TSTP Solution File: LCL230-1 by Metis---2.4

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL230-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n006.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 12:50:54 EDT 2022

% Result   : Unsatisfiable 156.35s 156.58s
% Output   : CNFRefutation 156.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   46 (  25 unt;   0 nHn;  22 RR)
%            Number of literals    :   74 (   0 equ;  29 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   :  108 (  14 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_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(or(p,q)),or(p,r))),or(p,or(not(q),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_343))
    | theorem(or(not(or(A,or(B,C))),X_343)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(or(A,or(B,C)))),bind(Y,$fot(or(B,or(A,C)))),bind(Z,$fot(X_343))]]) ).

cnf(refute_0_1,plain,
    ( ~ theorem(or(not(or(B,or(A,C))),X_343))
    | theorem(or(not(or(A,or(B,C))),X_343)) ),
    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_220852,or(not(or(X_220854,X_220855)),X_220853))),or(X_220852,or(not(X_220855),X_220853))))
    | theorem(or(not(or(not(or(X_220854,X_220855)),or(X_220852,X_220853))),or(X_220852,or(not(X_220855),X_220853)))) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(not(or(X_220854,X_220855)))),bind(B,$fot(X_220852)),bind(C,$fot(X_220853)),bind(X_343,$fot(or(X_220852,or(not(X_220855),X_220853))))]]) ).

cnf(refute_0_3,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_4,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_3]) ).

cnf(refute_0_5,plain,
    ( ~ theorem(or(not(or(not(or(X_3909,X_3910)),X_3908)),or(not(X_3910),X_3908)))
    | theorem(or(not(or(C,or(not(or(X_3909,X_3910)),X_3908))),or(C,or(not(X_3910),X_3908)))) ),
    inference(subst,[],[refute_0_4:[bind(A,$fot(or(not(or(X_3909,X_3910)),X_3908))),bind(B,$fot(or(not(X_3910),X_3908)))]]) ).

cnf(refute_0_6,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_7,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_6]) ).

cnf(refute_0_8,plain,
    ( ~ theorem(or(not(X_2507),or(not(or(not(or(X_2506,X_2507)),X_2505)),X_2505)))
    | theorem(or(not(or(not(or(X_2506,X_2507)),X_2505)),or(not(X_2507),X_2505))) ),
    inference(subst,[],[refute_0_7:[bind(A,$fot(not(X_2507))),bind(B,$fot(not(or(not(or(X_2506,X_2507)),X_2505)))),bind(C,$fot(X_2505))]]) ).

cnf(refute_0_9,plain,
    ( ~ theorem(or(not(or(B,C)),or(B,C)))
    | theorem(or(B,or(not(or(B,C)),C))) ),
    inference(subst,[],[refute_0_7:[bind(A,$fot(not(or(B,C))))]]) ).

cnf(refute_0_10,plain,
    axiom(or(not(or(X_23,X_23)),X_23)),
    inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).

cnf(refute_0_11,plain,
    ( ~ axiom(or(not(or(X_23,X_23)),X_23))
    | ~ theorem(or(X_23,X_23))
    | theorem(X_23) ),
    inference(subst,[],[rule_2:[bind(X,$fot(X_23)),bind(Y,$fot(or(X_23,X_23)))]]) ).

cnf(refute_0_12,plain,
    ( ~ theorem(or(X_23,X_23))
    | theorem(X_23) ),
    inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ theorem(or(or(not(X_134),X_134),or(not(X_134),X_134)))
    | theorem(or(not(X_134),X_134)) ),
    inference(subst,[],[refute_0_12:[bind(X_23,$fot(or(not(X_134),X_134)))]]) ).

cnf(refute_0_14,plain,
    ( ~ axiom(or(not(X_3),or(X_4,X_3)))
    | theorem(or(not(X_3),or(X_4,X_3))) ),
    inference(subst,[],[rule_1:[bind(X,$fot(or(not(X_3),or(X_4,X_3))))]]) ).

cnf(refute_0_15,plain,
    axiom(or(not(X_3),or(X_4,X_3))),
    inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).

cnf(refute_0_16,plain,
    theorem(or(not(X_3),or(X_4,X_3))),
    inference(resolve,[$cnf( axiom(or(not(X_3),or(X_4,X_3))) )],[refute_0_15,refute_0_14]) ).

cnf(refute_0_17,plain,
    theorem(or(not(X_128),or(X_127,X_128))),
    inference(subst,[],[refute_0_16:[bind(X_3,$fot(X_128)),bind(X_4,$fot(X_127))]]) ).

cnf(refute_0_18,plain,
    ( ~ theorem(or(not(X_128),or(X_127,X_128)))
    | theorem(or(X_127,or(not(X_128),X_128))) ),
    inference(subst,[],[refute_0_7:[bind(A,$fot(not(X_128))),bind(B,$fot(X_127)),bind(C,$fot(X_128))]]) ).

cnf(refute_0_19,plain,
    theorem(or(X_127,or(not(X_128),X_128))),
    inference(resolve,[$cnf( theorem(or(not(X_128),or(X_127,X_128))) )],[refute_0_17,refute_0_18]) ).

cnf(refute_0_20,plain,
    theorem(or(or(not(X_134),X_134),or(not(X_134),X_134))),
    inference(subst,[],[refute_0_19:[bind(X_127,$fot(or(not(X_134),X_134))),bind(X_128,$fot(X_134))]]) ).

cnf(refute_0_21,plain,
    theorem(or(not(X_134),X_134)),
    inference(resolve,[$cnf( theorem(or(or(not(X_134),X_134),or(not(X_134),X_134))) )],[refute_0_20,refute_0_13]) ).

