TSTP Solution File: LCL033-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL033-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:48:54 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of clauses : 47 ( 25 unt; 0 nHn; 15 RR)
% Number of literals : 76 ( 0 equ; 30 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 157 ( 78 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(c0_CAMerideth,axiom,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))) ).
cnf(prove_c0_2,negated_conjecture,
~ is_a_theorem(implies(a,implies(b,a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3))
| ~ is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3),implies(implies(X_3,X_4),implies(X_6,X_4))))
| is_a_theorem(implies(implies(X_3,X_4),implies(X_6,X_4))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3))),bind(Y,$fot(implies(implies(X_3,X_4),implies(X_6,X_4))))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3),implies(implies(X_3,X_4),implies(X_6,X_4)))),
inference(subst,[],[c0_CAMerideth:[bind(U,$fot(X_2)),bind(V,$fot(X_3)),bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3))
| is_a_theorem(implies(implies(X_3,X_4),implies(X_6,X_4))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_2),X_3),implies(implies(X_3,X_4),implies(X_6,X_4)))) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_23),implies(falsehood,X_23)))
| is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))) ),
inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_23)),bind(X_3,$fot(implies(falsehood,X_23)))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(falsehood,falsehood)),X_20),implies(X_18,X_20)))
| is_a_theorem(implies(implies(implies(X_18,X_20),X_4),implies(falsehood,X_4))) ),
inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_20)),bind(X_3,$fot(implies(X_18,X_20))),bind(X_6,$fot(falsehood))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_16,falsehood),implies(X_14,falsehood)),implies(falsehood,X_13)),implies(X_15,implies(falsehood,X_13))))
| is_a_theorem(implies(implies(implies(X_15,implies(falsehood,X_13)),X_16),implies(X_14,X_16))) ),
inference(subst,[],[refute_0_2:[bind(X_2,$fot(implies(falsehood,X_13))),bind(X_3,$fot(implies(X_15,implies(falsehood,X_13)))),bind(X_4,$fot(X_16)),bind(X_5,$fot(falsehood)),bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),implies(X_11,falsehood)),X_7),implies(implies(X_7,X),implies(Z,X)))),
inference(subst,[],[c0_CAMerideth:[bind(U,$fot(implies(X_11,falsehood))),bind(V,$fot(X_7))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),implies(X_11,falsehood)),X_7),implies(implies(X_7,X),implies(Z,X))))
| is_a_theorem(implies(implies(implies(implies(X_7,X),implies(Z,X)),implies(X,Y)),implies(X_11,implies(X,Y)))) ),
inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_7)),bind(X_3,$fot(implies(implies(X_7,X),implies(Z,X)))),bind(X_4,$fot(implies(X,Y))),bind(X_5,$fot(implies(Z,falsehood))),bind(X_6,$fot(X_11))]]) ).
cnf(refute_0_8,plain,
is_a_theorem(implies(implies(implies(implies(X_7,X),implies(Z,X)),implies(X,Y)),implies(X_11,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),implies(X_11,falsehood)),X_7),implies(implies(X_7,X),implies(Z,X)))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(implies(X_16,falsehood),implies(X_14,falsehood)),implies(falsehood,X_13)),implies(X_15,implies(falsehood,X_13)))),
inference(subst,[],[refute_0_8:[bind(X,$fot(falsehood)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14)),bind(X_11,$fot(X_15)),bind(X_7,$fot(X_16))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(X_15,implies(falsehood,X_13)),X_16),implies(X_14,X_16))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_16,falsehood),implies(X_14,falsehood)),implies(falsehood,X_13)),implies(X_15,implies(falsehood,X_13)))) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(falsehood,falsehood)),X_20),implies(X_18,X_20))),
inference(subst,[],[refute_0_10:[bind(X_13,$fot(falsehood)),bind(X_14,$fot(X_18)),bind(X_15,$fot(implies(X_4,X_5))),bind(X_16,$fot(X_20))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(X_18,X_20),X_4),implies(falsehood,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(falsehood,falsehood)),X_20),implies(X_18,X_20))) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_23),implies(falsehood,X_23))),
