TSTP Solution File: LCL075-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL075-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 12:49:13 EDT 2022
% Result : Unsatisfiable 1.05s 1.27s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of clauses : 38 ( 23 unt; 0 nHn; 16 RR)
% Number of literals : 57 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 130 ( 38 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(cn_CAMerideth,axiom,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(Z),not(U))),Z),V),implies(implies(V,X),implies(U,X)))) ).
cnf(prove_cn_3,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3))
| ~ is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3),implies(implies(X_3,X_4),implies(X_2,X_4))))
| is_a_theorem(implies(implies(X_3,X_4),implies(X_2,X_4))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3))),bind(Y,$fot(implies(implies(X_3,X_4),implies(X_2,X_4))))]]) ).
cnf(refute_0_1,plain,
is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3),implies(implies(X_3,X_4),implies(X_2,X_4)))),
inference(subst,[],[cn_CAMerideth:[bind(U,$fot(X_2)),bind(V,$fot(X_3)),bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3))
| is_a_theorem(implies(implies(X_3,X_4),implies(X_2,X_4))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),X_3),implies(implies(X_3,X_4),implies(X_2,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(not(X_115),not(X_115))),X_115),implies(X_112,X_115)))
| is_a_theorem(implies(implies(implies(X_112,X_115),X_4),implies(X_115,X_4))) ),
inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_115)),bind(X_3,$fot(implies(X_112,X_115))),bind(X_6,$fot(X_115))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),implies(X_31,implies(X_30,X_30))))
| is_a_theorem(implies(implies(implies(X_31,implies(X_30,X_30)),X_4),implies(X_2,X_4))) ),
inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(X_31,implies(X_30,X_30))))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_18),not(X_2))),X_18),implies(X_18,X_18)))
| is_a_theorem(implies(implies(implies(X_18,X_18),X_4),implies(X_2,X_4))) ),
inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(X_18,X_18))),bind(X_6,$fot(X_18))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_15,not(X_2)),implies(not(implies(not(X_2),X_14)),not(X_2))),implies(not(X_2),X_14)),implies(X_16,implies(not(X_2),X_14))))
| is_a_theorem(implies(implies(implies(X_16,implies(not(X_2),X_14)),X_15),implies(X_2,X_15))) ),
inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(X_16,implies(not(X_2),X_14)))),bind(X_4,$fot(X_15)),bind(X_5,$fot(not(X_2))),bind(X_6,$fot(implies(not(X_2),X_14)))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(implies(not(X_11),not(X_7))),not(U))),implies(not(X_11),not(X_7))),X_11),implies(implies(X_11,X),implies(U,X)))),
inference(subst,[],[cn_CAMerideth:[bind(V,$fot(X_11)),bind(Z,$fot(implies(not(X_11),not(X_7))))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(implies(not(X_11),not(X_7))),not(U))),implies(not(X_11),not(X_7))),X_11),implies(implies(X_11,X),implies(U,X))))
| is_a_theorem(implies(implies(implies(implies(X_11,X),implies(U,X)),implies(X,Y)),implies(X_7,implies(X,Y)))) ),
inference(subst,[],[refute_0_2:[bind(X_2,$fot(X_7)),bind(X_3,$fot(implies(implies(X_11,X),implies(U,X)))),bind(X_4,$fot(implies(X,Y))),bind(X_5,$fot(implies(not(implies(not(X_11),not(X_7))),not(U)))),bind(X_6,$fot(X_11))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(implies(implies(implies(implies(X_11,X),implies(U,X)),implies(X,Y)),implies(X_7,implies(X,Y)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(not(implies(not(X_11),not(X_7))),not(U))),implies(not(X_11),not(X_7))),X_11),implies(implies(X_11,X),implies(U,X)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(implies(implies(implies(implies(X_15,not(X_2)),implies(not(implies(not(X_2),X_14)),not(X_2))),implies(not(X_2),X_14)),implies(X_16,implies(not(X_2),X_14)))),
inference(subst,[],[refute_0_9:[bind(U,$fot(not(implies(not(X_2),X_14)))),bind(X,$fot(not(X_2))),bind(Y,$fot(X_14)),bind(X_11,$fot(X_15)),bind(X_7,$fot(X_16))]]) ).
cnf(refute_0_11,plain,
is_a_theorem(implies(implies(implies(X_16,implies(not(X_2),X_14)),X_15),implies(X_2,X_15))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_15,not(X_2)),implies(not(implies(not(X_2),X_14)),not(X_2))),implies(not(X_2),X_14)),implies(X_16,implies(not(X_2),X_14)))) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_18),not(X_2))),X_18),implies(X_18,X_18))),
inference(subst,[],[refute_0_11:[bind(X_14,$fot(not(X_2))),bind(X_15,$fot(X_18)),bind(X_16,$fot(implies(X_4,X_5))),bind(X_2,$fot(X_18))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(implies(implies(implies(X_18,X_18),X_4),implies(X_2,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_18),not(X_2))),X_18),implies(X_18,X_18))) )],[refute_0_12,refute_0_5]) ).
cnf(refute_0_14,plain,
is_a_theorem(implies(implies(implies(X_18,X_18),implies(X_18,X_18)),implies(X_2,implies(X_18,X_18)))),
inference(subst,[],[refute_0_13:[bind(X_4,$fot(implies(X_18,X_18)))]]) ).
