TSTP Solution File: LCL029-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL029-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:48:53 EDT 2022
% Result : Unsatisfiable 0.57s 0.80s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of clauses : 63 ( 36 unt; 0 nHn; 15 RR)
% Number of literals : 97 ( 0 equ; 35 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 169 ( 59 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(c0_1,axiom,
is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ).
cnf(c0_2,axiom,
is_a_theorem(implies(X,implies(Y,X))) ).
cnf(c0_3,axiom,
is_a_theorem(implies(implies(implies(X,Y),X),X)) ).
cnf(c0_4,axiom,
is_a_theorem(implies(falsehood,X)) ).
cnf(prove_c0_5,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(falsehood,X_186),X_185))
| ~ is_a_theorem(implies(implies(implies(falsehood,X_186),X_185),X_185))
| is_a_theorem(X_185) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(falsehood,X_186),X_185))),bind(Y,$fot(X_185))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(implies(implies(X_9,Y),X_9),X_9)),
inference(subst,[],[c0_3:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(X_9,Y),X_9))
| ~ is_a_theorem(implies(implies(implies(X_9,Y),X_9),X_9))
| is_a_theorem(X_9) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_9,Y),X_9))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(X_9,Y),X_9))
| is_a_theorem(X_9) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_9,Y),X_9),X_9)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_182),X_181),X_181),X_181),implies(implies(implies(falsehood,X_182),X_181),X_181)))
| is_a_theorem(implies(implies(implies(falsehood,X_182),X_181),X_181)) ),
inference(subst,[],[refute_0_3:[bind(Y,$fot(X_181)),bind(X_9,$fot(implies(implies(implies(falsehood,X_182),X_181),X_181)))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(X,Y))
| is_a_theorem(implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[c0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(falsehood,X_50),X_52),implies(X_51,X_52)))
| is_a_theorem(implies(implies(implies(X_51,X_52),Z),implies(implies(implies(falsehood,X_50),X_52),Z))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(implies(falsehood,X_50),X_52))),bind(Y,$fot(implies(X_51,X_52)))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(X_8,implies(Y,X_8))),
inference(subst,[],[c0_2:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(X_8)
| ~ is_a_theorem(implies(X_8,implies(Y,X_8)))
| is_a_theorem(implies(Y,X_8)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_8)),bind(Y,$fot(implies(Y,X_8)))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(X_8)
| is_a_theorem(implies(Y,X_8)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_8,implies(Y,X_8))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(implies(falsehood,X))
| is_a_theorem(implies(X_11,implies(falsehood,X))) ),
inference(subst,[],[refute_0_10:[bind(Y,$fot(X_11)),bind(X_8,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(X_11,implies(falsehood,X))),
inference(resolve,[$cnf( is_a_theorem(implies(falsehood,X)) )],[c0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(X_47,implies(falsehood,X))),
inference(subst,[],[refute_0_12:[bind(X_11,$fot(X_47))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(implies(X_47,implies(falsehood,X)))
| is_a_theorem(implies(implies(implies(falsehood,X),X_49),implies(X_47,X_49))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_47)),bind(Y,$fot(implies(falsehood,X))),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(implies(implies(implies(falsehood,X),X_49),implies(X_47,X_49))),
inference(resolve,[$cnf( is_a_theorem(implies(X_47,implies(falsehood,X))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(implies(falsehood,X_50),X_52),implies(X_51,X_52))),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_50)),bind(X_47,$fot(X_51)),bind(X_49,$fot(X_52))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(X_51,X_52),Z),implies(implies(implies(falsehood,X_50),X_52),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_50),X_52),implies(X_51,X_52))) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_182),X_181),X_181),X_181),implies(implies(implies(falsehood,X_182),X_181),X_181))),
inference(subst,[],[refute_0_17:[bind(Z,$fot(X_181)),bind(X_50,$fot(X_182)),bind(X_51,$fot(implies(implies(falsehood,X_182),X_181))),bind(X_52,$fot(X_181))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(falsehood,X_182),X_181),X_181)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_182),X_181),X_181),X_181),implies(implies(implies(falsehood,X_182),X_181),X_181))) )],[refute_0_18,refute_0_4]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(falsehood,X_186),X_185),X_185)),
inference(subst,[],[refute_0_19:[bind(X_181,$fot(X_185)),bind(X_182,$fot(X_186))]]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(falsehood,X_186),X_185))
| is_a_theorem(X_185) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_186),X_185),X_185)) )],[refute_0_20,refute_0_0]) ).
cnf(refute_0_22,plain,
( ~ is_a_theorem(implies(implies(falsehood,X_186),implies(implies(implies(X_1547,X_1548),falsehood),X_1547)))
| is_a_theorem(implies(implies(implies(X_1547,X_1548),falsehood),X_1547)) ),
inference(subst,[],[refute_0_21:[bind(X_185,$fot(implies(implies(implies(X_1547,X_1548),falsehood),X_1547)))]]) ).
