TSTP Solution File: MSC012+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 22:51:31 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 22 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 116 ( 51 ~; 56 |; 7 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 78 ( 4 sgn 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_to_right,axiom,
! [A,B] :
( ( p(A)
& less(A,B)
& p(B) )
=> goal ) ).
fof(right_to_left,axiom,
! [A] :
( p(A)
| ? [B] :
( less(A,B)
& p(B) ) ) ).
fof(transitive_less,axiom,
! [A,B,C] :
( ( less(A,B)
& less(B,C) )
=> less(A,C) ) ).
fof(serial_less,axiom,
! [A] :
? [B] : less(A,B) ).
fof(goal_to_be_proved,conjecture,
goal ).
fof(subgoal_0,plain,
goal,
inference(strip,[],[goal_to_be_proved]) ).
fof(negate_0_0,plain,
~ goal,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ less(A,B)
| ~ p(A)
| ~ p(B)
| goal ),
inference(canonicalize,[],[left_to_right]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ less(A,B)
| ~ p(A)
| ~ p(B)
| goal ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ goal,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
! [A] :
? [B] : less(A,B),
inference(canonicalize,[],[serial_less]) ).
fof(normalize_0_4,plain,
! [A] :
? [B] : less(A,B),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] : less(A,skolemFOFtoCNF_B_1(A)),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ less(A,B)
| ~ less(B,C)
| less(A,C) ),
inference(canonicalize,[],[transitive_less]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ less(A,B)
| ~ less(B,C)
| less(A,C) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( p(A)
| ? [B] :
( less(A,B)
& p(B) ) ),
inference(canonicalize,[],[right_to_left]) ).
fof(normalize_0_9,plain,
! [A] :
( p(A)
| ? [B] :
( less(A,B)
& p(B) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] :
( ( less(A,skolemFOFtoCNF_B(A))
| p(A) )
& ( p(A)
| p(skolemFOFtoCNF_B(A)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( p(A)
| p(skolemFOFtoCNF_B(A)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A] :
( less(A,skolemFOFtoCNF_B(A))
| p(A) ),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ less(A,B)
| ~ p(A)
| ~ p(B)
| goal ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ goal,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ less(A,B)
| ~ p(A)
| ~ p(B) ),
inference(resolve,[$cnf( goal )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ less(X_12,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12))))
| ~ p(X_12)
| ~ p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_12)),bind(B,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))))]]) ).
cnf(refute_0_4,plain,
less(A,skolemFOFtoCNF_B_1(A)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
less(X_6,skolemFOFtoCNF_B_1(X_6)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
( ~ less(A,B)
| ~ less(B,C)
| less(A,C) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( ~ less(X_6,skolemFOFtoCNF_B_1(X_6))
| ~ less(skolemFOFtoCNF_B_1(X_6),X_8)
| less(X_6,X_8) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_6)),bind(B,$fot(skolemFOFtoCNF_B_1(X_6))),bind(C,$fot(X_8))]]) ).
cnf(refute_0_8,plain,
( ~ less(skolemFOFtoCNF_B_1(X_6),X_8)
| less(X_6,X_8) ),
inference(resolve,[$cnf( less(X_6,skolemFOFtoCNF_B_1(X_6)) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ less(skolemFOFtoCNF_B_1(X_6),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6))))
| less(X_6,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))) ),
inference(subst,[],[refute_0_8:[bind(X_8,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))))]]) ).
cnf(refute_0_10,plain,
less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_B_1(X_9)))]]) ).
cnf(refute_0_11,plain,
( ~ less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9)))
| less(X_9,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))) ),
inference(subst,[],[refute_0_8:[bind(X_6,$fot(X_9)),bind(X_8,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))))]]) ).
cnf(refute_0_12,plain,
less(X_9,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))),
inference(resolve,[$cnf( less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_9))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
less(skolemFOFtoCNF_B_1(X_6),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))),
inference(subst,[],[refute_0_12:[bind(X_9,$fot(skolemFOFtoCNF_B_1(X_6)))]]) ).
cnf(refute_0_14,plain,
less(X_6,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))),
inference(resolve,[$cnf( less(skolemFOFtoCNF_B_1(X_6),skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_6)))) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
less(X_12,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))),
inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
( ~ p(X_12)
| ~ p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) ),
inference(resolve,[$cnf( less(X_12,skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
( p(A)
| p(skolemFOFtoCNF_B(A)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
( p(X_44)
| p(skolemFOFtoCNF_B(X_44)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_44))]]) ).