cnf(refute_0_15,plain,
( ~ is_a_theorem(implies(implies(X_21,X_21),X_23))
| ~ is_a_theorem(implies(implies(implies(X_21,X_21),X_23),implies(X_22,X_23)))
| is_a_theorem(implies(X_22,X_23)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(X_21,X_21),X_23))),bind(Y,$fot(implies(X_22,X_23)))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(implies(implies(implies(X_21,X_21),X_23),implies(X_22,X_23))),
inference(subst,[],[refute_0_13:[bind(X_18,$fot(X_21)),bind(X_2,$fot(X_22)),bind(X_4,$fot(X_23))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(X_21,X_21),X_23))
| is_a_theorem(implies(X_22,X_23)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_21,X_21),X_23),implies(X_22,X_23))) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
( ~ is_a_theorem(implies(implies(implies(X_18,X_18),implies(X_18,X_18)),implies(X_2,implies(X_18,X_18))))
| is_a_theorem(implies(X_28,implies(X_2,implies(X_18,X_18)))) ),
inference(subst,[],[refute_0_17:[bind(X_21,$fot(implies(X_18,X_18))),bind(X_22,$fot(X_28)),bind(X_23,$fot(implies(X_2,implies(X_18,X_18))))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(implies(X_28,implies(X_2,implies(X_18,X_18)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(X_18,X_18),implies(X_18,X_18)),implies(X_2,implies(X_18,X_18)))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),implies(X_31,implies(X_30,X_30)))),
inference(subst,[],[refute_0_19:[bind(X_18,$fot(X_30)),bind(X_2,$fot(X_31)),bind(X_28,$fot(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6)))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(implies(implies(implies(X_31,implies(X_30,X_30)),X_4),implies(X_2,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_6),not(X_2))),X_6),implies(X_31,implies(X_30,X_30)))) )],[refute_0_20,refute_0_4]) ).
cnf(refute_0_22,plain,
is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_115),not(X_115))),X_115),implies(X_112,X_115))),
inference(subst,[],[refute_0_21:[bind(X_2,$fot(X_112)),bind(X_30,$fot(not(X_115))),bind(X_31,$fot(implies(X_4,X_5))),bind(X_4,$fot(X_115))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(implies(implies(implies(X_112,X_115),X_4),implies(X_115,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_115),not(X_115))),X_115),implies(X_112,X_115))) )],[refute_0_22,refute_0_3]) ).
cnf(refute_0_24,plain,
is_a_theorem(implies(implies(implies(not(X_2200),not(X_2201)),X_2200),implies(not(X_2201),X_2200))),
inference(subst,[],[refute_0_23:[bind(X_112,$fot(not(X_2200))),bind(X_115,$fot(not(X_2201))),bind(X_4,$fot(X_2200))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(implies(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129),implies(X_128,X_129)))
| ~ is_a_theorem(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129))
| is_a_theorem(implies(X_128,X_129)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129))),bind(Y,$fot(implies(X_128,X_129)))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_118),not(X_2))),X_118),implies(implies(not(X_118),not(X_2)),X_118)))
| is_a_theorem(implies(implies(implies(implies(not(X_118),not(X_2)),X_118),X_4),implies(X_2,X_4))) ),
inference(subst,[],[refute_0_2:[bind(X_3,$fot(implies(implies(not(X_118),not(X_2)),X_118))),bind(X_6,$fot(X_118))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_118),not(X_2))),X_118),implies(implies(not(X_118),not(X_2)),X_118))),
inference(subst,[],[refute_0_23:[bind(X_112,$fot(implies(X_4,X_5))),bind(X_115,$fot(implies(not(X_118),not(X_2)))),bind(X_4,$fot(X_118))]]) ).
cnf(refute_0_28,plain,
is_a_theorem(implies(implies(implies(implies(not(X_118),not(X_2)),X_118),X_4),implies(X_2,X_4))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(X_4,X_5),implies(not(X_118),not(X_2))),X_118),implies(implies(not(X_118),not(X_2)),X_118))) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
is_a_theorem(implies(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129),implies(X_128,X_129))),
inference(subst,[],[refute_0_28:[bind(X_118,$fot(X_127)),bind(X_2,$fot(X_128)),bind(X_4,$fot(X_129))]]) ).
cnf(refute_0_30,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129))
| is_a_theorem(implies(X_128,X_129)) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(implies(not(X_127),not(X_128)),X_127),X_129),implies(X_128,X_129))) )],[refute_0_29,refute_0_25]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(implies(not(X_2200),not(X_2201)),X_2200),implies(not(X_2201),X_2200)))
| is_a_theorem(implies(X_2201,implies(not(X_2201),X_2200))) ),
inference(subst,[],[refute_0_30:[bind(X_127,$fot(X_2200)),bind(X_128,$fot(X_2201)),bind(X_129,$fot(implies(not(X_2201),X_2200)))]]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(X_2201,implies(not(X_2201),X_2200))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(implies(not(X_2200),not(X_2201)),X_2200),implies(not(X_2201),X_2200))) )],[refute_0_24,refute_0_31]) ).
cnf(refute_0_33,plain,
is_a_theorem(implies(a,implies(not(a),b))),
inference(subst,[],[refute_0_32:[bind(X_2200,$fot(b)),bind(X_2201,$fot(a))]]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(a,implies(not(a),b))) )],[refute_0_33,prove_cn_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : LCL075-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.09 % Command : metis --show proof --show saturation %s
% 0.09/0.29 % Computer : n011.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sun Jul 3 16:00:35 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.05/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/1.27
% 1.05/1.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.05/1.27
%------------------------------------------------------------------------------