TSTP Solution File: BOO028-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : BOO028-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 18:05:54 EDT 2023

% Result   : Unsatisfiable 0.68s 0.78s
% Output   : CNFRefutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   53 (  47 unt;   6 typ;   0 def)
%            Number of atoms       :   47 (  46 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   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  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  107 (  17 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    inverse: $i > $i ).

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

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

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

cnf(l2,axiom,
    multiply(X1,add(X2,add(X1,X3))) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).

cnf(l1,axiom,
    add(X1,multiply(X2,multiply(X1,X3))) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).

cnf(associativity_of_multiply,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).

cnf(b1,axiom,
    multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).

cnf(associativity_of_add,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).

cnf(commutativity_of_add,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).

cnf(b2,axiom,
    add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).

cnf(commutativity_of_multiply,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).

cnf(prove_multiply_add_property,negated_conjecture,
    multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add_property) ).

cnf(c_0_9,axiom,
    multiply(X1,add(X2,add(X1,X3))) = X1,
    l2 ).

cnf(c_0_10,axiom,
    add(X1,multiply(X2,multiply(X1,X3))) = X1,
    l1 ).

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

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

cnf(c_0_13,plain,
    multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_14,axiom,
    multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
    b1 ).

cnf(c_0_15,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    associativity_of_add ).

cnf(c_0_16,plain,
    add(X1,multiply(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

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

cnf(c_0_18,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_of_add ).

cnf(c_0_19,plain,
    add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,axiom,
    add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
    b2 ).

cnf(c_0_21,plain,
    multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,axiom,
    multiply(X1,X2) = multiply(X2,X1),
    commutativity_of_multiply ).

cnf(c_0_24,plain,
    multiply(X1,multiply(X2,inverse(X1))) = multiply(X1,inverse(X1)),
    inference(spm,[status(thm)],[c_0_21,c_0_16]) ).

cnf(c_0_25,plain,
    add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_15]) ).

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

cnf(c_0_27,plain,
    add(X1,multiply(X2,inverse(X2))) = X1,
    inference(spm,[status(thm)],[c_0_10,c_0_24]) ).

cnf(c_0_28,plain,
    add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
    inference(spm,[status(thm)],[c_0_25,c_0_20]) ).

cnf(c_0_29,plain,
    add(X1,inverse(inverse(X1))) = X1,
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_30,plain,
    add(X1,multiply(add(X2,inverse(X1)),X3)) = add(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_13]),c_0_26]) ).

cnf(c_0_31,plain,
    multiply(add(X1,X2),multiply(add(X1,inverse(X2)),X3)) = multiply(X1,X3),
    inference(spm,[status(thm)],[c_0_11,c_0_14]) ).

cnf(c_0_32,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_18]),c_0_29]) ).

cnf(c_0_33,plain,
    multiply(X1,add(multiply(X2,inverse(X1)),X3)) = multiply(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_21]) ).

cnf(c_0_34,plain,
    add(multiply(X1,X2),add(multiply(X1,inverse(X2)),X3)) = add(X1,X3),
    inference(spm,[status(thm)],[c_0_15,c_0_20]) ).

cnf(c_0_35,plain,
    add(X1,multiply(add(X2,X1),X3)) = add(X1,multiply(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

cnf(c_0_36,plain,
    multiply(X1,add(multiply(X2,X1),X3)) = multiply(X1,add(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32]) ).

cnf(c_0_37,plain,
    add(multiply(X1,X2),multiply(add(X3,X1),X2)) = multiply(add(X3,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_18]) ).

cnf(c_0_38,plain,
    add(X1,multiply(X2,add(X3,X1))) = add(X1,multiply(X3,X2)),
    inference(spm,[status(thm)],[c_0_35,c_0_23]) ).

cnf(c_0_39,plain,
    multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
    inference(spm,[status(thm)],[c_0_36,c_0_23]) ).

cnf(c_0_40,negated_conjecture,
    multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
    prove_multiply_add_property ).

cnf(c_0_41,plain,
    multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_12]),c_0_38]),c_0_38]) ).

cnf(c_0_42,plain,
    add(X1,multiply(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_23]) ).

cnf(c_0_43,plain,
    multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X3,X2)),
    inference(spm,[status(thm)],[c_0_39,c_0_18]) ).

cnf(c_0_44,negated_conjecture,
    add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_23]),c_0_23]) ).

cnf(c_0_45,plain,
    add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).

cnf(c_0_46,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : BOO028-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n011.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun Aug 27 08:21:09 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.68/0.78  % Version  : CSE_E---1.5
% 0.68/0.78  % Problem  : theBenchmark.p
% 0.68/0.78  % Proof found
% 0.68/0.78  % SZS status Theorem for theBenchmark.p
% 0.68/0.78  % SZS output start Proof
% See solution above
% 0.68/0.78  % Total time : 0.181000 s
% 0.68/0.78  % SZS output end Proof
% 0.68/0.78  % Total time : 0.184000 s
%------------------------------------------------------------------------------