TSTP Solution File: LCL222-1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL222-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 : Sun Jul 17 12:50:49 EDT 2022

% Result   : Unsatisfiable 119.98s 120.18s
% Output   : CNFRefutation 119.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   64 (  33 unt;   0 nHn;  32 RR)
%            Number of literals    :  105 (   0 equ;  42 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-1 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  174 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
    axiom(or(not(or(A,A)),A)) ).

cnf(axiom_1_3,axiom,
    axiom(or(not(A),or(B,A))) ).

cnf(axiom_1_4,axiom,
    axiom(or(not(or(A,B)),or(B,A))) ).

cnf(axiom_1_5,axiom,
    axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).

cnf(axiom_1_6,axiom,
    axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ).

cnf(rule_1,axiom,
    ( theorem(X)
    | ~ axiom(X) ) ).

cnf(rule_2,axiom,
    ( theorem(X)
    | ~ axiom(or(not(Y),X))
    | ~ theorem(Y) ) ).

cnf(rule_3,axiom,
    ( theorem(or(not(X),Z))
    | ~ axiom(or(not(X),Y))
    | ~ theorem(or(not(Y),Z)) ) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(or(not(or(not(q),p)),or(not(or(or(p,q),r)),or(p,r)))) ).

cnf(refute_0_0,plain,
    ( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
    | ~ theorem(or(not(or(B,or(A,C))),X_587))
    | theorem(or(not(or(A,or(B,C))),X_587)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(A,or(B,C)))),bind(Y,$fot(or(B,or(A,C)))),bind(Z,$fot(X_587))]]) ).

cnf(refute_0_1,plain,
    ( ~ theorem(or(not(or(B,or(A,C))),X_587))
    | theorem(or(not(or(A,or(B,C))),X_587)) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ theorem(or(not(or(X_141481,or(not(X_141482),X_141481))),or(not(or(X_141482,X_141483)),or(X_141481,X_141483))))
    | theorem(or(not(or(not(X_141482),or(X_141481,X_141481))),or(not(or(X_141482,X_141483)),or(X_141481,X_141483)))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_141482))),bind(B,$fot(X_141481)),bind(C,$fot(X_141481)),bind(X_587,$fot(or(not(or(X_141482,X_141483)),or(X_141481,X_141483))))]]) ).

cnf(refute_0_3,plain,
    ( ~ axiom(or(not(or(A,B)),or(B,A)))
    | ~ theorem(or(not(or(B,A)),X_587))
    | theorem(or(not(or(A,B)),X_587)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_587))]]) ).

cnf(refute_0_4,plain,
    ( ~ theorem(or(not(or(B,A)),X_587))
    | theorem(or(not(or(A,B)),X_587)) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ theorem(or(not(or(or(not(X_141449),X_141448),X_141448)),or(not(or(X_141449,X_141450)),or(X_141448,X_141450))))
    | theorem(or(not(or(X_141448,or(not(X_141449),X_141448))),or(not(or(X_141449,X_141450)),or(X_141448,X_141450)))) ),
    inference(subst,[],[refute_0_4:[bind(A,$fot(X_141448)),bind(B,$fot(or(not(X_141449),X_141448))),bind(X_587,$fot(or(not(or(X_141449,X_141450)),or(X_141448,X_141450))))]]) ).

cnf(refute_0_6,plain,
    axiom(or(not(X_585),or(B,X_585))),
    inference(subst,[],[axiom_1_3:[bind(A,$fot(X_585))]]) ).

cnf(refute_0_7,plain,
    ( ~ axiom(or(not(X_585),or(B,X_585)))
    | ~ theorem(or(not(or(B,X_585)),X_587))
    | theorem(or(not(X_585),X_587)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(X_585)),bind(Y,$fot(or(B,X_585))),bind(Z,$fot(X_587))]]) ).

cnf(refute_0_8,plain,
    ( ~ theorem(or(not(or(B,X_585)),X_587))
    | theorem(or(not(X_585),X_587)) ),
    inference(resolve,[$cnf( axiom(or(not(X_585),or(B,X_585))) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ theorem(or(not(or(not(X_141446),or(or(not(X_141446),X_141445),X_141445))),or(not(or(X_141446,X_141447)),or(X_141445,X_141447))))
    | theorem(or(not(or(or(not(X_141446),X_141445),X_141445)),or(not(or(X_141446,X_141447)),or(X_141445,X_141447)))) ),
    inference(subst,[],[refute_0_8:[bind(B,$fot(not(X_141446))),bind(X_585,$fot(or(or(not(X_141446),X_141445),X_141445))),bind(X_587,$fot(or(not(or(X_141446,X_141447)),or(X_141445,X_141447))))]]) ).

