%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV399+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : Wed Jul 20 20:31:29 EDT 2022
% Result : Theorem 2.62s 2.86s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 11 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 164 ( 69 ~; 68 |; 18 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 67 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity,axiom,
! [U,V,W] :
( ( less_than(U,V)
& less_than(V,W) )
=> less_than(U,W) ) ).
fof(totality,axiom,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ) ).
fof(stricly_smaller_definition,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( less_than(U,V)
& ~ less_than(V,U) ) ) ).
fof(l35_li3637,lemma,
! [U,V,W,X] :
( ( pair_in_list(U,V,W)
& less_than(X,W) )
=> pair_in_list(update_slb(U,X),V,W) ) ).
fof(l35_li3839,lemma,
! [U,V,W,X] :
( ( pair_in_list(U,V,W)
& strictly_less_than(W,X) )
=> pair_in_list(update_slb(U,X),V,X) ) ).
fof(l35_co,conjecture,
! [U] :
( ? [V,W] :
( pair_in_list(U,V,W)
& strictly_less_than(V,W) )
=> ! [X] :
? [Y,Z] :
( pair_in_list(update_slb(U,X),Y,Z)
& strictly_less_than(Y,Z) ) ) ).
fof(subgoal_0,plain,
! [U] :
( ? [V,W] :
( pair_in_list(U,V,W)
& strictly_less_than(V,W) )
=> ! [X] :
? [Y,Z] :
( pair_in_list(update_slb(U,X),Y,Z)
& strictly_less_than(Y,Z) ) ),
inference(strip,[],[l35_co]) ).
fof(negate_0_0,plain,
~ ! [U] :
( ? [V,W] :
( pair_in_list(U,V,W)
& strictly_less_than(V,W) )
=> ! [X] :
? [Y,Z] :
( pair_in_list(update_slb(U,X),Y,Z)
& strictly_less_than(Y,Z) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U] :
( ? [X] :
! [Y,Z] :
( ~ pair_in_list(update_slb(U,X),Y,Z)
| ~ strictly_less_than(Y,Z) )
& ? [V,W] :
( pair_in_list(U,V,W)
& strictly_less_than(V,W) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ? [X] :
! [Y,Z] :
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,X),Y,Z)
| ~ strictly_less_than(Y,Z) )
& ? [V,W] :
( pair_in_list(skolemFOFtoCNF_U,V,W)
& strictly_less_than(V,W) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X] :
! [Y,Z] :
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,X),Y,Z)
| ~ strictly_less_than(Y,Z) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y,Z] :
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),Y,Z)
| ~ strictly_less_than(Y,Z) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y,Z] :
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),Y,Z)
| ~ strictly_less_than(Y,Z) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [V,W] :
( pair_in_list(skolemFOFtoCNF_U,V,W)
& strictly_less_than(V,W) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)
& strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [U,V,W,X] :
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| pair_in_list(update_slb(U,X),V,W) ),
inference(canonicalize,[],[l35_li3637]) ).
fof(normalize_0_9,plain,
! [U,V,W,X] :
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| pair_in_list(update_slb(U,X),V,W) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
inference(canonicalize,[],[totality]) ).
fof(normalize_0_11,plain,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
! [U,V] :
( ~ strictly_less_than(U,V)
<=> ( ~ less_than(U,V)
| less_than(V,U) ) ),
inference(canonicalize,[],[stricly_smaller_definition]) ).
fof(normalize_0_14,plain,
! [U,V] :
( ~ strictly_less_than(U,V)
<=> ( ~ less_than(U,V)
| less_than(V,U) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [U,V] :
( ( ~ less_than(V,U)
| ~ strictly_less_than(U,V) )
& ( ~ strictly_less_than(U,V)
| less_than(U,V) )
& ( ~ less_than(U,V)
| less_than(V,U)
| strictly_less_than(U,V) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [U,V] :
( ~ less_than(V,U)
| ~ strictly_less_than(U,V) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [U,V,W] :
( ~ less_than(U,V)
| ~ less_than(V,W)
| less_than(U,W) ),
inference(canonicalize,[],[transitivity]) ).
fof(normalize_0_18,plain,
! [U,V,W] :
( ~ less_than(U,V)
| ~ less_than(V,W)
| less_than(U,W) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [U,V] :
( ~ less_than(U,V)
| less_than(V,U)
| strictly_less_than(U,V) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_20,plain,
! [U,V,W,X] :
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(canonicalize,[],[l35_li3839]) ).