cnf(refute_0_22,plain,
    theorem(or(not(or(B,C)),or(B,C))),
    inference(subst,[],[refute_0_21:[bind(X_134,$fot(or(B,C)))]]) ).

cnf(refute_0_23,plain,
    theorem(or(B,or(not(or(B,C)),C))),
    inference(resolve,[$cnf( theorem(or(not(or(B,C)),or(B,C))) )],[refute_0_22,refute_0_9]) ).

cnf(refute_0_24,plain,
    theorem(or(not(or(X_2317,X_2318)),or(not(or(not(or(X_2317,X_2318)),C)),C))),
    inference(subst,[],[refute_0_23:[bind(B,$fot(not(or(X_2317,X_2318))))]]) ).

cnf(refute_0_25,plain,
    axiom(or(not(X_341),or(B,X_341))),
    inference(subst,[],[axiom_1_3:[bind(A,$fot(X_341))]]) ).

cnf(refute_0_26,plain,
    ( ~ axiom(or(not(X_341),or(B,X_341)))
    | ~ theorem(or(not(or(B,X_341)),X_343))
    | theorem(or(not(X_341),X_343)) ),
    inference(subst,[],[rule_3:[bind(X,$fot(X_341)),bind(Y,$fot(or(B,X_341))),bind(Z,$fot(X_343))]]) ).

cnf(refute_0_27,plain,
    ( ~ theorem(or(not(or(B,X_341)),X_343))
    | theorem(or(not(X_341),X_343)) ),
    inference(resolve,[$cnf( axiom(or(not(X_341),or(B,X_341))) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( ~ theorem(or(not(or(X_2317,X_2318)),or(not(or(not(or(X_2317,X_2318)),C)),C)))
    | theorem(or(not(X_2318),or(not(or(not(or(X_2317,X_2318)),C)),C))) ),
    inference(subst,[],[refute_0_27:[bind(B,$fot(X_2317)),bind(X_341,$fot(X_2318)),bind(X_343,$fot(or(not(or(not(or(X_2317,X_2318)),C)),C)))]]) ).

cnf(refute_0_29,plain,
    theorem(or(not(X_2318),or(not(or(not(or(X_2317,X_2318)),C)),C))),
    inference(resolve,[$cnf( theorem(or(not(or(X_2317,X_2318)),or(not(or(not(or(X_2317,X_2318)),C)),C))) )],[refute_0_24,refute_0_28]) ).

cnf(refute_0_30,plain,
    theorem(or(not(X_2507),or(not(or(not(or(X_2506,X_2507)),X_2505)),X_2505))),
    inference(subst,[],[refute_0_29:[bind(C,$fot(X_2505)),bind(X_2317,$fot(X_2506)),bind(X_2318,$fot(X_2507))]]) ).

cnf(refute_0_31,plain,
    theorem(or(not(or(not(or(X_2506,X_2507)),X_2505)),or(not(X_2507),X_2505))),
    inference(resolve,[$cnf( theorem(or(not(X_2507),or(not(or(not(or(X_2506,X_2507)),X_2505)),X_2505))) )],[refute_0_30,refute_0_8]) ).

cnf(refute_0_32,plain,
    theorem(or(not(or(not(or(X_3909,X_3910)),X_3908)),or(not(X_3910),X_3908))),
    inference(subst,[],[refute_0_31:[bind(X_2505,$fot(X_3908)),bind(X_2506,$fot(X_3909)),bind(X_2507,$fot(X_3910))]]) ).

cnf(refute_0_33,plain,
    theorem(or(not(or(C,or(not(or(X_3909,X_3910)),X_3908))),or(C,or(not(X_3910),X_3908)))),
    inference(resolve,[$cnf( theorem(or(not(or(not(or(X_3909,X_3910)),X_3908)),or(not(X_3910),X_3908))) )],[refute_0_32,refute_0_5]) ).

cnf(refute_0_34,plain,
    theorem(or(not(or(X_220852,or(not(or(X_220854,X_220855)),X_220853))),or(X_220852,or(not(X_220855),X_220853)))),
    inference(subst,[],[refute_0_33:[bind(C,$fot(X_220852)),bind(X_3908,$fot(X_220853)),bind(X_3909,$fot(X_220854)),bind(X_3910,$fot(X_220855))]]) ).

cnf(refute_0_35,plain,
    theorem(or(not(or(not(or(X_220854,X_220855)),or(X_220852,X_220853))),or(X_220852,or(not(X_220855),X_220853)))),
    inference(resolve,[$cnf( theorem(or(not(or(X_220852,or(not(or(X_220854,X_220855)),X_220853))),or(X_220852,or(not(X_220855),X_220853)))) )],[refute_0_34,refute_0_2]) ).

cnf(refute_0_36,plain,
    theorem(or(not(or(not(or(p,q)),or(p,r))),or(p,or(not(q),r)))),
    inference(subst,[],[refute_0_35:[bind(X_220852,$fot(p)),bind(X_220853,$fot(r)),bind(X_220854,$fot(p)),bind(X_220855,$fot(q))]]) ).

cnf(refute_0_37,plain,
    $false,
    inference(resolve,[$cnf( theorem(or(not(or(not(or(p,q)),or(p,r))),or(p,or(not(q),r)))) )],[refute_0_36,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL230-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul  4 14:40:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 156.35/156.58  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 156.35/156.58  
% 156.35/156.58  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 156.35/156.59  
%------------------------------------------------------------------------------