cnf(refute_0_19,plain,
less(X_3,skolemFOFtoCNF_B_1(X_3)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_20,plain,
( ~ less(X_3,skolemFOFtoCNF_B_1(X_3))
| ~ p(X_3)
| ~ p(skolemFOFtoCNF_B_1(X_3)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_3)),bind(B,$fot(skolemFOFtoCNF_B_1(X_3)))]]) ).
cnf(refute_0_21,plain,
( ~ p(X_3)
| ~ p(skolemFOFtoCNF_B_1(X_3)) ),
inference(resolve,[$cnf( less(X_3,skolemFOFtoCNF_B_1(X_3)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ p(skolemFOFtoCNF_B(X_43))
| ~ p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(X_43))) ),
inference(subst,[],[refute_0_21:[bind(X_3,$fot(skolemFOFtoCNF_B(X_43)))]]) ).
cnf(refute_0_23,plain,
( p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_41)))
| p(skolemFOFtoCNF_B_1(X_41)) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_B_1(X_41)))]]) ).
cnf(refute_0_24,plain,
( ~ less(X_15,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15)))
| ~ p(X_15)
| ~ p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15))) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_15)),bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15))))]]) ).
cnf(refute_0_25,plain,
( less(A,skolemFOFtoCNF_B(A))
| p(A) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_26,plain,
( less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9)))
| p(skolemFOFtoCNF_B_1(X_9)) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_B_1(X_9)))]]) ).
cnf(refute_0_27,plain,
( ~ less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9)))
| less(X_9,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9))) ),
inference(subst,[],[refute_0_8:[bind(X_6,$fot(X_9)),bind(X_8,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9))))]]) ).
cnf(refute_0_28,plain,
( less(X_9,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9)))
| p(skolemFOFtoCNF_B_1(X_9)) ),
inference(resolve,[$cnf( less(skolemFOFtoCNF_B_1(X_9),skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_9))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( less(X_15,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15)))
| p(skolemFOFtoCNF_B_1(X_15)) ),
inference(subst,[],[refute_0_28:[bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_30,plain,
( ~ p(X_15)
| ~ p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15)))
| p(skolemFOFtoCNF_B_1(X_15)) ),
inference(resolve,[$cnf( less(X_15,skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_15))) )],[refute_0_29,refute_0_24]) ).
cnf(refute_0_31,plain,
( ~ p(X_41)
| ~ p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_41)))
| p(skolemFOFtoCNF_B_1(X_41)) ),
inference(subst,[],[refute_0_30:[bind(X_15,$fot(X_41))]]) ).
cnf(refute_0_32,plain,
( ~ p(X_41)
| p(skolemFOFtoCNF_B_1(X_41)) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_B(skolemFOFtoCNF_B_1(X_41))) )],[refute_0_23,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ p(skolemFOFtoCNF_B(A))
| p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(A))) ),
inference(subst,[],[refute_0_32:[bind(X_41,$fot(skolemFOFtoCNF_B(A)))]]) ).
cnf(refute_0_34,plain,
( p(A)
| p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(A))) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_B(A)) )],[refute_0_17,refute_0_33]) ).
cnf(refute_0_35,plain,
( p(X_43)
| p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(X_43))) ),
inference(subst,[],[refute_0_34:[bind(A,$fot(X_43))]]) ).
cnf(refute_0_36,plain,
( ~ p(skolemFOFtoCNF_B(X_43))
| p(X_43) ),
inference(resolve,[$cnf( p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B(X_43))) )],[refute_0_35,refute_0_22]) ).
cnf(refute_0_37,plain,
( ~ p(skolemFOFtoCNF_B(X_44))
| p(X_44) ),
inference(subst,[],[refute_0_36:[bind(X_43,$fot(X_44))]]) ).
cnf(refute_0_38,plain,
p(X_44),
inference(resolve,[$cnf( p(skolemFOFtoCNF_B(X_44)) )],[refute_0_18,refute_0_37]) ).
cnf(refute_0_39,plain,
p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))),
inference(subst,[],[refute_0_38:[bind(X_44,$fot(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))))]]) ).
cnf(refute_0_40,plain,
~ p(X_12),
inference(resolve,[$cnf( p(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(skolemFOFtoCNF_B_1(X_12)))) )],[refute_0_39,refute_0_16]) ).
cnf(refute_0_41,plain,
p(X_12),
inference(subst,[],[refute_0_38:[bind(X_44,$fot(X_12))]]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( p(X_12) )],[refute_0_41,refute_0_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MSC012+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.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 : Fri Jul 1 16:56:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------