TSTP Solution File: LCL006-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:48:44 EDT 2022
% Result : Unsatisfiable 193.31s 193.52s
% Output : CNFRefutation 193.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 4
% Syntax : Number of clauses : 75 ( 41 unt; 0 nHn; 32 RR)
% Number of literals : 118 ( 0 equ; 44 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(ec_4,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) ).
cnf(ec_5,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))) ).
cnf(prove_ec_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X_289,equivalent(equivalent(X_287,X_288),equivalent(X_288,X_287))))
| ~ is_a_theorem(equivalent(equivalent(X_289,equivalent(equivalent(X_287,X_288),equivalent(X_288,X_287))),X_289))
| is_a_theorem(X_289) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_289,equivalent(equivalent(X_287,X_288),equivalent(X_288,X_287))))),bind(Y,$fot(X_289))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X)))
| is_a_theorem(equivalent(Y,X)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(Y,X)))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(Y,X)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) )],[ec_4,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(X_149,equivalent(X_149,equivalent(equivalent(X_147,X_148),equivalent(X_148,X_147)))))
| is_a_theorem(equivalent(equivalent(X_149,equivalent(equivalent(X_147,X_148),equivalent(X_148,X_147))),X_149)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_149)),bind(Y,$fot(equivalent(X_149,equivalent(equivalent(X_147,X_148),equivalent(X_148,X_147)))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(X_15)
| ~ is_a_theorem(equivalent(X_15,equivalent(X_16,equivalent(X_16,X_15))))
| is_a_theorem(equivalent(X_16,equivalent(X_16,X_15))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_15)),bind(Y,$fot(equivalent(X_16,equivalent(X_16,X_15))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_13,X_12))),
inference(subst,[],[ec_4:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),Z))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z))))
| is_a_theorem(equivalent(X,equivalent(Y,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X,Y),Z))),bind(Y,$fot(equivalent(X,equivalent(Y,Z))))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),Z))
| is_a_theorem(equivalent(X,equivalent(Y,Z))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))) )],[ec_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_13,X_12)))
| is_a_theorem(equivalent(X_12,equivalent(X_13,equivalent(X_13,X_12)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_12)),bind(Y,$fot(X_13)),bind(Z,$fot(equivalent(X_13,X_12)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(X_12,equivalent(X_13,equivalent(X_13,X_12)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_12,X_13),equivalent(X_13,X_12))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(X_15,equivalent(X_16,equivalent(X_16,X_15)))),
inference(subst,[],[refute_0_9:[bind(X_12,$fot(X_15)),bind(X_13,$fot(X_16))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(X_15)
| is_a_theorem(equivalent(X_16,equivalent(X_16,X_15))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_15,equivalent(X_16,equivalent(X_16,X_15)))) )],[refute_0_10,refute_0_4]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X)))
| is_a_theorem(equivalent(X_36,equivalent(X_36,equivalent(equivalent(X,Y),equivalent(Y,X))))) ),
inference(subst,[],[refute_0_11:[bind(X_15,$fot(equivalent(equivalent(X,Y),equivalent(Y,X)))),bind(X_16,$fot(X_36))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(X_36,equivalent(X_36,equivalent(equivalent(X,Y),equivalent(Y,X))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(Y,X))) )],[ec_4,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(X_149,equivalent(X_149,equivalent(equivalent(X_147,X_148),equivalent(X_148,X_147))))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_147)),bind(Y,$fot(X_148)),bind(X_36,$fot(X_149))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(X_149,equivalent(equivalent(X_147,X_148),equivalent(X_148,X_147))),X_149)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_149,equivalent(X_149,equivalent(equivalent(X_147,X_148),equivalent(X_148,X_147))))) )],[refute_0_14,refute_0_3]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(X_289,equivalent(equivalent(X_287,X_288),equivalent(X_288,X_287))),X_289)),
inference(subst,[],[refute_0_15:[bind(X_147,$fot(X_287)),bind(X_148,$fot(X_288)),bind(X_149,$fot(X_289))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(equivalent(X_289,equivalent(equivalent(X_287,X_288),equivalent(X_288,X_287))))
| is_a_theorem(X_289) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_289,equivalent(equivalent(X_287,X_288),equivalent(X_288,X_287))),X_289)) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)),equivalent(X_32122,X_32120)),equivalent(equivalent(equivalent(X_32120,X_32121),equivalent(X_32121,X_32122)),equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)))))
| is_a_theorem(equivalent(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)),equivalent(X_32122,X_32120))) ),
inference(subst,[],[refute_0_17:[bind(X_287,$fot(equivalent(X_32120,X_32121))),bind(X_288,$fot(equivalent(X_32121,X_32122))),bind(X_289,$fot(equivalent(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)),equivalent(X_32122,X_32120))))]]) ).
