%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 01:20:21 PM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 31 unt; 0 def)
% Number of atoms : 121 ( 60 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 112 ( 28 ~; 16 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 22 ( 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [X0] : plus(X0,n1) = succ(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_l) ).
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
=> 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) = 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/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0008) ).
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
=> 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) = 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(f97,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(f99,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f100,axiom,
succ(succ(n0)) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f151,plain,
( ? [X2] :
( 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) != 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(f152,plain,
( ? [X2] :
( 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) != 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,[],[f151]) ).
fof(f205,plain,
( ? [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))))) != 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)
& 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,[],[f152]) ).
fof(f206,plain,
( 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) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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 = sK31
& leq(n0,sK31)
& leq(sK31,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,[sK31]),skolemize(X0,sK31)],[f205]) ).
fof(f287,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f288,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f323,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,[],[f206]) ).
fof(f326,plain,
pv47 = sK31,
inference(cnf_transformation,[],[f206]) ).
fof(f327,plain,
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) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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,[],[f206]) ).
fof(f370,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f97]) ).
fof(f372,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f99]) ).
fof(f373,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f100]) ).
fof(f382,plain,
! [X0] : plus(X0,n1) = plus(n1,X0),
inference(definition_unfolding,[],[f288,f287]) ).
fof(f396,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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))))) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),pv84),
inference(definition_unfolding,[],[f327,f326,f326,f326,f326,f326,f326]) ).
fof(f402,plain,
n4 = plus(plus(plus(plus(n0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f370,f287,f287,f287,f287]) ).
fof(f404,plain,
n1 = plus(n0,n1),
inference(definition_unfolding,[],[f372,f287]) ).
fof(f405,plain,
n2 = plus(plus(n0,n1),n1),
inference(definition_unfolding,[],[f373,f287,f287]) ).
fof(f408,plain,
n4 = plus(plus(plus(n1,n1),n1),n1),
inference(forward_demodulation,[],[f402,f404]) ).
fof(f429,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(plus(plus(n0,n1),n1),tptp_pi)),a_select2(sigma,tptp_sum_index)))),
inference(forward_demodulation,[],[f323,f405]) ).
fof(f430,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(plus(n0,n1),n1),tptp_pi)),a_select2(sigma,sK31))),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(plus(plus(n0,n1),n1),tptp_pi)),a_select2(sigma,tptp_sum_index))))) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(plus(n0,n1),n1),tptp_pi)),a_select2(sigma,sK31))),pv84),
inference(forward_demodulation,[],[f396,f405]) ).
fof(f436,plain,
n4 = plus(n1,plus(plus(n1,n1),n1)),
inference(forward_demodulation,[],[f408,f382]) ).
fof(f457,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(plus(n1,plus(n0,n1)),tptp_pi)),a_select2(sigma,tptp_sum_index)))),
inference(forward_demodulation,[],[f429,f382]) ).
fof(f458,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,plus(n0,n1)),tptp_pi)),a_select2(sigma,sK31))),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(plus(n1,plus(n0,n1)),tptp_pi)),a_select2(sigma,tptp_sum_index))))) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,plus(n0,n1)),tptp_pi)),a_select2(sigma,sK31))),pv84),
inference(forward_demodulation,[],[f430,f382]) ).
fof(f464,plain,
n4 = plus(n1,plus(n1,plus(n1,n1))),
inference(forward_demodulation,[],[f436,f382]) ).
fof(f485,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(plus(n1,n1),tptp_pi)),a_select2(sigma,tptp_sum_index)))),
inference(forward_demodulation,[],[f457,f404]) ).
fof(f486,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,n1),tptp_pi)),a_select2(sigma,sK31))),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(plus(n1,n1),tptp_pi)),a_select2(sigma,tptp_sum_index))))) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,n1),tptp_pi)),a_select2(sigma,sK31))),pv84),
inference(forward_demodulation,[],[f458,f404]) ).
fof(f506,plain,
pv84 = sum(n0,plus(n1,plus(n1,plus(n1,n1))),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(plus(n1,n1),tptp_pi)),a_select2(sigma,tptp_sum_index)))),
inference(forward_demodulation,[],[f485,f464]) ).
fof(f507,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,n1),tptp_pi)),a_select2(sigma,sK31))),pv84) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,n1),tptp_pi)),a_select2(sigma,sK31))),sum(n0,plus(n1,plus(n1,plus(n1,n1))),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(plus(n1,n1),tptp_pi)),a_select2(sigma,tptp_sum_index))))),
inference(forward_demodulation,[],[f486,f464]) ).
fof(f519,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,n1),tptp_pi)),a_select2(sigma,sK31))),pv84) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(plus(n1,n1),tptp_pi)),a_select2(sigma,sK31))),pv84),
inference(forward_demodulation,[],[f507,f506]) ).
fof(f520,plain,
$false,
inference(trivial_inequality_removal,[],[f519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 10:03:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.26 % (2932282)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (2932292)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3890589688:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.26 % (2932288)% WARNING: option uhcvi not known.
% 0.07/0.26 % (2932292) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2932282-2932292"...
% 0.07/0.26 % (2932288)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3853768696:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (2932287)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1987434680_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.26 % (2932292)...printing done.
% 0.07/0.26 % (2932289)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1982993108:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.26 % (2932290)dis+10_1_sil=32000:sp=arity:random_seed=2284785471:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.26 % (2932291)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1060477649:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.26 % (2932293)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=829674808:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % (2932292)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (2932292)------------------------------
% 0.07/0.26 % (2932292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (2932292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (2932292)CaDiCaL version: 2.1.3
% 0.07/0.26 % (2932292)Termination reason: Refutation
% 0.07/0.26 % (2932292)Time elapsed: 0.006 s
% 0.07/0.26 % (2932292)Peak memory usage: 12 MB
% 0.07/0.26 % (2932292)Instructions burned: 24 (million)
% 0.07/0.26 % (2932282)Success in time 0.041 s
% 0.33/0.27 % Vampire exiting
%------------------------------------------------------------------------------