TSTP Solution File: SWV167+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV167+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 20:30:21 EDT 2022
% Result : Theorem 96.52s 96.67s
% Output : CNFRefutation 96.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 244 ( 98 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 259 ( 67 ~; 63 |; 83 &)
% ( 3 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 75 ( 0 sgn 57 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt2,axiom,
! [X,Y] :
( ( leq(X,Y)
& X != Y )
=> gt(Y,X) ) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ).
fof(cl5_nebula_init_0011,conjecture,
( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select2(rho_init,C) = init )
& ! [D] :
( ( leq(n0,D)
& leq(D,pred(pv40)) )
=> a_select2(mu_init,D) = init )
& ! [E] :
( ( leq(n0,E)
& leq(E,pred(pv40)) )
=> a_select2(sigma_init,E) = init )
& ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select3(center_init,F,n0) = init )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(n0,H)
& leq(H,n4) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(n0,I)
& leq(I,n4) )
=> a_select2(sigmaold_init,I) = init ) ) )
=> ! [J] :
( ( leq(n0,J)
& leq(J,pv40) )
=> a_select2(mu_init,J) = init ) ) ).
fof(subgoal_0,plain,
( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select2(rho_init,C) = init )
& ! [D] :
( ( leq(n0,D)
& leq(D,pred(pv40)) )
=> a_select2(mu_init,D) = init )
& ! [E] :
( ( leq(n0,E)
& leq(E,pred(pv40)) )
=> a_select2(sigma_init,E) = init )
& ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select3(center_init,F,n0) = init )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(n0,H)
& leq(H,n4) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(n0,I)
& leq(I,n4) )
=> a_select2(sigmaold_init,I) = init ) ) )
=> ! [J] :
( ( leq(n0,J)
& leq(J,pv40) )
=> a_select2(mu_init,J) = init ) ),
inference(strip,[],[cl5_nebula_init_0011]) ).
fof(negate_0_0,plain,
~ ( ( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select2(rho_init,C) = init )
& ! [D] :
( ( leq(n0,D)
& leq(D,pred(pv40)) )
=> a_select2(mu_init,D) = init )
& ! [E] :
( ( leq(n0,E)
& leq(E,pred(pv40)) )
=> a_select2(sigma_init,E) = init )
& ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select3(center_init,F,n0) = init )
& ( gt(loopcounter,n1)
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) )
& ( gt(loopcounter,n1)
=> ! [H] :
( ( leq(n0,H)
& leq(H,n4) )
=> a_select2(rhoold_init,H) = init ) )
& ( gt(loopcounter,n1)
=> ! [I] :
( ( leq(n0,I)
& leq(I,n4) )
=> a_select2(sigmaold_init,I) = init ) ) )
=> ! [J] :
( ( leq(n0,J)
& leq(J,pv40) )
=> a_select2(mu_init,J) = init ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( a_select2(mu_init,pv40) = init
& a_select2(sigma_init,pv40) = init
& leq(n0,pv40)
& leq(pv40,n4)
& ( ~ gt(loopcounter,n1)
| ! [G] :
( ~ leq(G,n4)
| ~ leq(n0,G)
| a_select2(muold_init,G) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [H] :
( ~ leq(H,n4)
| ~ leq(n0,H)
| a_select2(rhoold_init,H) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [I] :
( ~ leq(I,n4)
| ~ leq(n0,I)
| a_select2(sigmaold_init,I) = init ) )
& ? [J] :
( a_select2(mu_init,J) != init
& leq(J,pv40)
& leq(n0,J) )
& ! [A] :
( ~ leq(A,n135299)
| ~ leq(n0,A)
| ! [B] :
( ~ leq(B,n4)
| ~ leq(n0,B)
| a_select3(q_init,A,B) = init ) )
& ! [C] :
( ~ leq(C,n4)
| ~ leq(n0,C)
| a_select2(rho_init,C) = init )
& ! [D] :
( ~ leq(D,pred(pv40))
| ~ leq(n0,D)
| a_select2(mu_init,D) = init )
& ! [E] :
( ~ leq(E,pred(pv40))
| ~ leq(n0,E)
| a_select2(sigma_init,E) = init )
& ! [F] :
( ~ leq(F,n4)
| ~ leq(n0,F)
| a_select3(center_init,F,n0) = init ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [J] :
( a_select2(mu_init,J) != init
& leq(J,pv40)
& leq(n0,J) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( a_select2(mu_init,skolemFOFtoCNF_J_12) != init
& leq(n0,skolemFOFtoCNF_J_12)
& leq(skolemFOFtoCNF_J_12,pv40) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
a_select2(mu_init,skolemFOFtoCNF_J_12) != init,
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
a_select2(mu_init,pv40) = init,
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [D] :
( ~ leq(D,pred(pv40))
| ~ leq(n0,D)
| a_select2(mu_init,D) = init ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
! [D] :
( ~ leq(D,pred(pv40))
| ~ leq(n0,D)
| a_select2(mu_init,D) = init ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(canonicalize,[],[leq_gt_pred]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( ~ leq(X,pred(Y))
| gt(Y,X) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
leq(skolemFOFtoCNF_J_12,pv40),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(canonicalize,[],[leq_gt2]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
leq(n0,skolemFOFtoCNF_J_12),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
a_select2(mu_init,skolemFOFtoCNF_J_12) != init,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
a_select2(mu_init,pv40) = init,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ leq(D,pred(pv40))
| ~ leq(n0,D)
| a_select2(mu_init,D) = init ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ leq(n0,skolemFOFtoCNF_J_12)
| ~ leq(skolemFOFtoCNF_J_12,pred(pv40))
| a_select2(mu_init,skolemFOFtoCNF_J_12) = init ),
inference(subst,[],[refute_0_2:[bind(D,$fot(skolemFOFtoCNF_J_12))]]) ).
