%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n026.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 04:38:41 EDT 2022

% Result   : Theorem 0.41s 0.61s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
    ! [B,C] : subset(intersection(B,C),B),
    input ).

fof(c50,axiom,
    ! [X35,X36] : subset(intersection(X35,X36),X35),
    inference(variable_rename,status(thm),[intersection_is_subset]) ).

cnf(c51,axiom,
    subset(intersection(X44,X45),X44),
    inference(split_conjunct,status(thm),[c50]) ).

fof(subset_of_union,axiom,
    ! [B,C] : subset(B,union(B,C)),
    input ).

fof(c52,axiom,
    ! [X37,X38] : subset(X37,union(X37,X38)),
    inference(variable_rename,status(thm),[subset_of_union]) ).

cnf(c53,axiom,
    subset(X47,union(X47,X46)),
    inference(split_conjunct,status(thm),[c52]) ).

fof(transitivity_of_subset,axiom,
    ! [B,C,D] :
      ( ( subset(B,C)
        & subset(C,D) )
     => subset(B,D) ),
    input ).

fof(c54,axiom,
    ! [B,C,D] :
      ( ~ subset(B,C)
      | ~ subset(C,D)
      | subset(B,D) ),
    inference(fof_nnf,status(thm),[transitivity_of_subset]) ).

fof(c55,axiom,
    ! [X39,X40,X41] :
      ( ~ subset(X39,X40)
      | ~ subset(X40,X41)
      | subset(X39,X41) ),
    inference(variable_rename,status(thm),[c54]) ).

cnf(c56,axiom,
    ( ~ subset(X104,X102)
    | ~ subset(X102,X103)
    | subset(X104,X103) ),
    inference(split_conjunct,status(thm),[c55]) ).

cnf(c83,plain,
    ( ~ subset(X121,X119)
    | subset(X121,union(X119,X120)) ),
    inference(resolution,status(thm),[c56,c53]) ).

cnf(c94,plain,
    subset(intersection(X124,X126),union(X124,X125)),
    inference(resolution,status(thm),[c83,c51]) ).

fof(prove_intersection_subset_of_union,conjecture,
    ! [B,C,D] : subset(intersection(B,C),union(B,D)),
    input ).

fof(c4,negated_conjecture,
    ~ ! [B,C,D] : subset(intersection(B,C),union(B,D)),
    inference(assume_negation,status(cth),[prove_intersection_subset_of_union]) ).

fof(c5,negated_conjecture,
    ? [B,C,D] : ~ subset(intersection(B,C),union(B,D)),
    inference(fof_nnf,status(thm),[c4]) ).

fof(c6,negated_conjecture,
    ? [X2,X3,X4] : ~ subset(intersection(X2,X3),union(X2,X4)),
    inference(variable_rename,status(thm),[c5]) ).

fof(c7,negated_conjecture,
    ~ subset(intersection(skolem0001,skolem0002),union(skolem0001,skolem0003)),
    inference(skolemize,status(esa),[c6]) ).

cnf(c8,negated_conjecture,
    ~ subset(intersection(skolem0001,skolem0002),union(skolem0001,skolem0003)),
    inference(split_conjunct,status(thm),[c7]) ).

cnf(c104,plain,
    $false,
    inference(resolution,status(thm),[c8,c94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.14/0.33  % Computer : n026.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Sun Jul 10 14:11:41 EDT 2022
% 0.14/0.33  % CPUTime  : 
% 0.41/0.61  # Version:  1.3
% 0.41/0.61  # SZS status Theorem
% 0.41/0.61  # SZS output start CNFRefutation
% See solution above
% 0.41/0.61  
% 0.41/0.61  # Initial clauses    : 27
% 0.41/0.61  # Processed clauses  : 28
% 0.41/0.61  # Factors computed   : 0
% 0.41/0.61  # Resolvents computed: 48
% 0.41/0.61  # Tautologies deleted: 2
% 0.41/0.61  # Forward subsumed   : 6
% 0.41/0.61  # Backward subsumed  : 0
% 0.41/0.61  # -------- CPU Time ---------
% 0.41/0.61  # User time          : 0.236 s
% 0.41/0.61  # System time        : 0.015 s
% 0.41/0.61  # Total time         : 0.251 s
%------------------------------------------------------------------------------