inference(subst,[],[refute_0_12:[bind(X_18,$fot(implies(X_4,X_5))),bind(X_20,$fot(implies(X_6,falsehood))),bind(X_4,$fot(X_23))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(X_6,falsehood)),X_23),implies(falsehood,X_23))) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(X_47)
| ~ is_a_theorem(implies(X_47,implies(falsehood,X_46)))
| is_a_theorem(implies(falsehood,X_46)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_47)),bind(Y,$fot(implies(falsehood,X_46)))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(X_32)
| ~ is_a_theorem(implies(X_32,implies(X_33,implies(falsehood,X_31))))
| is_a_theorem(implies(X_33,implies(falsehood,X_31))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_32)),bind(Y,$fot(implies(X_33,implies(falsehood,X_31))))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(implies(implies(implies(falsehood,X_23),implies(falsehood,X_27)),implies(X_6,implies(falsehood,X_27)))),
inference(subst,[],[refute_0_14:[bind(X_4,$fot(implies(falsehood,X_27)))]]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(X_19,implies(falsehood,X_17)),X_20))
| ~ is_a_theorem(implies(implies(implies(X_19,implies(falsehood,X_17)),X_20),implies(X_18,X_20)))
| is_a_theorem(implies(X_18,X_20)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_19,implies(falsehood,X_17)),X_20))),bind(Y,$fot(implies(X_18,X_20)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(implies(implies(X_19,implies(falsehood,X_17)),X_20),implies(X_18,X_20))),
inference(subst,[],[refute_0_10:[bind(X_13,$fot(X_17)),bind(X_14,$fot(X_18)),bind(X_15,$fot(X_19)),bind(X_16,$fot(X_20))]]) ).
cnf(refute_0_20,plain,
( ~ is_a_theorem(implies(implies(X_19,implies(falsehood,X_17)),X_20))
| is_a_theorem(implies(X_18,X_20)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_19,implies(falsehood,X_17)),X_20),implies(X_18,X_20))) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
( ~ is_a_theorem(implies(implies(implies(falsehood,X_23),implies(falsehood,X_27)),implies(X_6,implies(falsehood,X_27))))
| is_a_theorem(implies(X_28,implies(X_6,implies(falsehood,X_27)))) ),
inference(subst,[],[refute_0_20:[bind(X_17,$fot(X_27)),bind(X_18,$fot(X_28)),bind(X_19,$fot(implies(falsehood,X_23))),bind(X_20,$fot(implies(X_6,implies(falsehood,X_27))))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(X_28,implies(X_6,implies(falsehood,X_27)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_23),implies(falsehood,X_27)),implies(X_6,implies(falsehood,X_27)))) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(X_32,implies(X_33,implies(falsehood,X_31)))),
inference(subst,[],[refute_0_22:[bind(X_27,$fot(X_31)),bind(X_28,$fot(X_32)),bind(X_6,$fot(X_33))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(X_32)
| is_a_theorem(implies(X_33,implies(falsehood,X_31))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_32,implies(X_33,implies(falsehood,X_31)))) )],[refute_0_23,refute_0_16]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4)))
| is_a_theorem(implies(X_45,implies(falsehood,X_43))) ),
inference(subst,[],[refute_0_24:[bind(X_31,$fot(X_43)),bind(X_32,$fot(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4)))),bind(X_33,$fot(X_45))]]) ).
cnf(refute_0_26,plain,
is_a_theorem(implies(X_45,implies(falsehood,X_43))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))) )],[refute_0_14,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(X_47,implies(falsehood,X_46))),
inference(subst,[],[refute_0_26:[bind(X_43,$fot(X_46)),bind(X_45,$fot(X_47))]]) ).
cnf(refute_0_28,plain,
( ~ is_a_theorem(X_47)
| is_a_theorem(implies(falsehood,X_46)) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_47,implies(falsehood,X_46))) )],[refute_0_27,refute_0_15]) ).
cnf(refute_0_29,plain,
( ~ is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4)))
| is_a_theorem(implies(falsehood,X_48)) ),
inference(subst,[],[refute_0_28:[bind(X_46,$fot(X_48)),bind(X_47,$fot(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))))]]) ).
