TSTP Solution File: RNG003-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG003-1 : 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 : n029.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 13:48:21 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   40 (  20 unt;  10 typ;   0 def)
%            Number of atoms       :   47 (   7 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   36 (  19   ~;  17   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   5   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   47 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    additive_identity: $i ).

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

tff(decl_24,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_25,type,
    product: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    add: ( $i * $i ) > $i ).

tff(decl_27,type,
    additive_inverse: $i > $i ).

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

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

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

tff(decl_31,type,
    b: $i ).

cnf(associativity_of_addition1,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).

cnf(b_plus_c_is_d,hypothesis,
    sum(b,c,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_c_is_d) ).

cnf(a_plus_c_is_d,hypothesis,
    sum(a,c,d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_plus_c_is_d) ).

cnf(addition_is_well_defined,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).

cnf(left_inverse,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).

cnf(prove_a_equals_b,negated_conjecture,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_b) ).

cnf(c_0_9,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    associativity_of_addition1 ).

cnf(c_0_10,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1 ).

cnf(c_0_11,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    commutativity_of_addition ).

cnf(c_0_12,hypothesis,
    sum(b,c,d),
    b_plus_c_is_d ).

cnf(c_0_13,hypothesis,
    sum(a,c,d),
    a_plus_c_is_d ).

cnf(c_0_14,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,additive_identity)
    | ~ sum(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,hypothesis,
    sum(c,b,d),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined ).

cnf(c_0_17,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition ).

cnf(c_0_18,hypothesis,
    sum(c,a,d),
    inference(spm,[status(thm)],[c_0_11,c_0_13]) ).

cnf(c_0_19,hypothesis,
    ( sum(X1,d,b)
    | ~ sum(X1,c,additive_identity) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    left_inverse ).

cnf(c_0_21,plain,
    ( X1 = add(X2,X3)
    | ~ sum(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    sum(X1,X2,add(X2,X1)),
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_23,hypothesis,
    ( sum(X1,d,a)
    | ~ sum(X1,c,additive_identity) ),
    inference(spm,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_24,hypothesis,
    sum(additive_inverse(c),d,b),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

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

cnf(c_0_26,hypothesis,
    sum(additive_inverse(c),d,a),
    inference(spm,[status(thm)],[c_0_23,c_0_20]) ).

cnf(c_0_27,hypothesis,
    add(d,additive_inverse(c)) = b,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    a != b,
    prove_a_equals_b ).

cnf(c_0_29,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_25]),c_0_27]),c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG003-1 : 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
% 0.17/0.34  % Computer : n029.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.34  % DateTime   : Sun Aug 27 02:03:55 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.009000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.012000 s
%------------------------------------------------------------------------------