cnf(refute_0_10,plain,
    axiom(or(not(or(X_586,X_586)),X_586)),
    inference(subst,[],[axiom_1_2:[bind(A,$fot(X_586))]]) ).

cnf(refute_0_11,plain,
    ( ~ axiom(or(not(or(X_586,X_586)),X_586))
    | ~ theorem(or(not(X_586),X_587))
    | theorem(or(not(or(X_586,X_586)),X_587)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(X_586,X_586))),bind(Y,$fot(X_586)),bind(Z,$fot(X_587))]]) ).

cnf(refute_0_12,plain,
    ( ~ theorem(or(not(X_586),X_587))
    | theorem(or(not(or(X_586,X_586)),X_587)) ),
    inference(resolve,[$cnf( axiom(or(not(or(X_586,X_586)),X_586)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ theorem(or(not(or(not(X_6324),X_6323)),or(not(or(X_6324,X_6325)),or(X_6323,X_6325))))
    | theorem(or(not(or(or(not(X_6324),X_6323),or(not(X_6324),X_6323))),or(not(or(X_6324,X_6325)),or(X_6323,X_6325)))) ),
    inference(subst,[],[refute_0_12:[bind(X_586,$fot(or(not(X_6324),X_6323))),bind(X_587,$fot(or(not(or(X_6324,X_6325)),or(X_6323,X_6325))))]]) ).

cnf(refute_0_14,plain,
    ( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
    | ~ theorem(or(A,or(B,C)))
    | theorem(or(B,or(A,C))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).

cnf(refute_0_15,plain,
    ( ~ theorem(or(A,or(B,C)))
    | theorem(or(B,or(A,C))) ),
    inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ~ theorem(or(not(or(X_5915,X_5916)),or(not(or(not(X_5915),X_5914)),or(X_5914,X_5916))))
    | theorem(or(not(or(not(X_5915),X_5914)),or(not(or(X_5915,X_5916)),or(X_5914,X_5916)))) ),
    inference(subst,[],[refute_0_15:[bind(A,$fot(not(or(X_5915,X_5916)))),bind(B,$fot(not(or(not(X_5915),X_5914)))),bind(C,$fot(or(X_5914,X_5916)))]]) ).

cnf(refute_0_17,plain,
    ( ~ theorem(or(not(or(not(X_2406),X_2408)),or(not(or(X_2407,X_2406)),or(X_2408,X_2407))))
    | theorem(or(not(or(X_2407,X_2406)),or(not(or(not(X_2406),X_2408)),or(X_2408,X_2407)))) ),
    inference(subst,[],[refute_0_15:[bind(A,$fot(not(or(not(X_2406),X_2408)))),bind(B,$fot(not(or(X_2407,X_2406)))),bind(C,$fot(or(X_2408,X_2407)))]]) ).

cnf(refute_0_18,plain,
    axiom(or(not(or(not(A),X_2396)),or(not(or(X_2395,A)),or(X_2395,X_2396)))),
    inference(subst,[],[axiom_1_6:[bind(B,$fot(X_2396)),bind(C,$fot(X_2395))]]) ).

cnf(refute_0_19,plain,
    ( ~ axiom(or(not(or(X_7,X_8)),or(X_8,X_7)))
    | theorem(or(not(or(X_7,X_8)),or(X_8,X_7))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(X_7,X_8)),or(X_8,X_7))))]]) ).

cnf(refute_0_20,plain,
    axiom(or(not(or(X_7,X_8)),or(X_8,X_7))),
    inference(subst,[],[axiom_1_4:[bind(A,$fot(X_7)),bind(B,$fot(X_8))]]) ).

cnf(refute_0_21,plain,
    theorem(or(not(or(X_7,X_8)),or(X_8,X_7))),
    inference(resolve,[$cnf( axiom(or(not(or(X_7,X_8)),or(X_8,X_7))) )],[refute_0_20,refute_0_19]) ).

cnf(refute_0_22,plain,
    ( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
    | ~ theorem(or(not(A),B))
    | theorem(or(not(or(C,A)),or(C,B))) ),
    inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).

