]) ).

cnf(c_0_35,plain,
    multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]) ).

cnf(c_0_36,plain,
    add(X1,add(inverse(X1),X2)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_33]),c_0_14]) ).

cnf(c_0_37,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_15]),c_0_35]) ).

cnf(c_0_38,hypothesis,
    multiply(inverse(a),inverse(b)) = d,
    a_inverse_times_b_inverse_is_d ).

cnf(c_0_39,plain,
    add(inverse(X1),add(X1,X2)) = multiplicative_identity,
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,hypothesis,
    add(d,inverse(a)) = inverse(a),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_38]),c_0_20]) ).

cnf(c_0_41,plain,
    add(X1,multiply(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_22]) ).

cnf(c_0_42,hypothesis,
    add(inverse(a),inverse(d)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20]) ).

cnf(c_0_43,hypothesis,
    add(d,inverse(b)) = inverse(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_20]) ).

cnf(c_0_44,hypothesis,
    add(a,b) = c,
    a_plus_b_is_c ).

cnf(c_0_45,hypothesis,
    multiply(a,inverse(d)) = a,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_15]) ).

cnf(c_0_46,hypothesis,
    add(inverse(b),inverse(d)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_20]) ).

cnf(c_0_47,hypothesis,
    add(b,multiply(additive_identity,a)) = multiply(b,c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_44]),c_0_22]) ).

cnf(c_0_48,hypothesis,
    multiply(c,add(a,X1)) = add(a,multiply(X1,b)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_44]),c_0_22]) ).

cnf(c_0_49,hypothesis,
    add(a,inverse(d)) = inverse(d),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_20]) ).

cnf(c_0_50,hypothesis,
    multiply(b,inverse(d)) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_46]),c_0_15]) ).

cnf(c_0_51,plain,
    add(X1,add(X2,inverse(X1))) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_14]) ).

cnf(c_0_52,plain,
    add(X1,multiply(multiply(X2,X1),X3)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_41]),c_0_25]),c_0_28]),c_0_21]) ).

cnf(c_0_53,hypothesis,
    multiply(b,c) = b,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_26]),c_0_21]) ).

cnf(c_0_54,plain,
    multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_21]) ).

cnf(c_0_55,hypothesis,
    add(a,inverse(b)) = add(a,d),
    inference(spm,[status(thm)],[c_0_29,c_0_38]) ).

cnf(c_0_56,hypothesis,
    multiply(c,inverse(d)) = c,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_22]),c_0_50]),c_0_44]) ).

cnf(c_0_57,plain,
    add(inverse(X1),add(X2,X1)) = multiplicative_identity,
    inference(spm,[status(thm)],[c_0_51,c_0_37]) ).

cnf(c_0_58,hypothesis,
    add(c,multiply(b,X1)) = c,
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_59,plain,
    multiply(inverse(X1),add(X2,X1)) = multiply(inverse(X1),X2),
    inference(spm,[status(thm)],[c_0_54,c_0_37]) ).

cnf(c_0_60,hypothesis,
    add(b,add(a,d)) = multiplicative_identity,
    inference(spm,[status(thm)],[c_0_51,c_0_55]) ).

cnf(c_0_61,hypothesis,
    add(c,inverse(d)) = inverse(d),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_20]) ).

cnf(c_0_62,plain,
    add(X1,X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_30]),c_0_21]) ).

cnf(c_0_63,hypothesis,
    add(c,inverse(multiply(b,X1))) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_20]) ).

cnf(c_0_64,hypothesis,
    multiply(b,inverse(add(a,d))) = inverse(add(a,d)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_15]),c_0_22]) ).

cnf(c_0_65,hypothesis,
    add(inverse(c),inverse(d)) = multiplicative_identity,
    inference(spm,[status(thm)],[c_0_39,c_0_61]) ).

cnf(c_0_66,plain,
    multiply(X1,multiply(X2,inverse(X1))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_30]) ).

cnf(c_0_67,hypothesis,
    add(a,multiply(a,b)) = multiply(a,c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_62]),c_0_22]) ).

cnf(c_0_68,plain,
    add(X1,add(X2,X1)) = add(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_20]) ).

cnf(c_0_69,plain,
    multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
    inference(spm,[status(thm)],[c_0_13,c_0_20]) ).

cnf(c_0_70,plain,
    multiply(inverse(X1),add(X1,X2)) = multiply(inverse(X1),X2),
    inference(spm,[status(thm)],[c_0_34,c_0_37]) ).

cnf(c_0_71,hypothesis,
    add(c,add(a,d)) = multiplicative_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_37]) ).

cnf(c_0_72,hypothesis,
    multiply(d,inverse(c)) = d,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_65]),c_0_15]) ).

cnf(c_0_73,plain,
    multiply(inverse(X1),multiply(X2,X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_66,c_0_37]) ).

cnf(c_0_74,hypothesis,
    multiply(a,c) = a,
    inference(rw,[status(thm)],[c_0_67,c_0_24]) ).

cnf(c_0_75,plain,
    add(X1,multiply(X2,add(X3,X1))) = add(X1,multiply(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_68]),c_0_69]) ).

cnf(c_0_76,hypothesis,
    multiply(inverse(c),add(a,d)) = inverse(c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_15]) ).

cnf(c_0_77,hypothesis,
    add(d,inverse(c)) = inverse(c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_72]),c_0_20]) ).

cnf(c_0_78,hypothesis,
    multiply(a,inverse(c)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_22]) ).

cnf(c_0_79,negated_conjecture,
    inverse(c) != d,
    prove_c_inverse_is_d ).

cnf(c_0_80,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_22]),c_0_78]),c_0_21]),c_0_79]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : BOO014-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n003.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   : Sun Aug 27 07:59:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.66  % Version  : CSE_E---1.5
% 0.19/0.66  % Problem  : theBenchmark.p
% 0.19/0.66  % Proof found
% 0.19/0.66  % SZS status Theorem for theBenchmark.p
% 0.19/0.66  % SZS output start Proof
% See solution above
% 0.19/0.67  % Total time : 0.075000 s
% 0.19/0.67  % SZS output end Proof
% 0.19/0.67  % Total time : 0.077000 s
%------------------------------------------------------------------------------