cnf(refute_0_23,plain,
( ~ is_a_theorem(implies(implies(X_1019,falsehood),implies(X_1019,X_1020)))
| is_a_theorem(implies(implies(implies(X_1019,X_1020),Z),implies(implies(X_1019,falsehood),Z))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(X_1019,falsehood))),bind(Y,$fot(implies(X_1019,X_1020)))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(implies(implies(falsehood,X_186),implies(implies(X_1016,falsehood),implies(X_1016,X_1018))))
| is_a_theorem(implies(implies(X_1016,falsehood),implies(X_1016,X_1018))) ),
inference(subst,[],[refute_0_21:[bind(X_185,$fot(implies(implies(X_1016,falsehood),implies(X_1016,X_1018))))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_49),implies(implies(X,Y),X_49))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z)))),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(implies(implies(implies(Y,Z),implies(X,Z)),X_49),implies(implies(X,Y),X_49))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )],[c0_1,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(implies(falsehood,X_1011),implies(X,X_1011)),implies(X,X_1011)),implies(implies(X,falsehood),implies(X,X_1011)))),
inference(subst,[],[refute_0_26:[bind(Y,$fot(falsehood)),bind(Z,$fot(X_1011)),bind(X_49,$fot(implies(X,X_1011)))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(implies(implies(implies(implies(falsehood,X_588),X_587),X_587),X_585))
| ~ is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_588),X_587),X_587),X_585),implies(X_586,X_585)))
| is_a_theorem(implies(X_586,X_585)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(falsehood,X_588),X_587),X_587),X_585))),bind(Y,$fot(implies(X_586,X_585)))]]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(X_187,implies(implies(implies(falsehood,X_189),X_188),X_188)))
| is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_189),X_188),X_188),Z),implies(X_187,Z))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_187)),bind(Y,$fot(implies(implies(implies(falsehood,X_189),X_188),X_188)))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(falsehood,X_186),X_185),X_185))
| is_a_theorem(implies(Y,implies(implies(implies(falsehood,X_186),X_185),X_185))) ),
inference(subst,[],[refute_0_10:[bind(X_8,$fot(implies(implies(implies(falsehood,X_186),X_185),X_185)))]]) ).
cnf(refute_0_31,plain,
is_a_theorem(implies(Y,implies(implies(implies(falsehood,X_186),X_185),X_185))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_186),X_185),X_185)) )],[refute_0_20,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(X_187,implies(implies(implies(falsehood,X_189),X_188),X_188))),
inference(subst,[],[refute_0_31:[bind(Y,$fot(X_187)),bind(X_185,$fot(X_188)),bind(X_186,$fot(X_189))]]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_189),X_188),X_188),Z),implies(X_187,Z))),
inference(resolve,[$cnf( is_a_theorem(implies(X_187,implies(implies(implies(falsehood,X_189),X_188),X_188))) )],[refute_0_32,refute_0_29]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_588),X_587),X_587),X_585),implies(X_586,X_585))),
inference(subst,[],[refute_0_33:[bind(Z,$fot(X_585)),bind(X_187,$fot(X_586)),bind(X_188,$fot(X_587)),bind(X_189,$fot(X_588))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(implies(falsehood,X_588),X_587),X_587),X_585))
| is_a_theorem(implies(X_586,X_585)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(falsehood,X_588),X_587),X_587),X_585),implies(X_586,X_585))) )],[refute_0_34,refute_0_28]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(implies(implies(falsehood,X_1011),implies(X,X_1011)),implies(X,X_1011)),implies(implies(X,falsehood),implies(X,X_1011))))
| is_a_theorem(implies(X_1009,implies(implies(X,falsehood),implies(X,X_1011)))) ),
inference(subst,[],[refute_0_35:[bind(X_585,$fot(implies(implies(X,falsehood),implies(X,X_1011)))),bind(X_586,$fot(X_1009)),bind(X_587,$fot(implies(X,X_1011))),bind(X_588,$fot(X_1011))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_1009,implies(implies(X,falsehood),implies(X,X_1011)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(falsehood,X_1011),implies(X,X_1011)),implies(X,X_1011)),implies(implies(X,falsehood),implies(X,X_1011)))) )],[refute_0_27,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(implies(falsehood,X_186),implies(implies(X_1016,falsehood),implies(X_1016,X_1018)))),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_1016)),bind(X_1009,$fot(implies(falsehood,X_186))),bind(X_1011,$fot(X_1018))]]) ).
cnf(refute_0_39,plain,
is_a_theorem(implies(implies(X_1016,falsehood),implies(X_1016,X_1018))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(falsehood,X_186),implies(implies(X_1016,falsehood),implies(X_1016,X_1018)))) )],[refute_0_38,refute_0_24]) ).