cnf(refute_0_19,plain,
( ~ is_a_theorem(equivalent(X_9,equivalent(X_10,X_11)))
| ~ is_a_theorem(equivalent(equivalent(X_9,equivalent(X_10,X_11)),equivalent(equivalent(X_9,X_10),X_11)))
| is_a_theorem(equivalent(equivalent(X_9,X_10),X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_9,equivalent(X_10,X_11)))),bind(Y,$fot(equivalent(equivalent(X_9,X_10),X_11)))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(equivalent(X,Y),Z))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(equivalent(X,Y),Z))),bind(Y,$fot(equivalent(X,equivalent(Y,Z))))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(equivalent(X,Y),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),equivalent(X,equivalent(Y,Z)))) )],[ec_5,refute_0_20]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(X_9,equivalent(X_10,X_11)),equivalent(equivalent(X_9,X_10),X_11))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(equivalent(X_9,equivalent(X_10,X_11)))
| is_a_theorem(equivalent(equivalent(X_9,X_10),X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_9,equivalent(X_10,X_11)),equivalent(equivalent(X_9,X_10),X_11))) )],[refute_0_22,refute_0_19]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(X_14686,equivalent(equivalent(X_14689,X_14687),equivalent(equivalent(equivalent(X_14687,X_14688),equivalent(X_14688,X_14689)),X_14686))))
| is_a_theorem(equivalent(equivalent(X_14686,equivalent(X_14689,X_14687)),equivalent(equivalent(equivalent(X_14687,X_14688),equivalent(X_14688,X_14689)),X_14686))) ),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(equivalent(X_14689,X_14687))),bind(X_11,$fot(equivalent(equivalent(equivalent(X_14687,X_14688),equivalent(X_14688,X_14689)),X_14686))),bind(X_9,$fot(X_14686))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(equivalent(X_24,X_25))
| ~ is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))
| is_a_theorem(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_24,X_25))),bind(Y,$fot(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),X_13),equivalent(X,equivalent(Y,X_13)))),
inference(subst,[],[ec_5:[bind(Z,$fot(X_13))]]) ).
cnf(refute_0_27,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),X_13),equivalent(X,equivalent(Y,X_13))))
| is_a_theorem(equivalent(equivalent(X,Y),equivalent(X_13,equivalent(X,equivalent(Y,X_13))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(X_13)),bind(Z,$fot(equivalent(X,equivalent(Y,X_13))))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(X_13,equivalent(X,equivalent(Y,X_13))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),X_13),equivalent(X,equivalent(Y,X_13)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26))))),
inference(subst,[],[refute_0_28:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(X_13,$fot(X_26))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(equivalent(X_24,X_25))
| is_a_theorem(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26))))) )],[refute_0_29,refute_0_25]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(equivalent(equivalent(X_5600,X_5598),equivalent(equivalent(X_5598,X_5599),equivalent(X_5599,X_5600))))
| is_a_theorem(equivalent(X_26,equivalent(equivalent(X_5600,X_5598),equivalent(equivalent(equivalent(X_5598,X_5599),equivalent(X_5599,X_5600)),X_26)))) ),
inference(subst,[],[refute_0_30:[bind(X_24,$fot(equivalent(X_5600,X_5598))),bind(X_25,$fot(equivalent(equivalent(X_5598,X_5599),equivalent(X_5599,X_5600))))]]) ).
