TSTP Solution File: RNG001-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 13:48:20 EDT 2023

% Result   : Unsatisfiable 89.08s 89.29s
% Output   : CNFRefutation 89.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   65 (  19 unt;   6 typ;   0 def)
%            Number of atoms       :  135 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  154 (  78   ~;  76   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   4   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  172 (   8 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,
    additive_inverse: $i > $i ).

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

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

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

cnf(associativity_of_addition2,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).

cnf(additive_inverse1,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).

cnf(associativity_of_addition1,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).

cnf(distributivity1,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).

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

cnf(distributivity2,axiom,
    ( product(X1,X6,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ sum(X3,X5,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).

cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
    ~ product(a,additive_identity,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).

cnf(c_0_8,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    associativity_of_addition2 ).

cnf(c_0_9,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    additive_inverse1 ).

cnf(c_0_10,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    associativity_of_addition1 ).

cnf(c_0_11,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1 ).

cnf(c_0_12,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X4,additive_inverse(X2),X1)
    | ~ sum(X4,additive_identity,X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,additive_identity)
    | ~ sum(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    ( sum(additive_identity,X1,X2)
    | ~ sum(additive_inverse(additive_inverse(X1)),additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_15,plain,
    ( sum(additive_inverse(X1),X2,X3)
    | ~ sum(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_9]) ).

cnf(c_0_16,plain,
    ( sum(additive_identity,X1,X2)
    | ~ sum(additive_inverse(X1),X2,additive_identity) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,plain,
    ( sum(additive_identity,X1,X2)
    | ~ sum(X1,additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_15]) ).

cnf(c_0_18,plain,
    ( sum(additive_identity,additive_inverse(X1),X2)
    | ~ sum(X1,X2,additive_identity) ),
    inference(spm,[status(thm)],[c_0_17,c_0_15]) ).

cnf(c_0_19,plain,
    sum(additive_identity,additive_inverse(additive_inverse(X1)),X1),
    inference(spm,[status(thm)],[c_0_18,c_0_9]) ).

cnf(c_0_20,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    distributivity1 ).

cnf(c_0_21,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

cnf(c_0_22,plain,
    ( sum(additive_identity,X1,X2)
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_11]) ).

cnf(c_0_23,plain,
    sum(additive_identity,additive_inverse(additive_identity),additive_identity),
    inference(spm,[status(thm)],[c_0_17,c_0_9]) ).

cnf(c_0_24,plain,
    ( sum(X1,additive_inverse(X1),X2)
    | ~ sum(additive_identity,additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_19]) ).

cnf(c_0_25,plain,
    ( sum(X1,X2,additive_identity)
    | ~ sum(X1,X3,additive_inverse(X4))
    | ~ sum(X3,X4,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_26,plain,
    ( sum(X1,X2,multiply(X3,X4))
    | ~ product(X3,X5,X2)
    | ~ product(X3,X6,X1)
    | ~ sum(X6,X5,X4) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    sum(additive_identity,additive_identity,additive_inverse(additive_identity)),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(spm,[status(thm)],[c_0_24,c_0_11]) ).

cnf(c_0_29,plain,
    ( sum(additive_identity,X1,additive_identity)
    | ~ sum(additive_inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_11]) ).

cnf(c_0_30,plain,
    ( sum(X1,multiply(X2,X3),multiply(X2,X4))
    | ~ product(X2,X5,X1)
    | ~ sum(X5,X3,X4) ),
    inference(spm,[status(thm)],[c_0_26,c_0_21]) ).

cnf(c_0_31,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X4,additive_inverse(additive_inverse(X3)),X2)
    | ~ sum(X1,X4,additive_identity) ),
    inference(spm,[status(thm)],[c_0_10,c_0_19]) ).

cnf(c_0_32,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X4,additive_identity,X1)
    | ~ sum(X4,X2,X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_11]) ).

cnf(c_0_33,plain,
    sum(X1,additive_inverse(X1),additive_inverse(additive_identity)),
    inference(spm,[status(thm)],[c_0_24,c_0_27]) ).

cnf(c_0_34,plain,
    ( sum(X1,X2,X3)
    | ~ sum(additive_inverse(X1),X3,X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_28]) ).