cnf(refute_0_30,plain,
is_a_theorem(implies(falsehood,X_48)),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_23),X_4),implies(X_6,X_4))) )],[refute_0_14,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(X_62)
| ~ is_a_theorem(implies(X_62,implies(X_60,implies(X_61,X_60))))
| is_a_theorem(implies(X_60,implies(X_61,X_60))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_62)),bind(Y,$fot(implies(X_60,implies(X_61,X_60))))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(implies(falsehood,X_55),implies(X_57,X_55)),implies(X_55,implies(X_57,X_55)))),
inference(subst,[],[refute_0_14:[bind(X_23,$fot(X_55)),bind(X_4,$fot(implies(X_57,X_55))),bind(X_6,$fot(X_55))]]) ).
cnf(refute_0_33,plain,
( ~ is_a_theorem(implies(implies(implies(X_16,X_12),implies(X_14,X_12)),implies(X_12,X_13)))
| ~ is_a_theorem(implies(implies(implies(implies(X_16,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_15,implies(X_12,X_13))))
| is_a_theorem(implies(X_15,implies(X_12,X_13))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(X_16,X_12),implies(X_14,X_12)),implies(X_12,X_13)))),bind(Y,$fot(implies(X_15,implies(X_12,X_13))))]]) ).
cnf(refute_0_34,plain,
is_a_theorem(implies(implies(implies(implies(X_16,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_15,implies(X_12,X_13)))),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_12)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14)),bind(X_11,$fot(X_15)),bind(X_7,$fot(X_16))]]) ).
cnf(refute_0_35,plain,
( ~ is_a_theorem(implies(implies(implies(X_16,X_12),implies(X_14,X_12)),implies(X_12,X_13)))
| is_a_theorem(implies(X_15,implies(X_12,X_13))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_16,X_12),implies(X_14,X_12)),implies(X_12,X_13)),implies(X_15,implies(X_12,X_13)))) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(implies(implies(implies(falsehood,X_55),implies(X_57,X_55)),implies(X_55,implies(X_57,X_55))))
| is_a_theorem(implies(X_58,implies(X_55,implies(X_57,X_55)))) ),
inference(subst,[],[refute_0_35:[bind(X_12,$fot(X_55)),bind(X_13,$fot(implies(X_57,X_55))),bind(X_14,$fot(X_57)),bind(X_15,$fot(X_58)),bind(X_16,$fot(falsehood))]]) ).
cnf(refute_0_37,plain,
is_a_theorem(implies(X_58,implies(X_55,implies(X_57,X_55)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(falsehood,X_55),implies(X_57,X_55)),implies(X_55,implies(X_57,X_55)))) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(implies(X_62,implies(X_60,implies(X_61,X_60)))),
inference(subst,[],[refute_0_37:[bind(X_55,$fot(X_60)),bind(X_57,$fot(X_61)),bind(X_58,$fot(X_62))]]) ).
cnf(refute_0_39,plain,
( ~ is_a_theorem(X_62)
| is_a_theorem(implies(X_60,implies(X_61,X_60))) ),
inference(resolve,[$cnf( is_a_theorem(implies(X_62,implies(X_60,implies(X_61,X_60)))) )],[refute_0_38,refute_0_31]) ).
cnf(refute_0_40,plain,
( ~ is_a_theorem(implies(falsehood,X_48))
| is_a_theorem(implies(X_67,implies(X_68,X_67))) ),
inference(subst,[],[refute_0_39:[bind(X_60,$fot(X_67)),bind(X_61,$fot(X_68)),bind(X_62,$fot(implies(falsehood,X_48)))]]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(X_67,implies(X_68,X_67))),
inference(resolve,[$cnf( is_a_theorem(implies(falsehood,X_48)) )],[refute_0_30,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(a,implies(b,a))),
inference(subst,[],[refute_0_41:[bind(X_67,$fot(a)),bind(X_68,$fot(b))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(b,a))) )],[refute_0_42,prove_c0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL033-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.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 10:35:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------