cnf(refute_0_32,plain,
( ~ is_a_theorem(equivalent(X_2549,equivalent(X_2547,equivalent(equivalent(X_2547,X_2548),equivalent(X_2548,X_2549)))))
| is_a_theorem(equivalent(equivalent(X_2549,X_2547),equivalent(equivalent(X_2547,X_2548),equivalent(X_2548,X_2549)))) ),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(X_2547)),bind(X_11,$fot(equivalent(equivalent(X_2547,X_2548),equivalent(X_2548,X_2549)))),bind(X_9,$fot(X_2549))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_51,X_49),X_50),X_51))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_51,X_49),X_50),X_51),equivalent(X_49,X_50)))
| is_a_theorem(equivalent(X_49,X_50)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_51,X_49),X_50),X_51))),bind(Y,$fot(equivalent(X_49,X_50)))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_43,Y),Z),equivalent(X_43,equivalent(Y,Z)))),
inference(subst,[],[ec_5:[bind(X,$fot(X_43))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_43,Y),Z),equivalent(X_43,equivalent(Y,Z))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_43,Y),Z),X_43),equivalent(Y,Z))) ),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(X_43)),bind(X_11,$fot(equivalent(Y,Z))),bind(X_9,$fot(equivalent(equivalent(X_43,Y),Z)))]]) ).
cnf(refute_0_36,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_43,Y),Z),X_43),equivalent(Y,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_43,Y),Z),equivalent(X_43,equivalent(Y,Z)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_51,X_49),X_50),X_51),equivalent(X_49,X_50))),
inference(subst,[],[refute_0_36:[bind(Y,$fot(X_49)),bind(Z,$fot(X_50)),bind(X_43,$fot(X_51))]]) ).
cnf(refute_0_38,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_51,X_49),X_50),X_51))
| is_a_theorem(equivalent(X_49,X_50)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_51,X_49),X_50),X_51),equivalent(X_49,X_50))) )],[refute_0_37,refute_0_33]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_2546,X_49),equivalent(X_2544,equivalent(equivalent(X_2544,X_2546),equivalent(X_2546,X_49)))),X_2546))
| is_a_theorem(equivalent(X_49,equivalent(X_2544,equivalent(equivalent(X_2544,X_2546),equivalent(X_2546,X_49))))) ),
inference(subst,[],[refute_0_38:[bind(X_50,$fot(equivalent(X_2544,equivalent(equivalent(X_2544,X_2546),equivalent(X_2546,X_49))))),bind(X_51,$fot(X_2546))]]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(equivalent(X_1649,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_1649),X_1651)))))
| is_a_theorem(equivalent(X_16,equivalent(X_16,equivalent(X_1649,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_1649),X_1651))))))) ),
inference(subst,[],[refute_0_11:[bind(X_15,$fot(equivalent(X_1649,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_1649),X_1651))))))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(equivalent(X_37,equivalent(X_38,equivalent(X_39,equivalent(X_37,equivalent(X_38,X_39))))))
| is_a_theorem(equivalent(equivalent(X_38,equivalent(X_39,equivalent(X_37,equivalent(X_38,X_39)))),X_37)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_37)),bind(Y,$fot(equivalent(X_38,equivalent(X_39,equivalent(X_37,equivalent(X_38,X_39))))))]]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))
| is_a_theorem(equivalent(X_24,equivalent(X_25,equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))]]) ).
cnf(refute_0_43,plain,
is_a_theorem(equivalent(X_24,equivalent(X_25,equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26))))) )],[refute_0_29,refute_0_42]) ).
cnf(refute_0_44,plain,
is_a_theorem(equivalent(X_37,equivalent(X_38,equivalent(X_39,equivalent(X_37,equivalent(X_38,X_39)))))),
inference(subst,[],[refute_0_43:[bind(X_24,$fot(X_37)),bind(X_25,$fot(X_38)),bind(X_26,$fot(X_39))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(equivalent(equivalent(X_38,equivalent(X_39,equivalent(X_37,equivalent(X_38,X_39)))),X_37)),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_37,equivalent(X_38,equivalent(X_39,equivalent(X_37,equivalent(X_38,X_39)))))) )],[refute_0_44,refute_0_41]) ).
