TSTP Solution File: SET014-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET014-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 14:32:03 EDT 2023

% Result   : Unsatisfiable 5.61s 5.74s
% Output   : CNFRefutation 5.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   32 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  12   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    member_of_1_not_of_2: ( $i * $i ) > $i ).

tff(decl_26,type,
    complement: $i > $i ).

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

tff(decl_28,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_29,type,
    equal_sets: ( $i * $i ) > $o ).

tff(decl_30,type,
    equal_elements: ( $i * $i ) > $o ).

tff(decl_31,type,
    as: $i ).

tff(decl_32,type,
    cs: $i ).

tff(decl_33,type,
    bs: $i ).

cnf(membership_in_subsets,axiom,
    ( member(X1,X3)
    | ~ member(X1,X2)
    | ~ subset(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).

cnf(b_subset_of_c,hypothesis,
    subset(bs,cs),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).

cnf(member_of_union_is_member_of_one_set,axiom,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_union_is_member_of_one_set) ).

cnf(subsets_axiom1,axiom,
    ( subset(X1,X2)
    | member(member_of_1_not_of_2(X1,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).

cnf(a_subset_of_c,hypothesis,
    subset(as,cs),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).

cnf(subsets_axiom2,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).

cnf(prove_a_union_b_subset_of_c,negated_conjecture,
    ~ subset(union(as,bs),cs),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).

cnf(c_0_7,axiom,
    ( member(X1,X3)
    | ~ member(X1,X2)
    | ~ subset(X2,X3) ),
    membership_in_subsets ).

cnf(c_0_8,hypothesis,
    subset(bs,cs),
    b_subset_of_c ).

cnf(c_0_9,axiom,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    member_of_union_is_member_of_one_set ).

cnf(c_0_10,axiom,
    ( subset(X1,X2)
    | member(member_of_1_not_of_2(X1,X2),X1) ),
    subsets_axiom1 ).

cnf(c_0_11,hypothesis,
    subset(as,cs),
    a_subset_of_c ).

cnf(c_0_12,hypothesis,
    ( member(X1,cs)
    | ~ member(X1,bs) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_13,plain,
    ( subset(union(X1,X2),X3)
    | member(member_of_1_not_of_2(union(X1,X2),X3),X1)
    | member(member_of_1_not_of_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,hypothesis,
    ( member(X1,cs)
    | ~ member(X1,as) ),
    inference(spm,[status(thm)],[c_0_7,c_0_11]) ).

cnf(c_0_15,hypothesis,
    ( subset(union(X1,bs),X2)
    | member(member_of_1_not_of_2(union(X1,bs),X2),cs)
    | member(member_of_1_not_of_2(union(X1,bs),X2),X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    subsets_axiom2 ).

cnf(c_0_17,hypothesis,
    ( subset(union(as,bs),X1)
    | member(member_of_1_not_of_2(union(as,bs),X1),cs) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ~ subset(union(as,bs),cs),
    prove_a_union_b_subset_of_c ).

cnf(c_0_19,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SET014-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n003.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   : Sat Aug 26 16:34:39 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 5.61/5.74  % Version  : CSE_E---1.5
% 5.61/5.74  % Problem  : theBenchmark.p
% 5.61/5.74  % Proof found
% 5.61/5.74  % SZS status Theorem for theBenchmark.p
% 5.61/5.74  % SZS output start Proof
% See solution above
% 5.61/5.74  % Total time : 5.176000 s
% 5.61/5.74  % SZS output end Proof
% 5.61/5.74  % Total time : 5.179000 s
%------------------------------------------------------------------------------