cnf(refute_0_23,plain,
    ( ~ theorem(or(not(A),B))
    | theorem(or(not(or(C,A)),or(C,B))) ),
    inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ theorem(or(not(or(X_7,X_8)),or(X_8,X_7)))
    | theorem(or(not(or(X_135,or(X_7,X_8))),or(X_135,or(X_8,X_7)))) ),
    inference(subst,[],[refute_0_23:[bind(A,$fot(or(X_7,X_8))),bind(B,$fot(or(X_8,X_7))),bind(C,$fot(X_135))]]) ).

cnf(refute_0_25,plain,
    theorem(or(not(or(X_135,or(X_7,X_8))),or(X_135,or(X_8,X_7)))),
    inference(resolve,[$cnf( theorem(or(not(or(X_7,X_8)),or(X_8,X_7))) )],[refute_0_21,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( ~ axiom(or(not(X_585),or(X_135,or(X_7,X_8))))
    | ~ theorem(or(not(or(X_135,or(X_7,X_8))),or(X_135,or(X_8,X_7))))
    | theorem(or(not(X_585),or(X_135,or(X_8,X_7)))) ),
    inference(subst,[],[rule_3:[bind(X,$fot(X_585)),bind(Y,$fot(or(X_135,or(X_7,X_8)))),bind(Z,$fot(or(X_135,or(X_8,X_7))))]]) ).

cnf(refute_0_27,plain,
    ( ~ axiom(or(not(X_585),or(X_135,or(X_7,X_8))))
    | theorem(or(not(X_585),or(X_135,or(X_8,X_7)))) ),
    inference(resolve,[$cnf( theorem(or(not(or(X_135,or(X_7,X_8))),or(X_135,or(X_8,X_7)))) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( ~ axiom(or(not(or(not(A),X_2396)),or(not(or(X_2395,A)),or(X_2395,X_2396))))
    | theorem(or(not(or(not(A),X_2396)),or(not(or(X_2395,A)),or(X_2396,X_2395)))) ),
    inference(subst,[],[refute_0_27:[bind(X_135,$fot(not(or(X_2395,A)))),bind(X_585,$fot(or(not(A),X_2396))),bind(X_7,$fot(X_2395)),bind(X_8,$fot(X_2396))]]) ).

cnf(refute_0_29,plain,
    theorem(or(not(or(not(A),X_2396)),or(not(or(X_2395,A)),or(X_2396,X_2395)))),
    inference(resolve,[$cnf( axiom(or(not(or(not(A),X_2396)),or(not(or(X_2395,A)),or(X_2395,X_2396)))) )],[refute_0_18,refute_0_28]) ).

cnf(refute_0_30,plain,
    theorem(or(not(or(not(X_2406),X_2408)),or(not(or(X_2407,X_2406)),or(X_2408,X_2407)))),
    inference(subst,[],[refute_0_29:[bind(A,$fot(X_2406)),bind(X_2395,$fot(X_2407)),bind(X_2396,$fot(X_2408))]]) ).

cnf(refute_0_31,plain,
    theorem(or(not(or(X_2407,X_2406)),or(not(or(not(X_2406),X_2408)),or(X_2408,X_2407)))),
    inference(resolve,[$cnf( theorem(or(not(or(not(X_2406),X_2408)),or(not(or(X_2407,X_2406)),or(X_2408,X_2407)))) )],[refute_0_30,refute_0_17]) ).

cnf(refute_0_32,plain,
    theorem(or(not(or(X_5525,X_5524)),or(not(or(not(X_5524),X_2408)),or(X_2408,X_5525)))),
    inference(subst,[],[refute_0_31:[bind(X_2406,$fot(X_5524)),bind(X_2407,$fot(X_5525))]]) ).

cnf(refute_0_33,plain,
    ( ~ theorem(or(not(or(X_5525,X_5524)),or(not(or(not(X_5524),X_2408)),or(X_2408,X_5525))))
    | theorem(or(not(or(X_5524,X_5525)),or(not(or(not(X_5524),X_2408)),or(X_2408,X_5525)))) ),
    inference(subst,[],[refute_0_4:[bind(A,$fot(X_5524)),bind(B,$fot(X_5525)),bind(X_587,$fot(or(not(or(not(X_5524),X_2408)),or(X_2408,X_5525))))]]) ).

