TSTP Solution File: SWV135+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV135+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 20:30:14 EDT 2022
% Result : Theorem 4.28s 4.48s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 26 unt; 0 def)
% Number of atoms : 151 ( 27 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 132 ( 51 ~; 39 |; 31 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ).
fof(pred_succ,axiom,
! [X] : pred(succ(X)) = X ).
fof(leq_succ_gt,axiom,
! [X,Y] :
( leq(succ(X),Y)
=> gt(Y,X) ) ).
fof(gauss_array_0005,conjecture,
( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
=> leq(n0,pv1325) ) ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(successor_2,axiom,
succ(succ(n0)) = n2 ).
fof(subgoal_0,plain,
( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
=> leq(n0,pv1325) ),
inference(strip,[],[gauss_array_0005]) ).
fof(negate_0_0,plain,
~ ( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3) )
=> leq(n0,pv1325) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(canonicalize,[],[leq_gt_pred]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( ~ leq(X,pred(Y))
| gt(Y,X) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[leq_gt1]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ~ leq(n0,pv1325)
& leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(pv1325,n3)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
leq(n2,pv1325),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(canonicalize,[],[leq_succ_gt_equiv]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( ~ leq(X,Y)
| gt(succ(Y),X) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(canonicalize,[],[leq_succ_gt]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[successor_2]) ).
fof(normalize_0_15,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_0_16,plain,
! [X] : pred(succ(X)) = X,
inference(canonicalize,[],[pred_succ]) ).
fof(normalize_0_17,plain,
! [X] : pred(succ(X)) = X,
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ leq(n0,pv1325),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ gt(succ(pv1325),n0)
| leq(n0,pred(succ(pv1325))) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(n0)),bind(Y,$fot(succ(pv1325)))]]) ).
cnf(refute_0_2,plain,
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ gt(succ(pv1325),n1)
| leq(n1,succ(pv1325)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(n1)),bind(Y,$fot(succ(pv1325)))]]) ).
cnf(refute_0_4,plain,
leq(n2,pv1325),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ leq(n2,pv1325)
| gt(succ(pv1325),n2) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(n2)),bind(Y,$fot(pv1325))]]) ).
cnf(refute_0_7,plain,
gt(succ(pv1325),n2),
inference(resolve,[$cnf( leq(n2,pv1325) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ gt(succ(pv1325),n2)
| leq(n2,succ(pv1325)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(n2)),bind(Y,$fot(succ(pv1325)))]]) ).
cnf(refute_0_9,plain,
leq(n2,succ(pv1325)),
inference(resolve,[$cnf( gt(succ(pv1325),n2) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ leq(succ(n1),X_1163)
| gt(X_1163,n1) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(n1)),bind(Y,$fot(X_1163))]]) ).
cnf(refute_0_12,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
succ(succ(n0)) = succ(succ(n0)),
introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).
cnf(refute_0_15,plain,
( succ(n0) != n1
| succ(succ(n0)) != succ(succ(n0))
| succ(succ(n0)) = succ(n1) ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) ),[1,0],$fot(n1)]]) ).
cnf(refute_0_16,plain,
( succ(n0) != n1
| succ(succ(n0)) = succ(n1) ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
succ(succ(n0)) = succ(n1),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
( succ(succ(n0)) != n2
| succ(succ(n0)) != succ(n1)
| succ(n1) = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),n2) ),[0],$fot(succ(n1))]]) ).
cnf(refute_0_19,plain,
( succ(succ(n0)) != n2
| succ(n1) = n2 ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
succ(n1) = n2,
inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_12,refute_0_19]) ).
cnf(refute_0_21,plain,
( succ(n1) != n2
| ~ leq(n2,X_1163)
| leq(succ(n1),X_1163) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(n1),X_1163) ),[0],$fot(n2)]]) ).
cnf(refute_0_22,plain,
( ~ leq(n2,X_1163)
| leq(succ(n1),X_1163) ),
inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ leq(n2,X_1163)
| gt(X_1163,n1) ),
inference(resolve,[$cnf( leq(succ(n1),X_1163) )],[refute_0_22,refute_0_11]) ).
cnf(refute_0_24,plain,
( ~ leq(n2,succ(pv1325))
| gt(succ(pv1325),n1) ),
inference(subst,[],[refute_0_23:[bind(X_1163,$fot(succ(pv1325)))]]) ).
cnf(refute_0_25,plain,
gt(succ(pv1325),n1),
inference(resolve,[$cnf( leq(n2,succ(pv1325)) )],[refute_0_9,refute_0_24]) ).
cnf(refute_0_26,plain,
leq(n1,succ(pv1325)),
inference(resolve,[$cnf( gt(succ(pv1325),n1) )],[refute_0_25,refute_0_3]) ).
cnf(refute_0_27,plain,
( ~ leq(succ(n0),X_1163)
| gt(X_1163,n0) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(n0)),bind(Y,$fot(X_1163))]]) ).
cnf(refute_0_28,plain,
( succ(n0) != n1
| ~ leq(n1,X_1163)
| leq(succ(n0),X_1163) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(n0),X_1163) ),[0],$fot(n1)]]) ).
cnf(refute_0_29,plain,
( ~ leq(n1,X_1163)
| leq(succ(n0),X_1163) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_13,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ leq(n1,X_1163)
| gt(X_1163,n0) ),
inference(resolve,[$cnf( leq(succ(n0),X_1163) )],[refute_0_29,refute_0_27]) ).
cnf(refute_0_31,plain,
( ~ leq(n1,succ(pv1325))
| gt(succ(pv1325),n0) ),
inference(subst,[],[refute_0_30:[bind(X_1163,$fot(succ(pv1325)))]]) ).
cnf(refute_0_32,plain,
gt(succ(pv1325),n0),
inference(resolve,[$cnf( leq(n1,succ(pv1325)) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
leq(n0,pred(succ(pv1325))),
inference(resolve,[$cnf( gt(succ(pv1325),n0) )],[refute_0_32,refute_0_1]) ).
cnf(refute_0_34,plain,
pred(succ(X)) = X,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_35,plain,
pred(succ(pv1325)) = pv1325,
inference(subst,[],[refute_0_34:[bind(X,$fot(pv1325))]]) ).
cnf(refute_0_36,plain,
( pred(succ(pv1325)) != pv1325
| ~ leq(n0,pred(succ(pv1325)))
| leq(n0,pv1325) ),
introduced(tautology,[equality,[$cnf( leq(n0,pred(succ(pv1325))) ),[1],$fot(pv1325)]]) ).
cnf(refute_0_37,plain,
( ~ leq(n0,pred(succ(pv1325)))
| leq(n0,pv1325) ),
inference(resolve,[$cnf( $equal(pred(succ(pv1325)),pv1325) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
leq(n0,pv1325),
inference(resolve,[$cnf( leq(n0,pred(succ(pv1325))) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
~ leq(n0,pv1325),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( leq(n0,pv1325) )],[refute_0_38,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV135+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.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 : Tue Jun 14 17:01:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.28/4.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/4.48
% 4.28/4.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.28/4.48
%------------------------------------------------------------------------------