fof(normalize_0_21,plain,
! [U,V,W,X] :
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),Y,Z)
| ~ strictly_less_than(Y,Z) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_2,plain,
pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| pair_in_list(update_slb(U,X),V,W) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( ~ less_than(X_223,skolemFOFtoCNF_W)
| ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_223),skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W)),bind(X,$fot(X_223))]]) ).
cnf(refute_0_5,plain,
( ~ less_than(X_223,skolemFOFtoCNF_W)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_223),skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W)
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_5:[bind(X_223,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_7,plain,
( less_than(U,V)
| less_than(V,U) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| less_than(skolemFOFtoCNF_W,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_7:[bind(U,$fot(skolemFOFtoCNF_W)),bind(V,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_9,plain,
strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ less_than(V,U)
| ~ strictly_less_than(U,V) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_11,plain,
( ~ less_than(skolemFOFtoCNF_W,skolemFOFtoCNF_V)
| ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_10:[bind(U,$fot(skolemFOFtoCNF_V)),bind(V,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_12,plain,
~ less_than(skolemFOFtoCNF_W,skolemFOFtoCNF_V),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_W,skolemFOFtoCNF_V) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ less_than(U,V)
| ~ less_than(V,W)
| less_than(U,W) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( ~ less_than(X_50,skolemFOFtoCNF_V)
| ~ less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| less_than(X_50,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_14:[bind(U,$fot(X_50)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_16,plain,
( ~ less_than(X_50,skolemFOFtoCNF_V)
| less_than(X_50,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_16:[bind(X_50,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_18,plain,
( less_than(X_29,X_30)
| less_than(X_30,X_29) ),
inference(subst,[],[refute_0_7:[bind(U,$fot(X_30)),bind(V,$fot(X_29))]]) ).
cnf(refute_0_19,plain,
( ~ less_than(U,V)
| less_than(V,U)
| strictly_less_than(U,V) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_20,plain,
( ~ less_than(X_29,X_30)
| less_than(X_30,X_29)
| strictly_less_than(X_29,X_30) ),
inference(subst,[],[refute_0_19:[bind(U,$fot(X_29)),bind(V,$fot(X_30))]]) ).
cnf(refute_0_21,plain,
( less_than(X_30,X_29)
| strictly_less_than(X_29,X_30) ),
inference(resolve,[$cnf( less_than(X_29,X_30) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_21:[bind(X_29,$fot(skolemFOFtoCNF_V)),bind(X_30,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_23,plain,
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_X)
| ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_24,plain,
( less_than(X_1057,skolemFOFtoCNF_W)
| strictly_less_than(skolemFOFtoCNF_W,X_1057) ),
inference(subst,[],[refute_0_21:[bind(X_29,$fot(skolemFOFtoCNF_W)),bind(X_30,$fot(X_1057))]]) ).
cnf(refute_0_25,plain,
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_26,plain,
( ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| ~ strictly_less_than(skolemFOFtoCNF_W,X_1056)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_1056),skolemFOFtoCNF_V,X_1056) ),
inference(subst,[],[refute_0_25:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W)),bind(X,$fot(X_1056))]]) ).
cnf(refute_0_27,plain,
( ~ strictly_less_than(skolemFOFtoCNF_W,X_1056)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_1056),skolemFOFtoCNF_V,X_1056) ),
inference(resolve,[$cnf( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ strictly_less_than(skolemFOFtoCNF_W,X_1057)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_1057),skolemFOFtoCNF_V,X_1057) ),
inference(subst,[],[refute_0_27:[bind(X_1056,$fot(X_1057))]]) ).
cnf(refute_0_29,plain,
( less_than(X_1057,skolemFOFtoCNF_W)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_1057),skolemFOFtoCNF_V,X_1057) ),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_W,X_1057) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W)
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_29:[bind(X_1057,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_31,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_X)
| less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_X) )],[refute_0_30,refute_0_23]) ).
cnf(refute_0_32,plain,
( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_X) )],[refute_0_22,refute_0_31]) ).
cnf(refute_0_33,plain,
( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W) )],[refute_0_32,refute_0_6]) ).
cnf(refute_0_34,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W)
| less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_33,refute_0_1]) ).
cnf(refute_0_35,plain,
less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_9,refute_0_34]) ).
cnf(refute_0_36,plain,
less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_V) )],[refute_0_35,refute_0_17]) ).
cnf(refute_0_37,plain,
pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W) )],[refute_0_36,refute_0_6]) ).
cnf(refute_0_38,plain,
~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W),
inference(resolve,[$cnf( pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_X),skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_37,refute_0_1]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W) )],[refute_0_9,refute_0_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV399+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.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 : Wed Jun 15 17:37:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.62/2.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.62/2.86
% 2.62/2.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.62/2.87
%------------------------------------------------------------------------------