TSTP Solution File: GRP039-7 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 00:13:48 EDT 2023

% Result   : Unsatisfiable 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   53 (  31 unt;   9 typ;   0 def)
%            Number of atoms       :   68 (  28 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   44 (  20   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   42 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    element_in_O2: ( $i * $i ) > $i ).

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

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

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

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

cnf(associativity,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X1),X1) = identity,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(right_inverse,axiom,
    multiply(X1,inverse(X1)) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

cnf(b_times_a_inverse_is_c,negated_conjecture,
    multiply(b,inverse(a)) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).

cnf(closure_of_multiply,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | multiply(X1,X2) != X3 ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).

cnf(inverse_inverse,axiom,
    inverse(inverse(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_inverse) ).

cnf(b_in_O2,negated_conjecture,
    subgroup_member(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).

cnf(a_times_c_is_d,negated_conjecture,
    multiply(a,c) = d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).

cnf(prove_d_in_O2,negated_conjecture,
    ~ subgroup_member(d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).

cnf(right_identity,axiom,
    multiply(X1,identity) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).

cnf(closure_of_inverse,axiom,
    ( subgroup_member(inverse(X1))
    | ~ subgroup_member(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).

cnf(property_of_O2,axiom,
    ( subgroup_member(X1)
    | subgroup_member(X2)
    | multiply(X1,element_in_O2(X1,X2)) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).

cnf(an_element_in_O2,axiom,
    ( subgroup_member(X1)
    | subgroup_member(X2)
    | subgroup_member(element_in_O2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).

cnf(c_0_14,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_15,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_16,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_17,axiom,
    multiply(X1,inverse(X1)) = identity,
    right_inverse ).

cnf(c_0_18,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    multiply(b,inverse(a)) = c,
    b_times_a_inverse_is_c ).

cnf(c_0_20,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | multiply(X1,X2) != X3 ),
    closure_of_multiply ).

cnf(c_0_21,plain,
    multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
    inference(spm,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    multiply(inverse(b),c) = inverse(a),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,axiom,
    inverse(inverse(X1)) = X1,
    inverse_inverse ).

cnf(c_0_24,plain,
    ( subgroup_member(multiply(X1,X2))
    | ~ subgroup_member(X2)
    | ~ subgroup_member(X1) ),
    inference(er,[status(thm)],[c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    subgroup_member(b),
    b_in_O2 ).

cnf(c_0_26,negated_conjecture,
    multiply(a,c) = d,
    a_times_c_is_d ).

cnf(c_0_27,negated_conjecture,
    ~ subgroup_member(d),
    prove_d_in_O2 ).

cnf(c_0_28,negated_conjecture,
    multiply(inverse(b),multiply(c,a)) = identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_29,axiom,
    multiply(X1,identity) = X1,
    right_identity ).

cnf(c_0_30,negated_conjecture,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_25])]) ).

cnf(c_0_31,axiom,
    ( subgroup_member(inverse(X1))
    | ~ subgroup_member(X1) ),
    closure_of_inverse ).

cnf(c_0_32,negated_conjecture,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(a) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_27]) ).

cnf(c_0_33,axiom,
    ( subgroup_member(X1)
    | subgroup_member(X2)
    | multiply(X1,element_in_O2(X1,X2)) = X2 ),
    property_of_O2 ).

cnf(c_0_34,plain,
    ( subgroup_member(X1)
    | ~ subgroup_member(multiply(X2,X1))
    | ~ subgroup_member(inverse(X2)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_18]) ).

cnf(c_0_35,negated_conjecture,
    multiply(c,a) = b,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_23]),c_0_29]) ).

cnf(c_0_36,negated_conjecture,
    ~ subgroup_member(a),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    multiply(inverse(a),d) = c,
    inference(spm,[status(thm)],[c_0_18,c_0_26]) ).

cnf(c_0_38,plain,
    ( multiply(inverse(X1),X2) = element_in_O2(X1,X2)
    | subgroup_member(X1)
    | subgroup_member(X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    ~ subgroup_member(inverse(c)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25])]),c_0_36]) ).

cnf(c_0_40,axiom,
    ( subgroup_member(X1)
    | subgroup_member(X2)
    | subgroup_member(element_in_O2(X1,X2)) ),
    an_element_in_O2 ).

cnf(c_0_41,negated_conjecture,
    element_in_O2(a,d) = c,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_36]),c_0_27]) ).

cnf(c_0_42,negated_conjecture,
    ~ subgroup_member(c),
    inference(spm,[status(thm)],[c_0_39,c_0_31]) ).

cnf(c_0_43,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_27]),c_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 28 20:43:49 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.013000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.016000 s
%------------------------------------------------------------------------------