cnf(refute_0_46,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_1530,X_1528),equivalent(X_39,equivalent(X_1530,equivalent(equivalent(X_1530,X_1528),X_39)))),X_1530)),
inference(subst,[],[refute_0_45:[bind(X_37,$fot(X_1530)),bind(X_38,$fot(equivalent(X_1530,X_1528)))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_1530,X_1528),equivalent(X_39,equivalent(X_1530,equivalent(equivalent(X_1530,X_1528),X_39)))),X_1530))
| is_a_theorem(equivalent(X_1528,equivalent(X_39,equivalent(X_1530,equivalent(equivalent(X_1530,X_1528),X_39))))) ),
inference(subst,[],[refute_0_38:[bind(X_49,$fot(X_1528)),bind(X_50,$fot(equivalent(X_39,equivalent(X_1530,equivalent(equivalent(X_1530,X_1528),X_39))))),bind(X_51,$fot(X_1530))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(equivalent(X_1528,equivalent(X_39,equivalent(X_1530,equivalent(equivalent(X_1530,X_1528),X_39))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_1530,X_1528),equivalent(X_39,equivalent(X_1530,equivalent(equivalent(X_1530,X_1528),X_39)))),X_1530)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(equivalent(X_1649,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_1649),X_1651))))),
inference(subst,[],[refute_0_48:[bind(X_1528,$fot(X_1649)),bind(X_1530,$fot(X_1650)),bind(X_39,$fot(X_1651))]]) ).
cnf(refute_0_50,plain,
is_a_theorem(equivalent(X_16,equivalent(X_16,equivalent(X_1649,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_1649),X_1651))))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_1649,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_1649),X_1651))))) )],[refute_0_49,refute_0_40]) ).
cnf(refute_0_51,plain,
is_a_theorem(equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),equivalent(X_2390,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))))))),
inference(subst,[],[refute_0_50:[bind(X_16,$fot(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))))),bind(X_1649,$fot(X_2390))]]) ).
cnf(refute_0_52,plain,
( ~ is_a_theorem(equivalent(X_63,equivalent(X_61,equivalent(X_62,X_63))))
| ~ is_a_theorem(equivalent(equivalent(X_63,equivalent(X_61,equivalent(X_62,X_63))),equivalent(X_61,X_62)))
| is_a_theorem(equivalent(X_61,X_62)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_63,equivalent(X_61,equivalent(X_62,X_63))))),bind(Y,$fot(equivalent(X_61,X_62)))]]) ).
cnf(refute_0_53,plain,
( ~ is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))
| is_a_theorem(equivalent(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26))),equivalent(X_24,X_25))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(equivalent(X_24,X_25))),bind(Y,$fot(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26)))))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(equivalent(equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26))),equivalent(X_24,X_25))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_24,X_25),equivalent(X_26,equivalent(X_24,equivalent(X_25,X_26))))) )],[refute_0_29,refute_0_53]) ).
cnf(refute_0_55,plain,
is_a_theorem(equivalent(equivalent(X_63,equivalent(X_61,equivalent(X_62,X_63))),equivalent(X_61,X_62))),
inference(subst,[],[refute_0_54:[bind(X_24,$fot(X_61)),bind(X_25,$fot(X_62)),bind(X_26,$fot(X_63))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(equivalent(X_63,equivalent(X_61,equivalent(X_62,X_63))))
| is_a_theorem(equivalent(X_61,X_62)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_63,equivalent(X_61,equivalent(X_62,X_63))),equivalent(X_61,X_62))) )],[refute_0_55,refute_0_52]) ).
cnf(refute_0_57,plain,
( ~ is_a_theorem(equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),equivalent(X_2390,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651)))))))
| is_a_theorem(equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),X_2390)) ),
inference(subst,[],[refute_0_56:[bind(X_61,$fot(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))))),bind(X_62,$fot(X_2390)),bind(X_63,$fot(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651)))))]]) ).
cnf(refute_0_58,plain,
is_a_theorem(equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),X_2390)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),equivalent(equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))),equivalent(X_2390,equivalent(X_1651,equivalent(X_1650,equivalent(equivalent(X_1650,X_2390),X_1651))))))) )],[refute_0_51,refute_0_57]) ).
cnf(refute_0_59,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_2546,X_49),equivalent(X_2544,equivalent(equivalent(X_2544,X_2546),equivalent(X_2546,X_49)))),X_2546)),
inference(subst,[],[refute_0_58:[bind(X_1650,$fot(X_2544)),bind(X_1651,$fot(equivalent(X_2546,X_49))),bind(X_2390,$fot(X_2546))]]) ).
