TSTP Solution File: RNG025-6 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG025-6 : 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 : Thu Aug 31 13:48:32 EDT 2023

% Result   : Unsatisfiable 1.59s 1.71s
% Output   : CNFRefutation 1.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   55 (  47 unt;   8 typ;   0 def)
%            Number of atoms       :   47 (  46 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   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  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   86 (   2 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    additive_inverse: $i > $i ).

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

tff(decl_27,type,
    commutator: ( $i * $i ) > $i ).

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

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

cnf(associativity_for_addition,axiom,
    add(X1,add(X2,X3)) = add(add(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).

cnf(right_additive_inverse,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).

cnf(left_additive_identity,axiom,
    add(additive_identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).

cnf(additive_inverse_additive_inverse,axiom,
    additive_inverse(additive_inverse(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).

cnf(commutativity_for_addition,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).

cnf(distribute1,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).

cnf(distribute2,axiom,
    multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).

cnf(right_alternative,axiom,
    multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_alternative) ).

cnf(right_multiplicative_zero,axiom,
    multiply(X1,additive_identity) = additive_identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).

cnf(right_additive_identity,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).

cnf(left_alternative,axiom,
    multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_alternative) ).

cnf(prove_flexible_law,negated_conjecture,
    associator(x,y,x) != additive_identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_flexible_law) ).

cnf(associator,axiom,
    associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).

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

cnf(c_0_14,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    right_additive_inverse ).

cnf(c_0_15,axiom,
    add(additive_identity,X1) = X1,
    left_additive_identity ).

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

cnf(c_0_17,axiom,
    additive_inverse(additive_inverse(X1)) = X1,
    additive_inverse_additive_inverse ).

cnf(c_0_18,plain,
    add(additive_inverse(X1),add(X1,X2)) = X2,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

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

cnf(c_0_20,plain,
    add(additive_inverse(X1),add(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,plain,
    add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_20]),c_0_19]) ).

cnf(c_0_22,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distribute1 ).

cnf(c_0_23,axiom,
    multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
    distribute2 ).

cnf(c_0_24,axiom,
    multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
    right_alternative ).

cnf(c_0_25,plain,
    add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,axiom,
    multiply(X1,additive_identity) = additive_identity,
    right_multiplicative_zero ).

cnf(c_0_27,plain,
    additive_inverse(additive_identity) = additive_identity,
    inference(spm,[status(thm)],[c_0_15,c_0_14]) ).

cnf(c_0_28,axiom,
    add(X1,additive_identity) = X1,
    right_additive_identity ).

cnf(c_0_29,plain,
    add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,axiom,
    multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
    left_alternative ).

cnf(c_0_31,plain,
    additive_inverse(multiply(X1,additive_inverse(X2))) = multiply(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_14]),c_0_26]),c_0_27]),c_0_28]) ).

cnf(c_0_32,plain,
    add(multiply(X1,multiply(X1,X2)),multiply(X3,multiply(X2,X2))) = multiply(add(multiply(X1,X1),multiply(X3,X2)),X2),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,plain,
    additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
    inference(spm,[status(thm)],[c_0_17,c_0_31]) ).

cnf(c_0_34,plain,
    multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,multiply(add(X1,X2),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_22]),c_0_23]) ).

cnf(c_0_35,plain,
    add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
    inference(spm,[status(thm)],[c_0_13,c_0_19]) ).

cnf(c_0_36,negated_conjecture,
    associator(x,y,x) != additive_identity,
    prove_flexible_law ).

cnf(c_0_37,axiom,
    associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
    associator ).

cnf(c_0_38,plain,
    add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,X2))) = multiply(multiply(X1,X2),add(X3,X2)),
    inference(spm,[status(thm)],[c_0_22,c_0_24]) ).

cnf(c_0_39,plain,
    multiply(multiply(X1,add(X1,X2)),additive_inverse(X2)) = multiply(X1,multiply(add(X1,X2),additive_inverse(X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_33]),c_0_33]) ).

cnf(c_0_40,plain,
    add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
    inference(spm,[status(thm)],[c_0_35,c_0_19]) ).

cnf(c_0_41,plain,
    add(X1,add(X2,additive_inverse(X1))) = X2,
    inference(spm,[status(thm)],[c_0_16,c_0_19]) ).

cnf(c_0_42,negated_conjecture,
    add(multiply(multiply(x,y),x),additive_inverse(multiply(x,multiply(y,x)))) != additive_identity,
    inference(rw,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_43,plain,
    multiply(multiply(X1,add(X1,X2)),X1) = multiply(X1,multiply(add(X1,X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]),c_0_22]),c_0_40]),c_0_41]),c_0_40]),c_0_41]) ).

cnf(c_0_44,negated_conjecture,
    add(multiply(multiply(x,y),x),multiply(x,multiply(y,additive_inverse(x)))) != additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_33]),c_0_33]) ).

cnf(c_0_45,plain,
    multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_43,c_0_16]) ).

cnf(c_0_46,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_22]),c_0_22]),c_0_14]),c_0_26]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17  % Problem    : RNG025-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.17  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.18/0.38  % Computer : n003.cluster.edu
% 0.18/0.38  % Model    : x86_64 x86_64
% 0.18/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38  % Memory   : 8042.1875MB
% 0.18/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38  % CPULimit   : 300
% 0.18/0.38  % WCLimit    : 300
% 0.18/0.38  % DateTime   : Sun Aug 27 02:42:09 EDT 2023
% 0.18/0.38  % CPUTime  : 
% 0.24/0.65  start to proof: theBenchmark
% 1.59/1.71  % Version  : CSE_E---1.5
% 1.59/1.71  % Problem  : theBenchmark.p
% 1.59/1.71  % Proof found
% 1.59/1.71  % SZS status Theorem for theBenchmark.p
% 1.59/1.71  % SZS output start Proof
% See solution above
% 1.59/1.72  % Total time : 1.050000 s
% 1.59/1.72  % SZS output end Proof
% 1.59/1.72  % Total time : 1.052000 s
%------------------------------------------------------------------------------