%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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  : 600s
% DateTime : Tue Jul 19 03:30:58 EDT 2022

% Result   : Unsatisfiable 0.20s 0.42s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   21 (   7 unt;   8 nHn;  14 RR)
%            Number of literals    :   41 (   0 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   28 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(intersection_axiom1,axiom,
    ( member(h(Set1,Set2,Intersection),Intersection)
    | intersection(Set1,Set2,Intersection)
    | member(h(Set1,Set2,Intersection),Set1) ) ).

cnf(intersection_axiom2,axiom,
    ( member(h(Set1,Set2,Intersection),Intersection)
    | intersection(Set1,Set2,Intersection)
    | member(h(Set1,Set2,Intersection),Set2) ) ).

cnf(not_member_of_difference,axiom,
    ( ~ member(Element,Set1)
    | ~ member(Element,Set2)
    | ~ difference(A_set,Set1,Set2) ) ).

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

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

cnf(prove_aI_bDa_is_empty,negated_conjecture,
    ~ member(A,aI_bDa) ).

cnf(refute_0_0,plain,
    ~ member(h(X_117,X_118,aI_bDa),aI_bDa),
    inference(subst,[],[prove_aI_bDa_is_empty:[bind(A,$fot(h(X_117,X_118,aI_bDa)))]]) ).

cnf(refute_0_1,plain,
    ( intersection(X_117,X_118,aI_bDa)
    | member(h(X_117,X_118,aI_bDa),X_117)
    | member(h(X_117,X_118,aI_bDa),aI_bDa) ),
    inference(subst,[],[intersection_axiom1:[bind(Intersection,$fot(aI_bDa)),bind(Set1,$fot(X_117)),bind(Set2,$fot(X_118))]]) ).

cnf(refute_0_2,plain,
    ( intersection(X_117,X_118,aI_bDa)
    | member(h(X_117,X_118,aI_bDa),X_117) ),
    inference(resolve,[$cnf( member(h(X_117,X_118,aI_bDa),aI_bDa) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( intersection(a,bDa,aI_bDa)
    | member(h(a,bDa,aI_bDa),a) ),
    inference(subst,[],[refute_0_2:[bind(X_117,$fot(a)),bind(X_118,$fot(bDa))]]) ).

cnf(refute_0_4,plain,
    ( ~ difference(b,a,bDa)
    | ~ member(X_100,a)
    | ~ member(X_100,bDa) ),
    inference(subst,[],[not_member_of_difference:[bind(A_set,$fot(b)),bind(Element,$fot(X_100)),bind(Set1,$fot(a)),bind(Set2,$fot(bDa))]]) ).

cnf(refute_0_5,plain,
    ( ~ member(X_100,a)
    | ~ member(X_100,bDa) ),
    inference(resolve,[$cnf( difference(b,a,bDa) )],[b_minus_a,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ member(h(X_154,bDa,aI_bDa),a)
    | ~ member(h(X_154,bDa,aI_bDa),bDa) ),
    inference(subst,[],[refute_0_5:[bind(X_100,$fot(h(X_154,bDa,aI_bDa)))]]) ).

cnf(refute_0_7,plain,
    ~ member(h(X_146,X_147,aI_bDa),aI_bDa),
    inference(subst,[],[prove_aI_bDa_is_empty:[bind(A,$fot(h(X_146,X_147,aI_bDa)))]]) ).

cnf(refute_0_8,plain,
    ( intersection(X_146,X_147,aI_bDa)
    | member(h(X_146,X_147,aI_bDa),X_147)
    | member(h(X_146,X_147,aI_bDa),aI_bDa) ),
    inference(subst,[],[intersection_axiom2:[bind(Intersection,$fot(aI_bDa)),bind(Set1,$fot(X_146)),bind(Set2,$fot(X_147))]]) ).

cnf(refute_0_9,plain,
    ( intersection(X_146,X_147,aI_bDa)
    | member(h(X_146,X_147,aI_bDa),X_147) ),
    inference(resolve,[$cnf( member(h(X_146,X_147,aI_bDa),aI_bDa) )],[refute_0_8,refute_0_7]) ).

cnf(refute_0_10,plain,
    ( intersection(X_154,bDa,aI_bDa)
    | member(h(X_154,bDa,aI_bDa),bDa) ),
    inference(subst,[],[refute_0_9:[bind(X_146,$fot(X_154)),bind(X_147,$fot(bDa))]]) ).

cnf(refute_0_11,plain,
    ( ~ member(h(X_154,bDa,aI_bDa),a)
    | intersection(X_154,bDa,aI_bDa) ),
    inference(resolve,[$cnf( member(h(X_154,bDa,aI_bDa),bDa) )],[refute_0_10,refute_0_6]) ).

cnf(refute_0_12,plain,
    ( ~ member(h(a,bDa,aI_bDa),a)
    | intersection(a,bDa,aI_bDa) ),
    inference(subst,[],[refute_0_11:[bind(X_154,$fot(a))]]) ).

cnf(refute_0_13,plain,
    intersection(a,bDa,aI_bDa),
    inference(resolve,[$cnf( member(h(a,bDa,aI_bDa),a) )],[refute_0_3,refute_0_12]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( intersection(a,bDa,aI_bDa) )],[refute_0_13,a_intersection_bDa]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n023.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  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 20:42:10 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42  
% 0.20/0.42  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.42  
%------------------------------------------------------------------------------