cnf(refute_0_60,plain,
is_a_theorem(equivalent(X_49,equivalent(X_2544,equivalent(equivalent(X_2544,X_2546),equivalent(X_2546,X_49))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_2546,X_49),equivalent(X_2544,equivalent(equivalent(X_2544,X_2546),equivalent(X_2546,X_49)))),X_2546)) )],[refute_0_59,refute_0_39]) ).
cnf(refute_0_61,plain,
is_a_theorem(equivalent(X_2549,equivalent(X_2547,equivalent(equivalent(X_2547,X_2548),equivalent(X_2548,X_2549))))),
inference(subst,[],[refute_0_60:[bind(X_2544,$fot(X_2547)),bind(X_2546,$fot(X_2548)),bind(X_49,$fot(X_2549))]]) ).
cnf(refute_0_62,plain,
is_a_theorem(equivalent(equivalent(X_2549,X_2547),equivalent(equivalent(X_2547,X_2548),equivalent(X_2548,X_2549)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_2549,equivalent(X_2547,equivalent(equivalent(X_2547,X_2548),equivalent(X_2548,X_2549))))) )],[refute_0_61,refute_0_32]) ).
cnf(refute_0_63,plain,
is_a_theorem(equivalent(equivalent(X_5600,X_5598),equivalent(equivalent(X_5598,X_5599),equivalent(X_5599,X_5600)))),
inference(subst,[],[refute_0_62:[bind(X_2547,$fot(X_5598)),bind(X_2548,$fot(X_5599)),bind(X_2549,$fot(X_5600))]]) ).
cnf(refute_0_64,plain,
is_a_theorem(equivalent(X_26,equivalent(equivalent(X_5600,X_5598),equivalent(equivalent(equivalent(X_5598,X_5599),equivalent(X_5599,X_5600)),X_26)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_5600,X_5598),equivalent(equivalent(X_5598,X_5599),equivalent(X_5599,X_5600)))) )],[refute_0_63,refute_0_31]) ).
cnf(refute_0_65,plain,
is_a_theorem(equivalent(X_14686,equivalent(equivalent(X_14689,X_14687),equivalent(equivalent(equivalent(X_14687,X_14688),equivalent(X_14688,X_14689)),X_14686)))),
inference(subst,[],[refute_0_64:[bind(X_26,$fot(X_14686)),bind(X_5598,$fot(X_14687)),bind(X_5599,$fot(X_14688)),bind(X_5600,$fot(X_14689))]]) ).
cnf(refute_0_66,plain,
is_a_theorem(equivalent(equivalent(X_14686,equivalent(X_14689,X_14687)),equivalent(equivalent(equivalent(X_14687,X_14688),equivalent(X_14688,X_14689)),X_14686))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_14686,equivalent(equivalent(X_14689,X_14687),equivalent(equivalent(equivalent(X_14687,X_14688),equivalent(X_14688,X_14689)),X_14686)))) )],[refute_0_65,refute_0_24]) ).
cnf(refute_0_67,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)),equivalent(X_32122,X_32120)),equivalent(equivalent(equivalent(X_32120,X_32121),equivalent(X_32121,X_32122)),equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121))))),
inference(subst,[],[refute_0_66:[bind(X_14686,$fot(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)))),bind(X_14687,$fot(X_32120)),bind(X_14688,$fot(X_32121)),bind(X_14689,$fot(X_32122))]]) ).
cnf(refute_0_68,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)),equivalent(X_32122,X_32120))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121)),equivalent(X_32122,X_32120)),equivalent(equivalent(equivalent(X_32120,X_32121),equivalent(X_32121,X_32122)),equivalent(equivalent(X_32121,X_32122),equivalent(X_32120,X_32121))))) )],[refute_0_67,refute_0_18]) ).
cnf(refute_0_69,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))),
inference(subst,[],[refute_0_68:[bind(X_32120,$fot(c)),bind(X_32121,$fot(a)),bind(X_32122,$fot(b))]]) ).
cnf(refute_0_70,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,a)),equivalent(b,c))) )],[refute_0_69,prove_ec_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.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 3 21:56:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 193.31/193.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 193.31/193.52
% 193.31/193.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 193.31/193.53
%------------------------------------------------------------------------------