TSTP Solution File: GRP037-3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP037-3 : 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 : n028.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 00:13:46 EDT 2023

% Result   : Unsatisfiable 0.18s 0.57s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   31 (  13 unt;   8 typ;   0 def)
%            Number of atoms       :   37 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   30 (  16   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   29 (   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,
    subgroup_member: $i > $o ).

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

tff(decl_28,type,
    another_inverse: $i > $i ).

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

cnf(product_right_cancellation,hypothesis,
    ( X4 = X2
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(right_identity,axiom,
    product(X1,identity,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).

cnf(another_right_identity,hypothesis,
    ( product(X1,another_identity,X1)
    | ~ subgroup_member(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_right_identity) ).

cnf(a_is_in_subgroup,hypothesis,
    subgroup_member(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_in_subgroup) ).

cnf(left_inverse,axiom,
    product(inverse(X1),X1,identity),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).

cnf(product_left_cancellation,hypothesis,
    ( X4 = X1
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(another_left_inverse,hypothesis,
    ( product(another_inverse(X1),X1,another_identity)
    | ~ subgroup_member(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',another_left_inverse) ).

cnf(prove_two_inverses_are_equal,negated_conjecture,
    inverse(a) != another_inverse(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).

cnf(c_0_8,hypothesis,
    ( X4 = X2
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

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

cnf(c_0_10,hypothesis,
    ( product(X1,another_identity,X1)
    | ~ subgroup_member(X1) ),
    another_right_identity ).

cnf(c_0_11,hypothesis,
    subgroup_member(a),
    a_is_in_subgroup ).

cnf(c_0_12,hypothesis,
    ( identity = X1
    | ~ product(X2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,hypothesis,
    product(a,another_identity,a),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,axiom,
    product(inverse(X1),X1,identity),
    left_inverse ).

cnf(c_0_15,hypothesis,
    identity = another_identity,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,hypothesis,
    ( X4 = X1
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_17,plain,
    product(inverse(X1),X1,another_identity),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,hypothesis,
    ( product(another_inverse(X1),X1,another_identity)
    | ~ subgroup_member(X1) ),
    another_left_inverse ).

cnf(c_0_19,hypothesis,
    ( X1 = inverse(X2)
    | ~ product(X1,X2,another_identity) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,hypothesis,
    product(another_inverse(a),a,another_identity),
    inference(spm,[status(thm)],[c_0_18,c_0_11]) ).

cnf(c_0_21,negated_conjecture,
    inverse(a) != another_inverse(a),
    prove_two_inverses_are_equal ).

cnf(c_0_22,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP037-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 02:59:25 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.57  % Version  : CSE_E---1.5
% 0.18/0.57  % Problem  : theBenchmark.p
% 0.18/0.57  % Proof found
% 0.18/0.57  % SZS status Theorem for theBenchmark.p
% 0.18/0.57  % SZS output start Proof
% See solution above
% 0.18/0.58  % Total time : 0.013000 s
% 0.18/0.58  % SZS output end Proof
% 0.18/0.58  % Total time : 0.016000 s
%------------------------------------------------------------------------------