TSTP Solution File: SWV160+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV160+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 20:30:19 EDT 2022
% Result : Theorem 1.37s 1.53s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 110 ( 36 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 107 ( 29 ~; 16 |; 46 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ).
fof(cl5_nebula_norm_0010,conjecture,
( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10)) )
=> ( pv10 = C
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ) ).
fof(subgoal_0,plain,
( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10))
& pv10 = C )
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ),
inference(strip,[],[cl5_nebula_norm_0010]) ).
fof(negate_0_0,plain,
~ ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10))
& pv10 = C )
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ? [C] :
( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) != n1
& pv10 = C
& leq(C,pred(pv10))
& leq(n0,C) )
& ! [A] :
( ~ leq(A,pred(pv47))
| ~ leq(n0,A)
| a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) )
& ! [B] :
( ~ leq(B,pred(pv10))
| ~ leq(n0,B)
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [C] :
( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) != n1
& pv10 = C
& leq(C,pred(pv10))
& leq(n0,C) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,skolemFOFtoCNF_C,tptp_sum_index))) != n1
& pv10 = skolemFOFtoCNF_C
& leq(n0,skolemFOFtoCNF_C)
& leq(skolemFOFtoCNF_C,pred(pv10)) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
leq(skolemFOFtoCNF_C,pred(pv10)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
pv10 = skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(canonicalize,[],[leq_gt_pred]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( ~ leq(X,pred(Y))
| gt(Y,X) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ leq(X,pred(Y))
| gt(Y,X) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] : ~ gt(X,X),
inference(canonicalize,[],[irreflexivity_gt]) ).
fof(normalize_0_10,plain,
! [X] : ~ gt(X,X),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
leq(skolemFOFtoCNF_C,pred(pv10)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
pv10 = skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( pv10 != skolemFOFtoCNF_C
| skolemFOFtoCNF_C = pv10 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(pv10)),bind(Y0,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_C = pv10,
inference(resolve,[$cnf( $equal(pv10,skolemFOFtoCNF_C) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_C != pv10
| ~ leq(skolemFOFtoCNF_C,pred(pv10))
| leq(pv10,pred(pv10)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_C,pred(pv10)) ),[0],$fot(pv10)]]) ).
cnf(refute_0_8,plain,
( ~ leq(skolemFOFtoCNF_C,pred(pv10))
| leq(pv10,pred(pv10)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,pv10) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
leq(pv10,pred(pv10)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_C,pred(pv10)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ leq(X,pred(Y))
| gt(Y,X) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ leq(pv10,pred(pv10))
| gt(pv10,pv10) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(pv10)),bind(Y,$fot(pv10))]]) ).
cnf(refute_0_12,plain,
gt(pv10,pv10),
inference(resolve,[$cnf( leq(pv10,pred(pv10)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
~ gt(X,X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
~ gt(pv10,pv10),
inference(subst,[],[refute_0_13:[bind(X,$fot(pv10))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( gt(pv10,pv10) )],[refute_0_12,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV160+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.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 09:35:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.37/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/1.53
% 1.37/1.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.37/1.54
%------------------------------------------------------------------------------