cnf(refute_0_34,plain,
    theorem(or(not(or(X_5524,X_5525)),or(not(or(not(X_5524),X_2408)),or(X_2408,X_5525)))),
    inference(resolve,[$cnf( theorem(or(not(or(X_5525,X_5524)),or(not(or(not(X_5524),X_2408)),or(X_2408,X_5525)))) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    theorem(or(not(or(X_5915,X_5916)),or(not(or(not(X_5915),X_5914)),or(X_5914,X_5916)))),
    inference(subst,[],[refute_0_34:[bind(X_2408,$fot(X_5914)),bind(X_5524,$fot(X_5915)),bind(X_5525,$fot(X_5916))]]) ).

cnf(refute_0_36,plain,
    theorem(or(not(or(not(X_5915),X_5914)),or(not(or(X_5915,X_5916)),or(X_5914,X_5916)))),
    inference(resolve,[$cnf( theorem(or(not(or(X_5915,X_5916)),or(not(or(not(X_5915),X_5914)),or(X_5914,X_5916)))) )],[refute_0_35,refute_0_16]) ).

cnf(refute_0_37,plain,
    theorem(or(not(or(not(X_6324),X_6323)),or(not(or(X_6324,X_6325)),or(X_6323,X_6325)))),
    inference(subst,[],[refute_0_36:[bind(X_5914,$fot(X_6323)),bind(X_5915,$fot(X_6324)),bind(X_5916,$fot(X_6325))]]) ).

cnf(refute_0_38,plain,
    theorem(or(not(or(or(not(X_6324),X_6323),or(not(X_6324),X_6323))),or(not(or(X_6324,X_6325)),or(X_6323,X_6325)))),
    inference(resolve,[$cnf( theorem(or(not(or(not(X_6324),X_6323)),or(not(or(X_6324,X_6325)),or(X_6323,X_6325)))) )],[refute_0_37,refute_0_13]) ).

cnf(refute_0_39,plain,
    theorem(or(not(or(or(not(X_6324),X_60110),or(not(X_6324),X_60110))),or(not(or(X_6324,X_6325)),or(X_60110,X_6325)))),
    inference(subst,[],[refute_0_38:[bind(X_6323,$fot(X_60110))]]) ).

cnf(refute_0_40,plain,
    ( ~ theorem(or(not(or(or(not(X_6324),X_60110),or(not(X_6324),X_60110))),or(not(or(X_6324,X_6325)),or(X_60110,X_6325))))
    | theorem(or(not(or(not(X_6324),or(or(not(X_6324),X_60110),X_60110))),or(not(or(X_6324,X_6325)),or(X_60110,X_6325)))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_6324))),bind(B,$fot(or(not(X_6324),X_60110))),bind(C,$fot(X_60110)),bind(X_587,$fot(or(not(or(X_6324,X_6325)),or(X_60110,X_6325))))]]) ).

cnf(refute_0_41,plain,
    theorem(or(not(or(not(X_6324),or(or(not(X_6324),X_60110),X_60110))),or(not(or(X_6324,X_6325)),or(X_60110,X_6325)))),
    inference(resolve,[$cnf( theorem(or(not(or(or(not(X_6324),X_60110),or(not(X_6324),X_60110))),or(not(or(X_6324,X_6325)),or(X_60110,X_6325)))) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    theorem(or(not(or(not(X_141446),or(or(not(X_141446),X_141445),X_141445))),or(not(or(X_141446,X_141447)),or(X_141445,X_141447)))),
    inference(subst,[],[refute_0_41:[bind(X_60110,$fot(X_141445)),bind(X_6324,$fot(X_141446)),bind(X_6325,$fot(X_141447))]]) ).

cnf(refute_0_43,plain,
    theorem(or(not(or(or(not(X_141446),X_141445),X_141445)),or(not(or(X_141446,X_141447)),or(X_141445,X_141447)))),
    inference(resolve,[$cnf( theorem(or(not(or(not(X_141446),or(or(not(X_141446),X_141445),X_141445))),or(not(or(X_141446,X_141447)),or(X_141445,X_141447)))) )],[refute_0_42,refute_0_9]) ).

