%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET003-1 : 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 : n019.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 14:31:57 EDT 2023

% Result   : Unsatisfiable 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   21 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  10   ~;  10   |;   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  :   14 (   6   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-3 aty)
%            Number of variables   :   18 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    member: ( $i * $i ) > $o ).

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

tff(decl_24,type,
    member_of_1_not_of_2: ( $i * $i ) > $i ).

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

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

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

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

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

cnf(member_of_set2_is_member_of_union,axiom,
    ( member(X4,X3)
    | ~ union(X1,X2,X3)
    | ~ member(X4,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set2_is_member_of_union) ).

cnf(a_union_a_is_aUa,hypothesis,
    union(a,a,aUa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_a_is_aUa) ).

cnf(subsets_axiom2,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).

cnf(subsets_axiom1,axiom,
    ( subset(X1,X2)
    | member(member_of_1_not_of_2(X1,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).

cnf(prove_a_is_a_subset_of_aUa,negated_conjecture,
    ~ subset(a,aUa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_is_a_subset_of_aUa) ).

cnf(c_0_5,axiom,
    ( member(X4,X3)
    | ~ union(X1,X2,X3)
    | ~ member(X4,X2) ),
    member_of_set2_is_member_of_union ).

cnf(c_0_6,hypothesis,
    union(a,a,aUa),
    a_union_a_is_aUa ).

cnf(c_0_7,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    subsets_axiom2 ).

cnf(c_0_8,hypothesis,
    ( member(X1,aUa)
    | ~ member(X1,a) ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,hypothesis,
    ( subset(X1,aUa)
    | ~ member(member_of_1_not_of_2(X1,aUa),a) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

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

cnf(c_0_11,negated_conjecture,
    ~ subset(a,aUa),
    prove_a_is_a_subset_of_aUa ).

cnf(c_0_12,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34  % Computer : n019.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Sat Aug 26 11:06:43 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.004000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.007000 s
%------------------------------------------------------------------------------