%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:08:16 PM UTC 2026
% Result : Theorem 1.76s 1.14s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 140 ( 46 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 160 ( 52 ~; 36 |; 60 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 38 ( 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( leq(X0,X1)
& X0 != X1 )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f53,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)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv47)) )
=> a_select3(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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))))) )
& ! [X1] :
( ( leq(n0,X1)
& leq(X1,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 ) )
=> ! [X2] :
( ( leq(n0,X2)
& leq(X2,pv47) )
=> ( pv47 != X2
=> a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0007) ).
fof(f54,negated_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)
& ! [X0] :
( ( leq(n0,X0)
& leq(X0,pred(pv47)) )
=> a_select3(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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))))) )
& ! [X1] :
( ( leq(n0,X1)
& leq(X1,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 ) )
=> ! [X2] :
( ( leq(n0,X2)
& leq(X2,pv47) )
=> ( pv47 != X2
=> a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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))))) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f102,plain,
( ? [X2] :
( a_select3(q,pv10,X2) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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)))))
& pv47 != X2
& leq(n0,X2)
& leq(X2,pv47) )
& 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)
& ! [X0] :
( a_select3(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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,X0)
| ~ leq(X0,pred(pv47)) )
& ! [X1] :
( sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f103,plain,
( ? [X2] :
( a_select3(q,pv10,X2) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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)))))
& pv47 != X2
& leq(n0,X2)
& leq(X2,pv47) )
& 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)
& ! [X0] :
( a_select3(q,pv10,X0) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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,X0)
| ~ leq(X0,pred(pv47)) )
& ! [X1] :
( sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1
| ~ leq(n0,X1)
| ~ leq(X1,pred(pv10)) ) ),
inference(flattening,[],[f102]) ).
fof(f106,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f107,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f106]) ).
fof(f126,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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)))))
& pv47 != X0
& leq(n0,X0)
& leq(X0,pv47) )
& 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)
& ! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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,X1)
| ~ leq(X1,pred(pv47)) )
& ! [X2] :
( n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index))
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ) ),
inference(rectify,[],[f103]) ).
fof(f127,plain,
( a_select3(q,pv10,sK0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),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)))))
& pv47 != sK0
& leq(n0,sK0)
& leq(sK0,pv47)
& 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)
& ! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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,X1)
| ~ leq(X1,pred(pv47)) )
& ! [X2] :
( n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index))
| ~ leq(n0,X2)
| ~ leq(X2,pred(pv10)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f132,plain,
! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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,X1)
| ~ leq(X1,pred(pv47)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f137,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)))),
inference(cnf_transformation,[],[f127]) ).
fof(f138,plain,
leq(sK0,pv47),
inference(cnf_transformation,[],[f127]) ).
fof(f139,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f127]) ).
fof(f140,plain,
pv47 != sK0,
inference(cnf_transformation,[],[f127]) ).
fof(f141,plain,
a_select3(q,pv10,sK0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),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))))),
inference(cnf_transformation,[],[f127]) ).
fof(f145,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f147,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f166,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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,X1)
| ~ leq(X1,minus(pv47,n1)) ),
inference(definition_unfolding,[],[f132,f166]) ).
fof(f215,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f145,f166]) ).
fof(f371,plain,
a_select3(q,pv10,sK0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),pv84),
inference(forward_demodulation,[],[f141,f137]) ).
fof(f440,plain,
! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),pv84)
| ~ leq(n0,X1)
| ~ leq(X1,minus(pv47,n1)) ),
inference(forward_demodulation,[],[f211,f137]) ).
fof(f441,plain,
( a_select3(q,pv10,sK0) != a_select3(q,pv10,sK0)
| ~ leq(n0,sK0)
| ~ leq(sK0,minus(pv47,n1)) ),
inference(superposition,[],[f371,f440]) ).
fof(f442,plain,
( ~ leq(n0,sK0)
| ~ leq(sK0,minus(pv47,n1)) ),
inference(trivial_inequality_removal,[],[f441]) ).
fof(f443,plain,
~ leq(sK0,minus(pv47,n1)),
inference(forward_subsumption_resolution,[],[f442,f139]) ).
fof(f444,plain,
~ gt(pv47,sK0),
inference(resolution,[],[f443,f215]) ).
fof(f449,plain,
( ~ leq(sK0,pv47)
| pv47 = sK0 ),
inference(resolution,[],[f444,f147]) ).
fof(f450,plain,
pv47 = sK0,
inference(forward_subsumption_resolution,[],[f449,f138]) ).
fof(f452,plain,
$false,
inference(forward_subsumption_resolution,[],[f450,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 10:03:24 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.76/1.14 % (2147236)Detected formulas, will run a generic FOF schedule.
% 1.76/1.14 % (2147241)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2134865383:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.76/1.14 % (2147243)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2392462376:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.76/1.14 % (2147244)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2409491147:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.76/1.14 % (2147247)dis-21_1_sil=8000:lcm=predicate:random_seed=3813493785:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.76/1.14 % (2147245)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1150110089:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.76/1.14 % (2147246)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=518553424:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.76/1.14 % (2147242)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1260864631:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.76/1.14 % (2147245)First to succeed.
% 1.76/1.14 % (2147245)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2147236"
% 1.76/1.14 % (2147247)Also succeeded, but the first one will report.
% 1.76/1.14 % (2147244)Instruction limit reached!
% 1.76/1.14 % (2147244)------------------------------
% 1.76/1.14 % (2147244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.76/1.14 % (2147244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.76/1.14 % (2147244)CaDiCaL version: 2.1.3
% 1.76/1.14 % (2147244)Termination reason: Instruction limit
% 1.76/1.14 % (2147244)Termination phase: Saturation
% 1.76/1.14 % (2147244)Time elapsed: 0.069 s
% 1.76/1.14 % (2147244)Peak memory usage: 89 MB
% 1.76/1.14 % (2147244)Instructions burned: 110 (million)
% 1.76/1.14 % (2147246)Instruction limit reached!
% 1.76/1.14 % (2147246)------------------------------
% 1.76/1.14 % (2147246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.76/1.14 % (2147246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.76/1.14 % (2147246)CaDiCaL version: 2.1.3
% 1.76/1.14 % (2147246)Termination reason: Instruction limit
% 1.76/1.14 % (2147246)Termination phase: Saturation
% 1.76/1.14 % (2147246)Time elapsed: 0.089 s
% 1.76/1.14 % (2147246)Peak memory usage: 89 MB
% 1.76/1.14 % (2147246)Instructions burned: 139 (million)
% 1.76/1.14 % (2147255)lrs+10_1_sil=8000:sp=occurrence:random_seed=127928826:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.76/1.14 % (2147256)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4188645043:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.76/1.14 % (2147245)Refutation found. Thanks to Tanya!
% 1.76/1.14 % SZS status Theorem for theBenchmark
% 1.76/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.24 % (2147245)------------------------------
% 3.69/1.24 % (2147245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.24 % (2147245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.24 % (2147245)CaDiCaL version: 2.1.3
% 3.69/1.24 % (2147245)Termination reason: Refutation
% 3.69/1.24 % (2147245)Time elapsed: 0.011 s
% 3.69/1.24 % (2147245)Peak memory usage: 88 MB
% 3.69/1.24 % (2147245)Instructions burned: 17 (million)
% 3.69/1.24 % (2147245)------------------------------
% 3.69/1.24 % (2147245)------------------------------
% 3.69/1.24 % (2147236)Success in time 0.451 s
% 3.69/1.24 % Vampire exiting
%------------------------------------------------------------------------------