cnf(refute_0_44,plain,
    theorem(or(not(or(or(not(X_141449),X_141448),X_141448)),or(not(or(X_141449,X_141450)),or(X_141448,X_141450)))),
    inference(subst,[],[refute_0_43:[bind(X_141445,$fot(X_141448)),bind(X_141446,$fot(X_141449)),bind(X_141447,$fot(X_141450))]]) ).

cnf(refute_0_45,plain,
    theorem(or(not(or(X_141448,or(not(X_141449),X_141448))),or(not(or(X_141449,X_141450)),or(X_141448,X_141450)))),
    inference(resolve,[$cnf( theorem(or(not(or(or(not(X_141449),X_141448),X_141448)),or(not(or(X_141449,X_141450)),or(X_141448,X_141450)))) )],[refute_0_44,refute_0_5]) ).

cnf(refute_0_46,plain,
    theorem(or(not(or(X_141481,or(not(X_141482),X_141481))),or(not(or(X_141482,X_141483)),or(X_141481,X_141483)))),
    inference(subst,[],[refute_0_45:[bind(X_141448,$fot(X_141481)),bind(X_141449,$fot(X_141482)),bind(X_141450,$fot(X_141483))]]) ).

cnf(refute_0_47,plain,
    theorem(or(not(or(not(X_141482),or(X_141481,X_141481))),or(not(or(X_141482,X_141483)),or(X_141481,X_141483)))),
    inference(resolve,[$cnf( theorem(or(not(or(X_141481,or(not(X_141482),X_141481))),or(not(or(X_141482,X_141483)),or(X_141481,X_141483)))) )],[refute_0_46,refute_0_2]) ).

cnf(refute_0_48,plain,
    theorem(or(not(or(not(or(X_170439,X_170438)),or(X_170439,X_170439))),or(not(or(or(X_170439,X_170438),X_141483)),or(X_170439,X_141483)))),
    inference(subst,[],[refute_0_47:[bind(X_141481,$fot(X_170439)),bind(X_141482,$fot(or(X_170439,X_170438)))]]) ).

cnf(refute_0_49,plain,
    ( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
    | ~ theorem(or(not(or(not(or(C,A)),or(C,B))),X_587))
    | theorem(or(not(or(not(A),B)),X_587)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(not(A),B))),bind(Y,$fot(or(not(or(C,A)),or(C,B)))),bind(Z,$fot(X_587))]]) ).

cnf(refute_0_50,plain,
    ( ~ theorem(or(not(or(not(or(C,A)),or(C,B))),X_587))
    | theorem(or(not(or(not(A),B)),X_587)) ),
    inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( ~ theorem(or(not(or(not(or(X_170439,X_170438)),or(X_170439,X_170439))),or(not(or(or(X_170439,X_170438),X_141483)),or(X_170439,X_141483))))
    | theorem(or(not(or(not(X_170438),X_170439)),or(not(or(or(X_170439,X_170438),X_141483)),or(X_170439,X_141483)))) ),
    inference(subst,[],[refute_0_50:[bind(A,$fot(X_170438)),bind(B,$fot(X_170439)),bind(C,$fot(X_170439)),bind(X_587,$fot(or(not(or(or(X_170439,X_170438),X_141483)),or(X_170439,X_141483))))]]) ).

cnf(refute_0_52,plain,
    theorem(or(not(or(not(X_170438),X_170439)),or(not(or(or(X_170439,X_170438),X_141483)),or(X_170439,X_141483)))),
    inference(resolve,[$cnf( theorem(or(not(or(not(or(X_170439,X_170438)),or(X_170439,X_170439))),or(not(or(or(X_170439,X_170438),X_141483)),or(X_170439,X_141483)))) )],[refute_0_48,refute_0_51]) ).

cnf(refute_0_53,plain,
    theorem(or(not(or(not(q),p)),or(not(or(or(p,q),r)),or(p,r)))),
    inference(subst,[],[refute_0_52:[bind(X_141483,$fot(r)),bind(X_170438,$fot(q)),bind(X_170439,$fot(p))]]) ).

cnf(refute_0_54,plain,
    $false,
    inference(resolve,[$cnf( theorem(or(not(or(not(q),p)),or(not(or(or(p,q),r)),or(p,r)))) )],[refute_0_53,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL222-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n005.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  : 600
% 0.13/0.34  % DateTime : Mon Jul  4 14:51:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 119.98/120.18  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 119.98/120.18  
% 119.98/120.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.98/120.18  
%------------------------------------------------------------------------------