TSTP Solution File: SWV409+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 20:31:31 EDT 2022
% Result : Theorem 2.64s 2.82s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 67 ( 12 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 221 ( 95 ~; 92 |; 25 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn 73 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(l45_li4647,lemma,
! [U,V] :
( contains_slb(U,V)
=> ? [W] : pair_in_list(U,V,W) ) ).
fof(l45_l48,lemma,
! [U,V,W,X] :
( ( pair_in_list(U,V,W)
& strictly_less_than(V,X)
& strictly_less_than(W,X) )
=> pair_in_list(update_slb(U,X),V,X) ) ).
fof(l45_l49,lemma,
! [U,V,W,X] :
( ( pair_in_list(U,V,W)
& strictly_less_than(V,X)
& less_than(X,W) )
=> ? [Y] :
( pair_in_list(update_slb(U,X),V,Y)
& less_than(X,Y) ) ) ).
fof(l45_co,conjecture,
! [U,V,W] :
( ( contains_slb(U,V)
& strictly_less_than(V,W) )
=> ( pair_in_list(update_slb(U,W),V,W)
| ? [X] :
( pair_in_list(update_slb(U,W),V,X)
& less_than(W,X) ) ) ) ).
fof(subgoal_0,plain,
! [U,V,W] :
( ( contains_slb(U,V)
& strictly_less_than(V,W)
& ~ pair_in_list(update_slb(U,W),V,W) )
=> ? [X] :
( pair_in_list(update_slb(U,W),V,X)
& less_than(W,X) ) ),
inference(strip,[],[l45_co]) ).
fof(negate_0_0,plain,
~ ! [U,V,W] :
( ( contains_slb(U,V)
& strictly_less_than(V,W)
& ~ pair_in_list(update_slb(U,W),V,W) )
=> ? [X] :
( pair_in_list(update_slb(U,W),V,X)
& less_than(W,X) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,V,W] :
( ~ pair_in_list(update_slb(U,W),V,W)
& contains_slb(U,V)
& strictly_less_than(V,W)
& ! [X] :
( ~ less_than(W,X)
| ~ pair_in_list(update_slb(U,W),V,X) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
& contains_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
& ! [X] :
( ~ less_than(skolemFOFtoCNF_W_1,X)
| ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,X) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ less_than(skolemFOFtoCNF_W_1,X)
| ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,X) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ less_than(skolemFOFtoCNF_W_1,X)
| ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,X) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_5,plain,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
inference(canonicalize,[],[totality]) ).
fof(normalize_0_6,plain,
! [U,V] :
( less_than(U,V)
| less_than(V,U) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [U,V] :
( ~ strictly_less_than(U,V)
<=> ( ~ less_than(U,V)
| less_than(V,U) ) ),
inference(canonicalize,[],[stricly_smaller_definition]) ).
fof(normalize_0_8,plain,
! [U,V] :
( ~ strictly_less_than(U,V)
<=> ( ~ less_than(U,V)
| less_than(V,U) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [U,V] :
( ~ less_than(U,V)
| less_than(V,U)
| strictly_less_than(U,V) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
contains_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_12,plain,
! [U,V] :
( ~ contains_slb(U,V)
| ? [W] : pair_in_list(U,V,W) ),
inference(canonicalize,[],[l45_li4647]) ).
fof(normalize_0_13,plain,
! [U,V] :
( ~ contains_slb(U,V)
| ? [W] : pair_in_list(U,V,W) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [U,V] :
( ~ contains_slb(U,V)
| pair_in_list(U,V,skolemFOFtoCNF_W(U,V)) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [U,V,W,X] :
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(canonicalize,[],[l45_l48]) ).
fof(normalize_0_16,plain,
! [U,V,W,X] :
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_W_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_18,plain,
! [U,V,W,X] :
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
inference(canonicalize,[],[l45_l49]) ).
fof(normalize_0_19,plain,
! [U,V,W,X] :
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| ? [Y] :
( less_than(X,Y)
& pair_in_list(update_slb(U,X),V,Y) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [U,V,W,X] :
( ( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| less_than(X,skolemFOFtoCNF_Y(U,V,X)) )
& ( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| pair_in_list(update_slb(U,X),V,skolemFOFtoCNF_Y(U,V,X)) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [U,V,W,X] :
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| pair_in_list(update_slb(U,X),V,skolemFOFtoCNF_Y(U,V,X)) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [U,V,W,X] :
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| less_than(X,skolemFOFtoCNF_Y(U,V,X)) ),
inference(conjunct,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
( ~ less_than(skolemFOFtoCNF_W_1,X)
| ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1))
| ~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)))]]) ).
cnf(refute_0_2,plain,
strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( less_than(U,V)
| less_than(V,U) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( less_than(X_33,X_34)
| less_than(X_34,X_33) ),
inference(subst,[],[refute_0_3:[bind(U,$fot(X_34)),bind(V,$fot(X_33))]]) ).
