TSTP Solution File: GRP035-3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP035-3 : 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 : n011.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 00:13:45 EDT 2023

% Result   : Unsatisfiable 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   50 (  25 unt;   8 typ;   0 def)
%            Number of atoms       :   73 (  10 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   64 (  33   ~;  31   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   65 (   1 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,
    a: $i ).

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

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

cnf(total_function2,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).

cnf(right_identity,axiom,
    product(X1,identity,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).

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/GRP003-0.ax',associativity2) ).

cnf(left_inverse,axiom,
    product(inverse(X1),X1,identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).

cnf(closure_of_product_and_inverse,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,inverse(X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).

cnf(right_inverse,axiom,
    product(X1,inverse(X1),identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).

cnf(b_is_in_subgroup,hypothesis,
    subgroup_member(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).

cnf(a_times_b_is_c,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).

cnf(a_is_in_subgroup,hypothesis,
    subgroup_member(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).

cnf(prove_c_is_in_subgroup,negated_conjecture,
    ~ subgroup_member(c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).

cnf(c_0_12,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_13,axiom,
    product(X1,identity,X1),
    right_identity ).

cnf(c_0_14,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_15,axiom,
    product(inverse(X1),X1,identity),
    left_inverse ).

cnf(c_0_16,plain,
    ( X1 = X2
    | ~ product(X2,identity,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_18,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,inverse(X2),X1)
    | ~ product(X4,identity,X3) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,plain,
    multiply(X1,identity) = X1,
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_21,plain,
    ( product(X1,X2,X3)
    | ~ product(X3,inverse(X2),X1) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_20]) ).

cnf(c_0_23,axiom,
    ( subgroup_member(X3)
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2)
    | ~ product(X1,inverse(X2),X3) ),
    closure_of_product_and_inverse ).

cnf(c_0_24,axiom,
    product(X1,inverse(X1),identity),
    right_inverse ).

cnf(c_0_25,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_17]) ).

cnf(c_0_26,plain,
    product(identity,X1,inverse(inverse(X1))),
    inference(spm,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_27,plain,
    multiply(identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_22,c_0_17]) ).

cnf(c_0_28,plain,
    ( subgroup_member(identity)
    | ~ subgroup_member(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,hypothesis,
    subgroup_member(b),
    b_is_in_subgroup ).

cnf(c_0_30,plain,
    ( subgroup_member(multiply(X1,inverse(X2)))
    | ~ subgroup_member(X2)
    | ~ subgroup_member(X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_17]) ).

cnf(c_0_31,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

cnf(c_0_32,hypothesis,
    subgroup_member(identity),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,hypothesis,
    product(a,b,c),
    a_times_b_is_c ).

cnf(c_0_34,plain,
    ( subgroup_member(multiply(X1,X2))
    | ~ subgroup_member(inverse(X2))
    | ~ subgroup_member(X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    ( subgroup_member(inverse(X1))
    | ~ subgroup_member(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_32])]) ).

cnf(c_0_36,hypothesis,
    ( X1 = c
    | ~ product(a,b,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_33]) ).

cnf(c_0_37,plain,
    ( subgroup_member(multiply(X1,X2))
    | ~ subgroup_member(X1)
    | ~ subgroup_member(X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,hypothesis,
    multiply(a,b) = c,
    inference(spm,[status(thm)],[c_0_36,c_0_17]) ).

cnf(c_0_39,hypothesis,
    subgroup_member(a),
    a_is_in_subgroup ).

cnf(c_0_40,negated_conjecture,
    ~ subgroup_member(c),
    prove_c_is_in_subgroup ).

cnf(c_0_41,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_29])]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP035-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n011.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   : Mon Aug 28 23:55:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.007000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.009000 s
%------------------------------------------------------------------------------