cnf(refute_0_40,plain,
is_a_theorem(implies(implies(X_1019,falsehood),implies(X_1019,X_1020))),
inference(subst,[],[refute_0_39:[bind(X_1016,$fot(X_1019)),bind(X_1018,$fot(X_1020))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(implies(implies(X_1019,X_1020),Z),implies(implies(X_1019,falsehood),Z))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_1019,falsehood),implies(X_1019,X_1020))) )],[refute_0_40,refute_0_23]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(implies(implies(implies(X_1543,X_1544),X_1543),X_1543),implies(implies(implies(X_1543,X_1544),falsehood),X_1543))),
inference(subst,[],[refute_0_41:[bind(Z,$fot(X_1543)),bind(X_1019,$fot(implies(X_1543,X_1544))),bind(X_1020,$fot(X_1543))]]) ).
cnf(refute_0_43,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_110,X_111),X_110),X_110),X_113))
| ~ is_a_theorem(implies(implies(implies(implies(implies(X_110,X_111),X_110),X_110),X_113),implies(X_112,X_113)))
| is_a_theorem(implies(X_112,X_113)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_110,X_111),X_110),X_110),X_113))),bind(Y,$fot(implies(X_112,X_113)))]]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(implies(implies(implies(X,Y),X),X))
| is_a_theorem(implies(X_11,implies(implies(implies(X,Y),X),X))) ),
inference(subst,[],[refute_0_10:[bind(Y,$fot(X_11)),bind(X_8,$fot(implies(implies(implies(X,Y),X),X)))]]) ).
cnf(refute_0_45,plain,
is_a_theorem(implies(X_11,implies(implies(implies(X,Y),X),X))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X,Y),X),X)) )],[c0_3,refute_0_44]) ).
cnf(refute_0_46,plain,
is_a_theorem(implies(X_47,implies(implies(implies(X,Y),X),X))),
inference(subst,[],[refute_0_45:[bind(X_11,$fot(X_47))]]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(implies(X_47,implies(implies(implies(X,Y),X),X)))
| is_a_theorem(implies(implies(implies(implies(implies(X,Y),X),X),X_49),implies(X_47,X_49))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_47)),bind(Y,$fot(implies(implies(implies(X,Y),X),X))),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),X),X),X_49),implies(X_47,X_49))),
inference(resolve,[$cnf( is_a_theorem(implies(X_47,implies(implies(implies(X,Y),X),X))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_110,X_111),X_110),X_110),X_113),implies(X_112,X_113))),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_110)),bind(Y,$fot(X_111)),bind(X_47,$fot(X_112)),bind(X_49,$fot(X_113))]]) ).
cnf(refute_0_50,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_110,X_111),X_110),X_110),X_113))
| is_a_theorem(implies(X_112,X_113)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_110,X_111),X_110),X_110),X_113),implies(X_112,X_113))) )],[refute_0_49,refute_0_43]) ).
cnf(refute_0_51,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_1543,X_1544),X_1543),X_1543),implies(implies(implies(X_1543,X_1544),falsehood),X_1543)))
| is_a_theorem(implies(X_1545,implies(implies(implies(X_1543,X_1544),falsehood),X_1543))) ),
inference(subst,[],[refute_0_50:[bind(X_110,$fot(X_1543)),bind(X_111,$fot(X_1544)),bind(X_112,$fot(X_1545)),bind(X_113,$fot(implies(implies(implies(X_1543,X_1544),falsehood),X_1543)))]]) ).
cnf(refute_0_52,plain,
is_a_theorem(implies(X_1545,implies(implies(implies(X_1543,X_1544),falsehood),X_1543))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_1543,X_1544),X_1543),X_1543),implies(implies(implies(X_1543,X_1544),falsehood),X_1543))) )],[refute_0_42,refute_0_51]) ).
cnf(refute_0_53,plain,
is_a_theorem(implies(implies(falsehood,X_186),implies(implies(implies(X_1547,X_1548),falsehood),X_1547))),
inference(subst,[],[refute_0_52:[bind(X_1543,$fot(X_1547)),bind(X_1544,$fot(X_1548)),bind(X_1545,$fot(implies(falsehood,X_186)))]]) ).
cnf(refute_0_54,plain,
is_a_theorem(implies(implies(implies(X_1547,X_1548),falsehood),X_1547)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(falsehood,X_186),implies(implies(implies(X_1547,X_1548),falsehood),X_1547))) )],[refute_0_53,refute_0_22]) ).
cnf(refute_0_55,plain,
is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
inference(subst,[],[refute_0_54:[bind(X_1547,$fot(a)),bind(X_1548,$fot(falsehood))]]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)) )],[refute_0_55,prove_c0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL029-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % 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 : Sun Jul 3 09:20:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.57/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.80
% 0.57/0.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.57/0.81
%------------------------------------------------------------------------------