TSTP Solution File: SWV159+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 73.65s 73.81s
% Output : CNFRefutation 73.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 90 ( 32 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 96 ( 25 ~; 13 |; 45 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0009,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,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,a_select3(q,C,tptp_sum_index)) = n1 ) ),
inference(strip,[],[cl5_nebula_norm_0009]) ).
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,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] :
( pv10 != C
& sum(n0,n4,a_select3(q,C,tptp_sum_index)) != n1
& 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] :
( pv10 != C
& sum(n0,n4,a_select3(q,C,tptp_sum_index)) != n1
& leq(C,pred(pv10))
& leq(n0,C) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( pv10 != skolemFOFtoCNF_C
& sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)) != n1
& 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,
! [B] :
( ~ leq(B,pred(pv10))
| ~ leq(n0,B)
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [B] :
( ~ leq(B,pred(pv10))
| ~ leq(n0,B)
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
leq(n0,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)) != n1,
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
leq(skolemFOFtoCNF_C,pred(pv10)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ leq(B,pred(pv10))
| ~ leq(n0,B)
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ leq(n0,skolemFOFtoCNF_C)
| ~ leq(skolemFOFtoCNF_C,pred(pv10))
| sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)) = n1 ),
inference(subst,[],[refute_0_1:[bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_3,plain,
( ~ leq(n0,skolemFOFtoCNF_C)
| sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)) = n1 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_C,pred(pv10)) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
leq(n0,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)) = n1,
inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_C) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)) != n1,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
$false,
inference(resolve,[$cnf( $equal(sum(n0,n4,a_select3(q,skolemFOFtoCNF_C,tptp_sum_index)),n1) )],[refute_0_5,refute_0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV159+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 04:09:00 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 73.65/73.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.65/73.81
% 73.65/73.81 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 73.65/73.82
%------------------------------------------------------------------------------