cnf(c_0_35,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X4,additive_inverse(X5),X1)
    | ~ sum(X4,X6,X3)
    | ~ sum(X5,X6,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_15]) ).

cnf(c_0_36,plain,
    ( sum(additive_identity,X1,additive_identity)
    | ~ sum(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_15]) ).

cnf(c_0_37,plain,
    ( sum(multiply(X1,X2),multiply(X1,X3),multiply(X1,X4))
    | ~ sum(X2,X3,X4) ),
    inference(spm,[status(thm)],[c_0_30,c_0_21]) ).

cnf(c_0_38,plain,
    ( sum(X1,additive_identity,X2)
    | ~ sum(X1,additive_inverse(X2),additive_identity) ),
    inference(spm,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_39,plain,
    ( sum(additive_inverse(additive_identity),X1,X2)
    | ~ sum(additive_identity,X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_40,plain,
    ( sum(additive_inverse(additive_identity),X1,X2)
    | ~ sum(X1,additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_33]) ).

cnf(c_0_41,plain,
    sum(X1,additive_identity,X1),
    inference(spm,[status(thm)],[c_0_34,c_0_9]) ).

cnf(c_0_42,plain,
    ( sum(X1,X2,X3)
    | ~ sum(additive_inverse(X1),X4,X2)
    | ~ sum(additive_identity,X4,X3) ),
    inference(spm,[status(thm)],[c_0_35,c_0_19]) ).

cnf(c_0_43,plain,
    ( sum(additive_identity,multiply(X1,X2),additive_identity)
    | ~ sum(X3,X2,X3) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_44,plain,
    ( sum(additive_inverse(additive_identity),additive_identity,X1)
    | ~ sum(additive_identity,additive_inverse(X1),additive_identity) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_45,plain,
    ( sum(X1,X2,X3)
    | ~ sum(additive_inverse(X4),X2,X3)
    | ~ sum(X4,X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_32,c_0_15]) ).

cnf(c_0_46,plain,
    sum(additive_inverse(additive_identity),X1,X1),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,plain,
    ( sum(X1,X2,X3)
    | ~ sum(additive_identity,X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(spm,[status(thm)],[c_0_42,c_0_15]) ).

cnf(c_0_48,plain,
    sum(additive_identity,multiply(X1,additive_identity),additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_19])]) ).

cnf(c_0_49,plain,
    ( sum(X1,X2,X2)
    | ~ sum(additive_identity,X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_50,axiom,
    ( product(X1,X6,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ sum(X3,X5,X7) ),
    distributivity2 ).

cnf(c_0_51,plain,
    ( sum(X1,X2,additive_identity)
    | ~ sum(X1,X2,multiply(X3,additive_identity)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_52,plain,
    sum(multiply(X1,additive_identity),X2,X2),
    inference(spm,[status(thm)],[c_0_49,c_0_48]) ).

cnf(c_0_53,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X5,multiply(X1,X6),X3)
    | ~ sum(X4,X6,X2) ),
    inference(spm,[status(thm)],[c_0_50,c_0_21]) ).

cnf(c_0_54,plain,
    sum(multiply(X1,additive_identity),multiply(X2,additive_identity),additive_identity),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_55,plain,
    ( product(X1,X2,additive_identity)
    | ~ product(X1,X3,multiply(X4,additive_identity))
    | ~ sum(X3,additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_56,negated_conjecture,
    ~ product(a,additive_identity,additive_identity),
    prove_a_times_additive_id_is_additive_id ).

cnf(c_0_57,plain,
    ( product(X1,X2,additive_identity)
    | ~ sum(additive_identity,additive_identity,X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_21]) ).

cnf(c_0_58,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG001-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n006.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 01:55:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.52  start to proof: theBenchmark
% 89.08/89.29  % Version  : CSE_E---1.5
% 89.08/89.29  % Problem  : theBenchmark.p
% 89.08/89.29  % Proof found
% 89.08/89.29  % SZS status Theorem for theBenchmark.p
% 89.08/89.29  % SZS output start Proof
% See solution above
% 89.08/89.29  % Total time : 88.753000 s
% 89.08/89.29  % SZS output end Proof
% 89.08/89.29  % Total time : 88.759000 s
%------------------------------------------------------------------------------