cnf(refute_0_4,plain,
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
( ~ gt(pv40,skolemFOFtoCNF_J_12)
| leq(skolemFOFtoCNF_J_12,pred(pv40)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_J_12)),bind(Y,$fot(pv40))]]) ).
cnf(refute_0_6,plain,
leq(skolemFOFtoCNF_J_12,pv40),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_8,plain,
( ~ leq(skolemFOFtoCNF_J_12,pv40)
| skolemFOFtoCNF_J_12 = pv40
| gt(pv40,skolemFOFtoCNF_J_12) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_J_12)),bind(Y,$fot(pv40))]]) ).
cnf(refute_0_9,plain,
( skolemFOFtoCNF_J_12 = pv40
| gt(pv40,skolemFOFtoCNF_J_12) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_J_12,pv40) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_J_12 = pv40
| leq(skolemFOFtoCNF_J_12,pred(pv40)) ),
inference(resolve,[$cnf( gt(pv40,skolemFOFtoCNF_J_12) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( ~ leq(n0,skolemFOFtoCNF_J_12)
| a_select2(mu_init,skolemFOFtoCNF_J_12) = init
| skolemFOFtoCNF_J_12 = pv40 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_J_12,pred(pv40)) )],[refute_0_10,refute_0_3]) ).
cnf(refute_0_12,plain,
leq(n0,skolemFOFtoCNF_J_12),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( a_select2(mu_init,skolemFOFtoCNF_J_12) = init
| skolemFOFtoCNF_J_12 = pv40 ),
inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_J_12) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_J_12 = pv40,
inference(resolve,[$cnf( $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),init) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
a_select2(mu_init,skolemFOFtoCNF_J_12) = a_select2(mu_init,skolemFOFtoCNF_J_12),
introduced(tautology,[refl,[$fot(a_select2(mu_init,skolemFOFtoCNF_J_12))]]) ).
cnf(refute_0_16,plain,
( a_select2(mu_init,skolemFOFtoCNF_J_12) != a_select2(mu_init,skolemFOFtoCNF_J_12)
| skolemFOFtoCNF_J_12 != pv40
| a_select2(mu_init,skolemFOFtoCNF_J_12) = a_select2(mu_init,pv40) ),
introduced(tautology,[equality,[$cnf( $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),a_select2(mu_init,skolemFOFtoCNF_J_12)) ),[1,1],$fot(pv40)]]) ).
cnf(refute_0_17,plain,
( skolemFOFtoCNF_J_12 != pv40
| a_select2(mu_init,skolemFOFtoCNF_J_12) = a_select2(mu_init,pv40) ),
inference(resolve,[$cnf( $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),a_select2(mu_init,skolemFOFtoCNF_J_12)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
a_select2(mu_init,skolemFOFtoCNF_J_12) = a_select2(mu_init,pv40),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_J_12,pv40) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_21,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( a_select2(mu_init,pv40) != init
| a_select2(mu_init,skolemFOFtoCNF_J_12) != a_select2(mu_init,pv40)
| a_select2(mu_init,skolemFOFtoCNF_J_12) = init ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(a_select2(mu_init,skolemFOFtoCNF_J_12))),bind(Y0,$fot(a_select2(mu_init,pv40))),bind(Z,$fot(init))]]) ).
cnf(refute_0_25,plain,
( a_select2(mu_init,pv40) != init
| a_select2(mu_init,skolemFOFtoCNF_J_12) = init ),
inference(resolve,[$cnf( $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),a_select2(mu_init,pv40)) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
a_select2(mu_init,skolemFOFtoCNF_J_12) = init,
inference(resolve,[$cnf( $equal(a_select2(mu_init,pv40),init) )],[refute_0_1,refute_0_25]) ).
cnf(refute_0_27,plain,
( a_select2(mu_init,skolemFOFtoCNF_J_12) != init
| init != init
| a_select2(mu_init,skolemFOFtoCNF_J_12) = init ),
introduced(tautology,[equality,[$cnf( ~ $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),init) ),[0],$fot(init)]]) ).
cnf(refute_0_28,plain,
( init != init
| a_select2(mu_init,skolemFOFtoCNF_J_12) = init ),
inference(resolve,[$cnf( $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),init) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
init != init,
inference(resolve,[$cnf( $equal(a_select2(mu_init,skolemFOFtoCNF_J_12),init) )],[refute_0_28,refute_0_0]) ).
cnf(refute_0_30,plain,
init = init,
introduced(tautology,[refl,[$fot(init)]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( $equal(init,init) )],[refute_0_30,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV167+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 13:33:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 96.52/96.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 96.52/96.67
% 96.52/96.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 96.52/96.68
%------------------------------------------------------------------------------