TSTP Solution File: GRP003-2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP003-2 : 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 : n031.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 00:13:33 EDT 2023

% Result   : Unsatisfiable 0.68s 0.78s
% Output   : CNFRefutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   58 (  17 unt;   6 typ;   0 def)
%            Number of atoms       :  108 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  114 (  58   ~;  56   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   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   :  130 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

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

cnf(product_substitution3,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).

cnf(total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).

cnf(associativity2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).

cnf(left_inverse,axiom,
    product(inverse(X1),X1,identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_inverse) ).

cnf(associativity1,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity1) ).

cnf(prove_right_identity,negated_conjecture,
    ~ product(a,identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_identity) ).

cnf(c_0_8,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    product_substitution3 ).

cnf(c_0_9,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_10,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_11,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    ( equalish(X1,X2)
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_13,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_14,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X3,X2)
    | ~ equalish(X1,X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_11]) ).

cnf(c_0_15,plain,
    equalish(multiply(identity,X1),X1),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X1,multiply(identity,X2)) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,plain,
    ( equalish(X1,multiply(X2,X3))
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_13]) ).

cnf(c_0_18,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_19,plain,
    equalish(X1,X1),
    inference(spm,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_20,plain,
    ( product(identity,X1,X2)
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiply(X5,X2),X3)
    | ~ product(X4,X5,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_13]) ).

cnf(c_0_22,plain,
    product(identity,multiply(identity,X1),X1),
    inference(spm,[status(thm)],[c_0_16,c_0_19]) ).

cnf(c_0_23,axiom,
    product(inverse(X1),X1,identity),
    left_inverse ).

cnf(c_0_24,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    associativity1 ).

cnf(c_0_25,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_11]) ).

cnf(c_0_26,plain,
    ( product(X1,X2,X2)
    | ~ product(identity,identity,X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,inverse(X2),X1)
    | ~ product(X4,identity,X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_28,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,identity)
    | ~ product(X4,X3,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_9]) ).

cnf(c_0_29,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_30,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X3)
    | ~ product(identity,X3,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_25]) ).

cnf(c_0_31,plain,
    ( product(X1,X2,X2)
    | ~ equalish(identity,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_11]) ).

cnf(c_0_32,plain,
    ( product(identity,X1,X2)
    | ~ product(inverse(inverse(X1)),identity,X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_23]) ).

cnf(c_0_33,plain,
    ( product(inverse(X1),X2,X3)
    | ~ product(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_28,c_0_23]) ).

cnf(c_0_34,plain,
    ( product(X1,X2,X3)
    | ~ equalish(multiply(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_13]) ).

cnf(c_0_35,plain,
    equalish(X1,multiply(identity,X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_15]) ).

cnf(c_0_36,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X3)
    | ~ equalish(X3,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_11]) ).

cnf(c_0_37,plain,
    ( equalish(X1,X2)
    | ~ equalish(identity,X3)
    | ~ product(X3,X2,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_31]) ).

cnf(c_0_38,plain,
    ( product(identity,X1,X2)
    | ~ product(inverse(X1),X2,identity) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
    product(X1,X2,multiply(identity,multiply(X1,X2))),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,plain,
    ( equalish(X1,X2)
    | ~ equalish(multiply(X3,X4),X1)
    | ~ product(X3,X4,X2) ),
    inference(spm,[status(thm)],[c_0_36,c_0_17]) ).

cnf(c_0_41,plain,
    ( equalish(multiply(X1,X2),X2)
    | ~ equalish(identity,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_13]) ).

cnf(c_0_42,plain,
    ( product(identity,X1,X2)
    | ~ product(X1,identity,X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_33]) ).

cnf(c_0_43,plain,
    ( product(X1,X2,X3)
    | ~ equalish(multiply(identity,multiply(X1,X2)),X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_39]) ).

cnf(c_0_44,plain,
    ( equalish(multiply(identity,X1),X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_13]) ).

cnf(c_0_45,plain,
    ( equalish(X1,X2)
    | ~ equalish(identity,X3)
    | ~ product(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_46,plain,
    product(identity,X1,multiply(X1,identity)),
    inference(spm,[status(thm)],[c_0_42,c_0_13]) ).

cnf(c_0_47,plain,
    ( product(X1,X2,X3)
    | ~ equalish(X3,multiply(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_48,plain,
    equalish(X1,multiply(X1,identity)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_19])]) ).

cnf(c_0_49,negated_conjecture,
    ~ product(a,identity,a),
    prove_right_identity ).

cnf(c_0_50,plain,
    product(X1,identity,X1),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP003-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.34  % Computer : n031.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit   : 300
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Tue Aug 29 01:55:25 EDT 2023
% 0.11/0.34  % CPUTime  : 
% 0.17/0.50  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
% 0.68/0.79  % Total time : 0.278000 s
% 0.68/0.79  % SZS output end Proof
% 0.68/0.79  % Total time : 0.281000 s
%------------------------------------------------------------------------------