cnf(refute_0_5,plain,
( ~ less_than(U,V)
| less_than(V,U)
| strictly_less_than(U,V) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ less_than(X_33,X_34)
| less_than(X_34,X_33)
| strictly_less_than(X_33,X_34) ),
inference(subst,[],[refute_0_5:[bind(U,$fot(X_33)),bind(V,$fot(X_34))]]) ).
cnf(refute_0_7,plain,
( less_than(X_34,X_33)
| strictly_less_than(X_33,X_34) ),
inference(resolve,[$cnf( less_than(X_33,X_34) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( less_than(X_654,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| strictly_less_than(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_654) ),
inference(subst,[],[refute_0_7:[bind(X_33,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_34,$fot(X_654))]]) ).
cnf(refute_0_9,plain,
contains_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
( ~ contains_slb(U,V)
| pair_in_list(U,V,skolemFOFtoCNF_W(U,V)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( ~ contains_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_10:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_12,plain,
pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( contains_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| ~ strictly_less_than(W,X)
| pair_in_list(update_slb(U,X),V,X) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_14,plain,
( ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,X_653)
| ~ strictly_less_than(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_653)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_653),skolemFOFtoCNF_V,X_653) ),
inference(subst,[],[refute_0_13:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X,$fot(X_653))]]) ).
cnf(refute_0_15,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,X_653)
| ~ strictly_less_than(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_653)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_653),skolemFOFtoCNF_V,X_653) ),
inference(resolve,[$cnf( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,X_654)
| ~ strictly_less_than(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_654)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_654),skolemFOFtoCNF_V,X_654) ),
inference(subst,[],[refute_0_15:[bind(X_653,$fot(X_654))]]) ).
cnf(refute_0_17,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,X_654)
| less_than(X_654,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_654),skolemFOFtoCNF_V,X_654) ),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_654) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
| less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_W_1) ),
inference(subst,[],[refute_0_17:[bind(X_654,$fot(skolemFOFtoCNF_W_1))]]) ).
cnf(refute_0_19,plain,
( less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_W_1) ),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1) )],[refute_0_2,refute_0_18]) ).
cnf(refute_0_20,plain,
~ pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_W_1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_21,plain,
less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_W_1) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| pair_in_list(update_slb(U,X),V,skolemFOFtoCNF_Y(U,V,X)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_23,plain,
( ~ less_than(X_1271,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,X_1271)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_1271),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,X_1271)) ),
inference(subst,[],[refute_0_22:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X,$fot(X_1271))]]) ).
cnf(refute_0_24,plain,
( ~ less_than(X_1271,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,X_1271)
| pair_in_list(update_slb(skolemFOFtoCNF_U,X_1271),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,X_1271)) ),
inference(resolve,[$cnf( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) ),
inference(subst,[],[refute_0_24:[bind(X_1271,$fot(skolemFOFtoCNF_W_1))]]) ).
cnf(refute_0_26,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
| pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) ),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1) )],[refute_0_2,refute_0_26]) ).
cnf(refute_0_28,plain,
~ less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)),
inference(resolve,[$cnf( pair_in_list(update_slb(skolemFOFtoCNF_U,skolemFOFtoCNF_W_1),skolemFOFtoCNF_V,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) )],[refute_0_27,refute_0_1]) ).
cnf(refute_0_29,plain,
( ~ less_than(X,W)
| ~ pair_in_list(U,V,W)
| ~ strictly_less_than(V,X)
| less_than(X,skolemFOFtoCNF_Y(U,V,X)) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_30,plain,
( ~ less_than(X_680,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,X_680)
| less_than(X_680,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,X_680)) ),
inference(subst,[],[refute_0_29:[bind(U,$fot(skolemFOFtoCNF_U)),bind(V,$fot(skolemFOFtoCNF_V)),bind(W,$fot(skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X,$fot(X_680))]]) ).
cnf(refute_0_31,plain,
( ~ less_than(X_680,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,X_680)
| less_than(X_680,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,X_680)) ),
inference(resolve,[$cnf( pair_in_list(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_12,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
| less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) ),
inference(subst,[],[refute_0_31:[bind(X_680,$fot(skolemFOFtoCNF_W_1))]]) ).
cnf(refute_0_33,plain,
( ~ strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)
| less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) ),
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_W(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)),
inference(resolve,[$cnf( strictly_less_than(skolemFOFtoCNF_V,skolemFOFtoCNF_W_1) )],[refute_0_2,refute_0_33]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( less_than(skolemFOFtoCNF_W_1,skolemFOFtoCNF_Y(skolemFOFtoCNF_U,skolemFOFtoCNF_V,skolemFOFtoCNF_W_1)) )],[refute_0_34,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : SWV409+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 17:10:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.64/2.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/2.82
% 2.64/2.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.64/2.82
%------------------------------------------------------------------------------