%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET008-1 : 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 : n021.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 14:31:58 EDT 2023

% Result   : Unsatisfiable 0.21s 0.58s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   29 (   7 unt;  12 typ;   0 def)
%            Number of atoms       :   33 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   29 (  13   ~;  16   |;   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  :   20 (   8   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   28 (   4 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,
    intersection: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

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

cnf(not_member_of_difference,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | ~ difference(X4,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax',not_member_of_difference) ).

cnf(b_minus_a,hypothesis,
    difference(b,a,bDa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_a) ).

cnf(prove_aI_bDa_is_empty,negated_conjecture,
    ~ member(X1,aI_bDa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aI_bDa_is_empty) ).

cnf(intersection_axiom2,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',intersection_axiom2) ).

cnf(intersection_axiom1,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',intersection_axiom1) ).

cnf(a_intersection_bDa,negated_conjecture,
    ~ intersection(a,bDa,aI_bDa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bDa) ).

cnf(c_0_6,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | ~ difference(X4,X2,X3) ),
    not_member_of_difference ).

cnf(c_0_7,hypothesis,
    difference(b,a,bDa),
    b_minus_a ).

cnf(c_0_8,negated_conjecture,
    ~ member(X1,aI_bDa),
    prove_aI_bDa_is_empty ).

cnf(c_0_9,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X2) ),
    intersection_axiom2 ).

cnf(c_0_10,hypothesis,
    ( ~ member(X1,bDa)
    | ~ member(X1,a) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    ( intersection(X1,X2,aI_bDa)
    | member(h(X1,X2,aI_bDa),X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,axiom,
    ( member(h(X1,X2,X3),X3)
    | intersection(X1,X2,X3)
    | member(h(X1,X2,X3),X1) ),
    intersection_axiom1 ).

cnf(c_0_13,hypothesis,
    ( intersection(X1,bDa,aI_bDa)
    | ~ member(h(X1,bDa,aI_bDa),a) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    ( intersection(X1,X2,aI_bDa)
    | member(h(X1,X2,aI_bDa),X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    ~ intersection(a,bDa,aI_bDa),
    a_intersection_bDa ).

cnf(c_0_16,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36  % Computer : n021.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 13:47:27 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.58  % Version  : CSE_E---1.5
% 0.21/0.58  % Problem  : theBenchmark.p
% 0.21/0.58  % Proof found
% 0.21/0.58  % SZS status Theorem for theBenchmark.p
% 0.21/0.58  % SZS output start Proof
% See solution above
% 0.21/0.58  % Total time : 0.007000 s
% 0.21/0.58  % SZS output end Proof
% 0.21/0.58  % Total time : 0.010000 s
%------------------------------------------------------------------------------