TSTP Solution File: SET009-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET009-1 : 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 : n001.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 14:31:59 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   41 (  10 unt;  11 typ;   0 def)
%            Number of atoms       :   63 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   63 (  30   ~;  33   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 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    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   46 (   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,
    difference: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

cnf(member_of_difference_or_set2,axiom,
    ( member(X1,X4)
    | member(X1,X3)
    | ~ member(X1,X2)
    | ~ difference(X2,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax',member_of_difference_or_set2) ).

cnf(b_minus_d,hypothesis,
    difference(b,d,bDd),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_d) ).

cnf(membership_in_subsets,axiom,
    ( member(X1,X3)
    | ~ member(X1,X2)
    | ~ subset(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).

cnf(d_is_a_subset_of_a,hypothesis,
    subset(d,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_a_subset_of_a) ).

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

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

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(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_bDa_is_a_subset_of_bDd,negated_conjecture,
    ~ subset(bDa,bDd),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_bDa_is_a_subset_of_bDd) ).

cnf(c_0_10,axiom,
    ( member(X1,X4)
    | member(X1,X3)
    | ~ member(X1,X2)
    | ~ difference(X2,X3,X4) ),
    member_of_difference_or_set2 ).

cnf(c_0_11,hypothesis,
    difference(b,d,bDd),
    b_minus_d ).

cnf(c_0_12,axiom,
    ( member(X1,X3)
    | ~ member(X1,X2)
    | ~ subset(X2,X3) ),
    membership_in_subsets ).

cnf(c_0_13,hypothesis,
    subset(d,a),
    d_is_a_subset_of_a ).

cnf(c_0_14,axiom,
    ( subset(X1,X2)
    | ~ member(member_of_1_not_of_2(X1,X2),X2) ),
    subsets_axiom2 ).

cnf(c_0_15,hypothesis,
    ( member(X1,d)
    | member(X1,bDd)
    | ~ member(X1,b) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,axiom,
    ( member(X4,X1)
    | ~ difference(X1,X2,X3)
    | ~ member(X4,X3) ),
    member_of_difference ).

cnf(c_0_17,hypothesis,
    difference(b,a,bDa),
    b_minus_a ).

cnf(c_0_18,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | ~ difference(X4,X2,X3) ),
    not_member_of_difference ).

cnf(c_0_19,hypothesis,
    ( member(X1,a)
    | ~ member(X1,d) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_20,hypothesis,
    ( subset(X1,bDd)
    | member(member_of_1_not_of_2(X1,bDd),d)
    | ~ member(member_of_1_not_of_2(X1,bDd),b) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,hypothesis,
    ( member(X1,b)
    | ~ member(X1,bDa) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,axiom,
    ( subset(X1,X2)
    | member(member_of_1_not_of_2(X1,X2),X1) ),
    subsets_axiom1 ).

cnf(c_0_23,hypothesis,
    ( ~ member(X1,bDa)
    | ~ member(X1,a) ),
    inference(spm,[status(thm)],[c_0_18,c_0_17]) ).

cnf(c_0_24,hypothesis,
    ( subset(X1,bDd)
    | member(member_of_1_not_of_2(X1,bDd),a)
    | ~ member(member_of_1_not_of_2(X1,bDd),b) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,hypothesis,
    ( subset(bDa,X1)
    | member(member_of_1_not_of_2(bDa,X1),b) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,negated_conjecture,
    ~ subset(bDa,bDd),
    prove_bDa_is_a_subset_of_bDd ).

cnf(c_0_27,hypothesis,
    ( subset(bDa,X1)
    | ~ member(member_of_1_not_of_2(bDa,X1),a) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_28,hypothesis,
    member(member_of_1_not_of_2(bDa,bDd),a),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_29,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_26]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET009-1 : 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
% 0.13/0.34  % Computer : n001.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   : Sat Aug 26 11:59:00 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.010000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.013000 s
%------------------------------------------------------------------------------